Modern Labor Economics Theory and Public Policy 14th edition By Ronald Ehrenberg, Robert Smith, Kevi

Answers to Chapter 1

10. Answer b. Normative statements are frequently connected to mandated transactions, not just voluntary transactions. These mandates can be driven by the quest for mutually beneficial gain, but they need not be. Other ethical principles or goals like fairness may be the driving force behind normative statements.

11. Answer d. If one person gains and no one else loses, that is a transaction that seemingly could be supported by unanimous consent. Therefore, if such a transaction can still be made, a Pareto efficient outcome has not been achieved.

12. Answer b. In most situations there are many different Pareto efficient outcomes, but many of these outcomes would probably be considered unfair. The outcome that is finally achieved may be arrived at voluntarily or by government mandate.

13. Answer d. Moving from one Pareto efficient outcome, even if it is to another Pareto efficient outcome, will make one person worse off at the same time it makes someone else better off. Deciding among Pareto efficient outcomes, therefore, involves some assessment of the fairness or equity of the outcomes. These judgments have traditionally been made in the political arena and are often influenced by each party’s initial income or wealth position. Most political systems have been willing to support at least some redistribution of wealth from the rich to the poor.

14. Answer d. Other reasons include price distortions caused by government taxes or the lack of a market where the transaction can be worked out.

15. Answer d. Also, in some instances, government action is the impediment to the Pareto efficient outcome. In these instances the government must get out of the way before the transaction can be completed.

16. Answer c. Least squares regression makes no assumptions with respect to the relationship between independent variables (those on the right side of the equation) or the size of the coefficients attached to these variables. For the estimated parameters to be unbiased estimates of the true values, however, the error term must be random.

17. Answer b. One can reject the hypothesis that the true value of a particular coefficient is zero only if the estimated parameter is more than twice the size of its standard error (the t-statistic will then be greater than 2). A small standard error is no guarantee of a non-zero parameter if the estimated parameter is also very small. A random error term helps to ensure that the estimates are as precise as possible, but the existence of a random error term does not have any bearing on the existence of a relationship between the independent and dependent variables.

18. Answer b. A coefficient in a multiple regression indicates the effect on the dependent variable, on average, of a one-unit change in the independent variable, assuming the other variables are held constant. A non-zero estimate for the coefficient does not ensure that the true value of the parameter is different from zero.

In this case,

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however, a parameter estimate four times as large as its standard error allows us to reject the hypothesis of a “true” value of zero.

19. Answer d. The relatively small value of the standard error means the coefficient on the W variable has been measured with a relatively small margin of error. Also, since the coefficient is 2.5 times its standard error, the hypothesis that the true value of the coefficient is zero can be rejected. However, a relationship that is significant in a statistical sense is not necessarily significant in an economic sense. Holding all else constant, in this equation, every $1 increase in the wage is accompanied by just a one-half hour reduction in total annual hours, a very insignificant amount.

20. Answer a. Since W and V are positively correlated, the coefficient on W would pick up some of the negative effect V exerts on H, making the coefficient on W smaller.

Problems 21a. The drawing is a model because it is a deliberate abstraction designed to illustrate certain key characteristics of human beings.

21b. The model highlights that human beings walk upright on two legs. It also highlights the relative size of the head and limbs. It pushes all the details of our appearance, particularly things like the shape of our hands and feet into the background. It also says nothing about the mental capacities that distinguish us from other animals. There are, of course, other characteristics that it doesn’t capture either.

21c. A simple drawing was easy to make. Anything more involved would require some artistic skill. Also, such a simple drawing highlights the idea that models are abstract. A more realistic drawing would not have gotten across the idea that “humans walk upright on two legs” any better than this simple drawing. In fact, a more realistic drawing might have obscured this point by focusing attention on other features.

21d. This is a positive model since it attempts to show “what is” true about human beings.

It does not attempt to assess our bodily design or illustrate “what should be.”

22a. The person is being inconsistent. If it is worth taking 30 minutes to save $5 in the first situation, it should also be worth it in the second situation. However, he may be acting like this because the percentage savings is much smaller in the second case. Studies of perception have revealed that the larger or more intense the stimulus (in this case the original expenditure on insurance), the larger any change (in this case the cost savings) has to be before it will be recognized.

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22b. No, a model with poor predictive power may still be useful in a normative sense, in this case as a guide to more rational decision making. In this example, if confronted with his inconsistency, the worker may realize that his choice in the second instance was obscured by the large dollar amounts. As a result he may be able to avoid similar mistakes in the future.

23a. The outcome is Pareto efficient because there is no way any of the remaining firms or workers can reach an agreement that is mutually beneficial. For example, firm 9 will only benefit from a wage below $360, but worker 9 will not benefit from anything below $400. Since all the mutually beneficial deals have already been made, the outcome is Pareto efficient.

23b. With deals below $480 prohibited, only firms 1, 2, and 3 will be interested in hiring.

On the other hand, all 10 workers would be willing to work. Suppose for simplicity that workers 1, 2, and 3 are hired. Worker 4, who has been shut out of the market, could easily strike a mutually beneficial deal with firm 4 by offering to work for, say, $400, but the law prohibits this. Since mutually beneficial deals can still be made, the outcome under the legislated wage is not Pareto efficient.

23c. The three workers who continue to be hired each gain $100 (the difference between the legislated wage of $480 and the wage of $380 that would have emerged if all mutually beneficial trades were allowed). The three firms that hire them each lose $100 relative to what they would have gained under the lower wage. The five workers who would have been hired under the lower wage also lose. Assuming workers 4 through 8 have been shut out, the total loss to these workers is $200 ($80 + $60 + $40 + $20). Combining the worker and firm losses yields a total loss of $500.

23d. The winners do not gain enough ($300) to compensate the losers (-$500) and still come out ahead. Such a law can only be justified using principles developed outside of economics. For example, those who gain might have been very poor to begin with, while those who lost might have been well off. In such a situation, the redistribution might be justified by appealing to notions of equity or fairness.

23e. Eight workers would be hired, the same outcome as in 23a.

23f. This is a Pareto efficient outcome since no mutually beneficial deals still exist. Even if person 9 were paid his minimum acceptable wage of $400, the firm would not gain by hiring him. While the outcome is Pareto efficient, it is not necessarily equitable since the firm has reaped all the benefits.

24a. See the scatter of points in Figure 1-2.

24b. See the straight line in Figure 1-2.

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Figure 1-2.

*24c. See Table 1-5 and the points plotted as squares in Figure 1-3.

Table 1-5.

UR

Actual %W

Predicted %W

Residual

5.4 6.5 5.4 5.5 5.0 4.4 3.7 3.7 3.5 3.4

3.4 3.0 3.4 2.8 2.8 3.6 4.3 5.0 6.1 6.7

3.3 2.1 3.3 3.2 3.7 4.4 5.2 5.2 5.4 5.5

0.1 0.9 0.1 -0.4 -0.9 -0.8 -0.9 -0.2 0.7 1.2

*24d. The residuals do not seem random. They tend to be positive when the unemployment rate is relatively high or relatively low, and negative otherwise. From the scatter of points in Figure 1-2, it appears a convex curve would fit the data better. *24e. See the solid curve in Figure 1-2.

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Figure 1-3.

*24f. See Table 1-6 and the points plotted as triangles in Figure 1-3. For six of the ten years the fit improved. There were two years where it worsened slightly and two years where it was essentially unchanged. The fit improved most at the lowest and highest values of the unemployment rate. For both values, the residual was 0.3 units less when the nonlinear function was used.

Table 1-6.

UR

Actual %W

Predicted %W

Residual

5.4 6.5 5.4 5.5 5.0 4.4 3.7 3.7 3.5 3.4

3.4 3.0 3.4 2.8 2.8 3.6 4.3 5.0 6.1 6.7

3.1 2.4 3.1 3.0 3.5 4.2 5.2 5.2 5.6 5.8

0.3 0.6 0.3 -0.2 -0.7 -0.6 -0.9 -0.2 0.5 0.9

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24g. See the scatter of points in Figure 1-4.

Figure 1-4.

24h. See the lines labeled “1960s” and “1970s” in Figure 1-4. The 1970s line lies 3.7 units above the 1960s line at every value of the unemployment rate.

24i. See the line labeled “Combined” in Figure 1-4. The omission of the D70 variable severely biases the coefficient on the unemployment variable in an upward direction. The D70 variable normally would exert a positive effect on the dependent variable. However, since D70 and the unemployment rate are positively correlated (notice that both unemployment and inflation were higher in the 1970s), when the D70 variable is omitted, most of its positive effect on the dependent variable will be attributed to the unemployment rate variable. Notice that omitting a variable is a problem here because the omitted variable and the remaining variable are correlated. Omitting a variable that is not correlated with the independent variable would not create bias in the estimated coefficient. *24j. To allow both the position and slope of the curve to be different, estimate the equation %Wt = a0 + a1URt + a2D70t + a3D70 URt + ei.

For the 1960s, the vertical intercept would be given by the estimate of a 0, while for the 1970s it would be given by a0 + a2. Similarly, for the 1960s, the slope would be given by the estimate of a1, while for the 1970s it would be given by a1 + a3.

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Applications 25a. The notion of exercising a preferential option for the poor is very different from promoting the norm of Pareto efficiency. Under Pareto efficiency, only mutually beneficial changes should be undertaken. But when exercising a preferential option for the poor, some parties may be called upon to sacrifice so that the poor can advance.

25b. When the goal is to promote Pareto efficient outcomes, the government mainly plays a facilitating role. Its task is to promote voluntary exchange based on accurate and complete information. When barriers to such transactions exist, however, the government sometimes can act in a way to overcome these barriers. Some examples of these actions include providing for the production of public goods, eliminating capital market imperfections, or establishing substitutes for the market.

Pope Leo XIII sees the task of government as promoting and protecting the interests of the poor and disadvantaged. Government need not act on behalf of all members of a society.

Rather, government actions must be judged by their impact on the poor, even when these actions require sacrifice by others.

26a. The survey suggests people care about where their income stands relative to others in the population.

26b. The norm of Pareto efficiency says that all mutually beneficial changes should be undertaken. In this case, many people disagree that the program should be enacted, even though everyone gains. Therefore the responses are inconsistent with the norm of Pareto efficiency.

26c. It appears that the premise of the question would have to have everyone gaining by roughly the same amount for the reform to be supported unanimously.

27a. Estimating the parameters 0 and 1 would require cross-sectional data on earnings and employee-generated revenues for a number of workers at one or more firms. Estimates of the parameters would be derived by choosing values for 0 and 1 such that the squared differences between the actual and predicted values of employee earnings were minimized.

Most statistical and spreadsheet programs have commands that will use this criterion to find the parameter estimates.

27b. The precision of an estimate is indicated by its standard error. If the estimated parameter is approximately twice the value of its standard error, it is possible to reject with reasonable confidence the hypothesis that the true value of the parameter equals zero. *27c. If the hypothesis is that parameter a1 equals one, rather than zero, then the value of the estimated parameter, minus one, must be approximately twice the standard error of estimated parameter.

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*27d. Frank’s hypothesis implies that the relationship between earnings and productivity is much flatter than the standard theory predicts. For a graphical depiction of this effect, see Figure 1-5. Line ab represents the relationship between E and R implicit in the standard model, while line cd would be consistent with Frank’s hypothesis. Consequently, the prediction would be that 0 would be much greater than it is in the standard model, while the value of 1 would be much less (and definitely less than one).

Figure 1-5.

*27e. The equation to be estimated is Ei = 0 + 1Ri + 2Di + 3DiRi + ei.

This equation allows both the intercept and slope to change as the degree of employee interaction increases. Since the hypothesis is that relationship between earnings and productivity flattens out as the degree of interaction increases, the expectation would be that the estimate of the parameter 2 would be greater than zero and the estimate of the parameter 3 would be less than zero. The effect of increased interaction is also shown in Figure 1-5. Line cd represents a possible relationship between E and R when there is modest worker interaction, while line ef represents a situation of more extensive interaction. *27f. It seems unlikely that D is correlated with the level of employee productivity (R) since high-productivity people can be found in all types of work environments. Therefore, eliminating D should not bias the estimates of the remaining parameters 0 and 1.

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ANSWERS TO CHAPTER 2 Review Questions 1. Answer a. To be classified as in the labor force, an individual must be employed, actively seeking work, or waiting to be recalled from a layoff. However, those actively seeking work or waiting to be recalled from a layoff are called unemployed. Hence, the labor force can be defined as those employed plus those unemployed.

2. Answer a. The labor force participation rate is defined as those in the labor force divided by the population. The labor force is those employed plus those unemployed.

3. Answer d. The unemployment rate is defined as the number unemployed divided by the labor force, but recall that the labor force is the number employed plus the number unemployed.

4. Answer c. The index of nominal wages for 1996 is the nominal wage in 1996 expressed as a percentage of the nominal wage in the base year. $11.18 x 100 = 117. $9.54

5. Answer b. The index of real wages is the index of nominal wages divided by the price index (with the result multiplied by 100).

117 x 100 = 92.

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6. Answer b. Since the index of real wages declined from 100 to 92, the real wage declined by 8 percent over the period.

7. Answer d. Although the words income, earnings, and wage are often used interchangeably in the English language, in this chapter they each refer to a different measure. The wage is defined as the payment per unit of time, while earnings equal the wage multiplied by the units of time worked. Adding employee benefits to earnings yields a worker’s total compensation. Total compensation plus any unearned income yields total income. Therefore, even if the real wage falls, total income may not fall if the time spent working increases, benefits increase, or unearned income increases.

8. Answer d. The demand curve represents the relationship between the wage and quantity of labor firms wish to hire provided all the other things that can influence the quantity of labor demanded are held constant. Responses a and b are examples of nonwage determinants of the total demand for labor in the market. Note that the demand curve is constructed independently of the supply curve.

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9. Answer d. The demand curve slopes downward in the long run because of the substitution and scale effects associated with a wage change. Answer a describes the substitution effect, and answer b describes the scale effect. Note that answer c simply repeats using different words the idea that the demand curve is downward sloping. It does not answer the question since it does not given an economic reason for the relationship.

10. Answer d. The demand curve as shown on the graph has a vertical intercept of 36 and a slope of -3 which implies that the equation is W = 36 - 3L  L = 12 -

1 W. 3

11. Answer c. When the price of capital rises, the firm will substitute relatively cheaper labor for capital (substitution effect). The optimal output of the firm will also fall, however, leading the firm to use less of all its inputs (scale effect). As long as the substitution effect dominates the scale effect, the quantity of labor demanded will increase and the demand curve for labor will shift to the right. (Note that a. reflects a change in the quantity of labor demanded, or a movement along the curve, not a shift in the curve.)

12. Answer b. The market supply curve is drawn holding working conditions and wages in other occupations constant. Wages in other occupations need not be at any particular level for the supply curve to be drawn. The presence of a union may mean that not all of the S curve will be relevant, but it would not change the fact that the market supply curve shows the number of workers willing to work at all the various wage levels.

13. Answer b. The supply curve as shown on the graph has a vertical intercept of 6 and a slope of 2 which implies that the equation is W = 6 + 2L  L =

1 W - 3.

2

14. Answer b. Individual firms offering comparable jobs in a competitive labor market will be constrained to pay the market clearing wage. In this case, an individual firm will be able to hire as much or as little labor as it wants at a wage of $18.

15. Answer d. At any wage other than the market clearing wage, a shortage (excess demand) or a surplus (excess supply) will create a tendency for the wage to change.

Also, when the wage is not at its market clearing value, an opportunity for mutually beneficial exchange between workers and firms will exist. Hence, once the market clearing wage has been attained, all the mutually beneficial deals will have been made, and it will only be possible to make someone better off by making someone else worse off.

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16. Answer b. Economic rent is the triangular area abc in Figure 2-5. The area of a triangle is given by the formula 1 Area = 2 (base) x (height) 1  Economic Rent = 2 (6,000) ($12) = $36,000.

Figure 2-5.

17. Answer c. With the wage fixed at $24, the supply curve effectively becomes a horizontal line at $24 and the quantity of labor demanded will fall to 1 L = 12 - 3 (24) = 4.

Note that the surplus will actually be 5 since the quantity supplied will increase to 9.

18. Answer d. If the wage is originally at the market clearing level, then quantity demanded will equal quantity supplied. When demand increases, quantity demanded will now be greater than quantity supplied at the market clearing wage. This means that there is a shortage of labor and upward pressure on the wage. As the wage rises, the shortage is eliminated and a new higher market clearing wage is established.

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19. Answer b. When demand increases, upward pressure is put on the wage and the employment level. When supply increases, downward pressure is put on the wage, and upward pressure is put on the employment level. As long as both supply and demand increase by the same amount, the pressures put on the wage will tend cancel out, while the pressures put on the employment level will reinforce. Thus employment will increase, but the effect on the wage depends on which shift is larger. If the shift in supply is greater than the shift in demand, wages will fall. If the shift in demand is greater than the shift in supply, wage will rise.

20. Answer b.

LD = LS  13 − 

1 1 W= W−2 3 2

5 W = 15  W* = $18.

6

1 W* = $18  13 − (18) = 7.

3

Problems 21a. Unemployment Rate =

U x 100 E+U



10 x 100 = 8 percent.

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21b. While an 8 percent or higher unemployment rate is not unusual during economic downturns (e.g., 1982-83) it is fairly high by historical standards. Of course, it is nowhere near the peak unemployment of 24.9 percent experienced during the Great Depression!

21c. While the unemployment rate has tended to fluctuate less in recent years, the average unemployment rate seems to be slowly climbing.

21d. If the labor force (L) equals E + U, and the population (POP) equals L + N, then the labor force participation rate (LFPR) is LFPR = 

L x 100 POP

10 + 115 x 100 = 62.5 percent.

10 + 115 + 75

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21e. No, this is not an unusually high labor force participation rate. Throughout the 1980s and 1990s the rate has been higher.

21f. Since 1950 the overall labor force participation rate rose modestly from about 60 percent in 1950 to the just over 67% percent in 2000 but fell to 66% by 2004. Over this period, however, the labor force participation rate of men dropped significantly from nearly 87 percent to 73 percent, while the rate for women increased from 34 percent to about 60 percent.

21g. The type of work has been changing steadily from goods producing to privatesector services.

22a. The reason for computing an index of real wages is to make it easier to compare the real purchasing power of a worker’s wage when product prices are changing. The steps carried out in computing the index essentially hold prices constant. Hence, any change in the index reflects a real change in the worker’s command over goods and services, purchasing power. Also, by expressing purchasing power as a percentage of the purchasing power enjoyed in the base year (which is then standardized to 100 percent) the index makes it easy to compute the percentage change in buying power over time.

22b. See Table 2-6 for the index of real wages computed using 1980 as the base year.

Table 2-6.

Year

Index of Nominal Wages

Price Index

Index of Real Wages

1945 1980 1997

14 100 184

22 100 195

64 100 94

22c. Over the period 1980 to 1997, real wages declined by 6 percent.

22d. This change understates the change in real compensation per worker since compensation includes both wages and employee benefits. Increases in employee benefits could easily offset the decline in real wages and make for an increase in real compensation per worker. Additionally, the price index may overstate the rate of inflation by ignoring substitution and changes in the quality of goods.

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23a. Equilibrium  LD = LS 1 1 W = W  W* = $10.

2 2 1 W* = $10  L* = 10 - (10) = 5.

2

 10 -

23b. See the curves labeled D and S in Figure 2-6. employment occur at point a.

The equilibrium wage and

Figure 2-6.

23c. At a wage of $6, the quantity supplied equals 3 (point b in Figure 2-6), while quantity demanded equals 7 (point c in Figure 2-6). The shortage of 4 units means that the market does not clear and that there will be upward pressure on wages. *23d. Note that at a wage of $6, firms would like to hire a total of 7 workers, but only 3 individuals are willing to work. Suppose that one of the firms shut out of the market offers to hire an additional worker at a wage of $10. The demand curve indicates that firms would be willing to pay up to $12 for a fourth worker, so this firm would still gain $2 by the offer. On the other hand, from the supply curve it is clear that it would take only a wage of $8 to get the fourth worker, so this worker earns economic rent of $2.

23e. No, economic rent refers to the difference between what the worker actually earns and the minimum he or she would be willing to accept. A worker is only considered overpaid in an economic sense if the actual wage is above the equilibrium wage in the market. *23f. With the union restricting labor supply to 4 units, the supply curve becomes a vertical line at 4. This is line S' in Figure 2-7.

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Figure 2-7.

Equilibrium occurs where LD = LS  10 -

1 W = 4  W* = $12.

2

The equilibrium is point b in Figure 2-7. Since the equilibrium wage and employment level in the absence of the union was point a, the four members of the union who continue to be employed gain the area of the rectangle bcde for a total of ($2) x (4) = $8.

This gain comes at the expense of the firms. However, since one more worker could have been hired if the wage stayed at $10, there is also a loss of economic rent equal to the area of triangle aef. This area is equal to $1 (0.5 x $2 x 1).

23g. The market demand for labor increases, for example, when the demand for the product the firm produces increases, when labor becomes more productive, when the price of capital falls and the scale effect dominates the substitution effect, when the price of capital rises and the substitution effect dominates the scale effect, or the number of firms increases. The market supply of labor decreases, for example, when wages in other occupations increase relative to the occupation being considered, when working conditions in the occupation worsen, or the number of workers in the area decreases.

Applications 24a. The unemployment rate decreases. Suppose that initially the number of unemployed workers is 3 and the number of people in the labor force is 9. Since the unemployment rate is the number unemployed divided by the labor force, the unemployment rate is 33.3 percent. If one of the unemployed workers drops out of the labor force, then the number unemployed would be 2 and the size of the labor force would be 8. Consequently, the unemployment rate drops to 25 percent.

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24b. When the unemployment rate drops, as it would in this case, it usually indicates the labor market is getting tighter, that is, employers are finding it harder to fill positions and prospects are improving from the workers’ perspective. In this case, however, even though the unemployment rate is going down, the labor market is actually getting looser.

Workers’ prospects are declining and employers would be able to draw on an increasingly desperate pool of workers. *25a. No, it is not plausible to think that firms would desire to hire more workers at higher wage rates. An alternative conclusion is that the data reflect a series of equilibrium points (that is, both supply and demand are changing, or that demand is shifting, and thus the demand curve cannot be identified from the data). *25b. If the demand curve for this category of labor shifted to the right over time along a stable supply curve, one would observe the wage and employment level rising together.

Such a situation is shown in Figure 2-8.

Figure 2-8.

26. Since the net effect of the reduction in computer prices is projected to be a decrease in employment, the decrease in employment coming about through the substitution effect must be larger in magnitude than the increase coming about through the scale effect.

27a. An investment tax credit would have an ambiguous effect on employment opportunities in the industries where it applied. When the price of capital is reduced, firms have an incentive to substitute the relatively cheaper capital for labor (substitution effect). On the other hand, the reduction in the price of capital leads to a reduction in the firm’s cost of producing another unit of output. This creates an incentive to expand output, and when a firm expands output, it uses more of all its inputs, including labor.

27b. Workers would see increased employment opportunities only if the positive scale effect associated with the investment tax credit exceeded the negative substitution effect.

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28a. This statement confuses a shift in the position of the demand curve (a change in demand) with movement along the demand curve (a change in quantity demanded). An increase in the supply of labor will cause the wage to fall, but this will lead to an increase in the quantity of labor demanded as the new equilibrium is established. The reduction in the wage will not cause a shift in demand as the statement suggests.

28b. Assuming the market is originally in equilibrium, when the supply of labor increases, an excess supply of labor is created at the current wage. This excess supply will put downward pressure on the wage. As the wage falls, the quantity of labor demanded by firms increases, and the quantity of labor supplied by individuals is reduced. The wage will stop falling when the excess supply has just been eliminated. At this new market clearing wage, the total level of employment will be greater than it was when the scenario began.

The market supply of labor will increase, for example, when working conditions in the occupation improve or wages in other occupations fall relative to this one. Also, as the number of workers in a particular area increases the supply curve will shift to the right.

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ANSWERS TO CHAPTER 3 Review Questions 1. Answer d. Competition ensures that the firm will be a wage taker. If the firm pays less than the going wage, no one will work for the firm. If the firm pays more, it will be at a cost disadvantage relative to rivals that did pay the going wage, and as a result the firm will be forced to close. Since the wage does not change as employment changes, the additional cost associated with hiring an additional worker is just the going wage that the firm pays.

2. Answer d. Competition ensures that the firm will be a price taker. If the firm sells for more than the going price, no one will buy the product. If the firm sells for less, it will not be taking in the amount of revenue it could and so earns less than comparable firms. If this continues the firm will be forced to close. Since the price does not change as output changes, the additional revenue associated with an additional unit of output is just the going price that the firm receives.

3. Answer d. Answers a and c simply repeat the premise of the question, they do not give any economic reasons for the relationship. Answer b has the relationship backwards. A decrease in the wage will trigger a higher level of employment and, in turn, a lower marginal product since a larger number of workers will be spread over a fixed capital stock.

4. Answer b. When the MRL gets very close to the MEL, all the moves that add to profit have been made.

5. Answer a. Recall that a monopsonist chooses a wage and labor combination below its MRPL curve. Monopoly in the output market would only affect whether the MRPL expression could be simplified to P◊MPL. The expression MRPL = MR◊MPL is a definition and is always true.

6. Answer b. To survive in a competitive market, a firm must maximize profits. How it gets to that point (e.g., trial and error, luck, etc.) does not matter. However, since the MRPL = MEL rule does lead to maximum profits, a firm that is maximizing profits is acting as if it did follow that rule. Thus, even if no firm understands or actually follows the rule, it is useful to consider because it has predictive power. In the end we should see firms operating at this point because if they do not, they will not be maximizing profits, and can be driven out by firms that do.

7. Answer b. To find the market demand, add the individual quantities that are demanded at the real wage of 10. Since L1 = 2.5, L2 = 5, and L3 = 10, the market quantity is 17.5.

8. Answer a.

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W $10 C $36 = =2 = = 3.

MPL 5 MPK 12

The firm should increase L and decrease K to bring about an equality. As L increases, MPL will fall, increasing the left side of the equation. As K decreases, MP K will rise, decreasing the right side of the equation. Currently, the marginal cost of output produced by capital is $3, and only $2 for that produced by labor. Alternatively, an additional dollar spent on labor currently yields one-half unit of additional output, but the same dollar spent on additional capital only increases output by one-third unit.

9. Answer a. As C falls, the MC of the firm falls and the output of the firm increases.

As output increases, the firm will use more of both capital and labor. This is called the scale effect of the price change. As long as this effect dominates the tendency of the firm to substitute capital for labor, the quantity of labor demanded should increase.

10. Answer d. In this question, capital and labor are used in fixed proportions in the production process. For example, if a firm uses one unit of labor and one unit of capital, it may be able to produce one unit of output, but if it adds another unit of capital without adding another unit of labor, output will not increase. In such a situation, the firm can not substitute capital for labor when the price of capital falls since this would take it away from the required proportion of labor and capital. The reduction in the price of capital, however, will reduce the marginal cost of production, leading to an increase in output (a scale effect) and an increase in the usage of both labor and capital. When the price of capital falls and labor usage increases, labor and capital are called gross complements.

11. Answer d. When the price of capital rises, in the long run the substitution and scale effects will combine to reduce the quantity of capital demanded. If the demand for labor shifts right as a result, that means labor usage is increasing. This occurs if the substitution effect of the capital price increase dominates the scale effect. In such a situation, labor and capital are called gross substitutes.

12. Answer d. The tax is the amount by which the demand curve is shifted down.

13. Answer c. As a result of the 4-unit tax, the equilibrium wage has been driven down by 2 (from 10 to 8). Therefore, the workers bear 50 percent of the tax in this example.

14. Answer a. In addition to the wage burden, workers see employment opportunities reduced by 1 (from 5 to 4) because of the tax.

15. Answer d. Who bears the burden of the tax is determined by which side of the market is least responsive to changes in the wage. When supply is perfectly vertical, the downward shift of the demand curve causes the wage to fall by the same amount.

16. Answer a. At the cost-minimizing combination of L and K, the isoquant is tangent to, and hence has the same slope as, the isoexpenditure line. Note that the slope of the isoexpenditure line is W/C = $16/$25 = 0.64.

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Answers to Chapter 3

17. Answer a. TC = $16(125) + $25(80) = $4,000. Notice also that the vertical intercept equals TC/C and the horizontal intercept equals TC/W. 18. Answer d. If C increases to $40 holding all else constant, the isoexpenditure line would connect 250 on the labor axis with 100 on the capital axis. This would make an output of 100 unattainable. To produce along the old isoquant, the isoexpenditure line would have to move out parallel, reflecting an increase in cost. If it did so, notice that a tangency would occur with the Q = 100 isoquant at a point that involved less capital and more labor.

Problems 19a. MR is the change in total revenue (R) associated with a one-unit change in output (Q), holding all else constant. More formally, if Q represents a small change in output, and R represents the resulting change in revenue, then MR =

R . Q

Similarly, MPL is the change in output associated with a one-unit change in labor, holding all else constant. Formally, the MPL can be written as MPL =

Q . L

By definition, MR◊MPL is the marginal revenue product (MRPL). Substituting the above expressions for MR and MPL yields R Q R x = , Q L L

which is by definition MRL, the additional revenue associated with a one-unit change in labor.

19b. If there is perfect competition in the output market, MR simplifies to P in the MRPL expression. With P constant, the MRPL slopes downward because MPL is assumed to diminish. With P constant, MRPL reaches zero when the MPL reaches zero. When the firm has monopoly power in the output market, the MRPL is downward sloping because both MR and MPL diminish as L increases. (For a monopoly, MR falls as Q increases, and Q increases as L increases.)

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Answers to Chapter 3

20a. The new MRPL (demand) curve has the equation MRPL = 40 - L. It is shown as curve D2 in Figure 3-7. Notice that the shift is not parallel since the curve reaches zero when the MPL reaches zero (at L = 40). If W stays at $10, the optimal level of labor to demand is 30.

Figure 3-7.

20b. The changes are identical to those in 25a.

20c. The changes are identical to those in 25a and 25b.

21a. See Figure 3-8.

Figure 3-8.

21b. The marginal product of labor curve now serves as the firm’s demand curve for labor.

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Answers to Chapter 3

22a. See Figure 3-9.

Figure 3-9.

22b. Let L standard for the total quantity demanded in the market. Then, L = L1 + L2 = 50 - (W/P) + 25 - 0.5(W/P) = 75 - 1.5(W/P) or W/P = 50 - (2/3)L. 23. The inequality suggests that if the firm produced one less unit of output by using less capital, its total cost of production would go down by $5. If the firm then proceeded to produce that same unit of output using labor, its total costs would only go up by $4. In other words, the firm could produce the same total output by changing its mix of labor and capital. If the firm can produce the same output at a lower cost with a different input mix, it could not have been at the optimal mix of labor and capital. *24a. If P = 56 - 2Q, then MR = 56 - 4Q. As W increases from $4 to $9 again, the MC will still rise from $16 to $24. What will be the change in optimal output? Originally, MR = MC  56 - 4Q = 16  Q* = 10. After the rise in MC, MR = MC  56 - 4Q = 24  Q* = 8. So originally, with an output of 10, L* = 20 and K* = 5. Holding output constant at 10, the change in W will lead to L* = 13.33 and K* = 7.5. Allowing output to adjust downward to 8 yields L* = (4/3)8 = 10.67 and K* = (3/4)8 = 6.

The net result of W increasing from $4 to $9 was that L* fell from 20 to 10.67 (a reduction of 9.33 units), and K* rose from 5 to 6 units (an increase of one unit). This net result, however, can be explained by a substitution effect where L* fell from 20 to 13.33 (a reduction of 6.67) and a scale effect where L* fell even further from 13.33 to 10.67 (an additional reduction of 2.67). Similarly, the increase in K* can be explained by a substitution effect where K* increased from 5 to 7.5 (a 2.5 unit increase), and also a scale effect where K* fell from 7.5 to 6 (a 1.5 unit decrease).

24b. Since the substitution effect on capital of the wage increase dominated the scale effect, labor and capital are gross substitutes, and the demand for capital will shift right (increase) as the wage increases.

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Answers to Chapter 3

*25a. Originally, L* = 20 and K* = 5. After the change in C, the expressions for the optimal levels of L and K become L* = 3Q and K* = (1/3)Q. If the original output level of 10 were maintained, the firm would substitute labor for capital so that L* = 30 and K* = 3.33. However, output does not remain at 10 since MC rises from $16 to $24. As the MC rises to $24, output falls to Q* = 6. At the new level of output, L* = (3)6 = 18 and K* = (1/3)6 = 2.

The net result of C increasing from $16 to $36 was that L* fell from 20 to 18 (a reduction of 2 units, and K* fell from 5 to 2 units (an decrease of three units). This net result can be explained by a substitution effect where L* rose from 20 to 30 (an increase of 10) and a scale effect where L* fell from 30 to 18 (a reduction of 12). Similarly, the decrease in K* can be explained by a substitution effect where K* fell from 5 to 3.33 (a 1.67 unit decrease), and also a scale effect where K* fell from 3.33 to 2 (a 1.33 unit decrease).

25b. Since the scale effect on labor of the capital price increase dominated the substitution effect, labor and capital are gross complements, and the demand for labor will shift left (decrease) as the price of capital increases.

26a. MPL is the change in output associated with a one-unit change in labor, holding all else constant. More formally, if L represents a small change in labor, and Q represents the resulting change in output, then MPL =

Q . L

Using this formula, the movement from point a to b implies MPL = 2/4 = 0.5. For the movement from b to c, MPL = 2/5 = 0.4.

26b. The diagram does show a diminishing marginal product of labor. It does not help to explain why the MPL falls, however. The diagram is drawn assuming a diminishing MPL and so simply reflects that assumption.

27a. The substitution effect is zero on both inputs, since holding output constant, the increase in the price of capital has no effect on the optimal input mix. The firm will remain at point a as long as it wishes to produce 70 units of output.

27b. The scale effect is a reduction in 20 units of both labor and capital. The firm moves from point a to point b.

27c. Labor and capital are gross complements since labor has been reduced in response to an increase in the price of capital.

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Answers to Chapter 3

27d. The total cost level has increased. Originally TC = $5(70) + $10(70) = $1,050.

After the price change and the adjustment in the input mix, TC = $5(50) + $20(50) = $1,250. Without the scale adjustment, however, the increase in cost would have been much worse.

Applications 28a. Equilibrium occurs where WD = WS. 30 - 0.04L = 0.05L - 15  0.09L = 45  L* = 500  W* = $10.

28b. The $9 per unit payroll tax shifts the demand curve down vertically by $9.

30 - 0.04L - 9 = 0.05L - 15  0.09L = 36  L* = 400  W* = $5.

The cost of labor (per unit) to the employer is the $5 wage plus the $9 tax for a total of $14.

28c. Since workers see their wage reduced from $10 to $5, they bear five-ninths of the tax. The firm sees its labor costs per unit rise from $10 to $14, so they bear the remaining four-ninths of the tax.

28d. Like the payroll tax, mandated benefits impose real per-unit labor costs on firms.

The effect of such costs would be to shift the demand for labor down and thereby reduce wages and employment levels. When all adjustments required by the market have been made, workers are likely to have born a significant share of the cost of such programs. *29a. The demand curve is the MRPL curve.

MRPL = MR◊MPL. K = 16  Q = 4 L .

MR = 20 - Q = 20 - 4 L .

MRPL = (20 - 4 L )

312

2 40 = - 8.

L L

Answers to Chapter 3

29b. Profit maximization occurs where MRPL = W. 40 - 8 = 10  L* = 4.94.

L Q* = 4 4.94 = 8.89  P* = $15.56. *29c. MRPL = 15

2 30 = L L Profit maximization 

30 = 10 L

 L* = 9  Q* = 12. *29d. See Figure 3-10.

Figure 3-10.

29e. In the long run the increase in output should lead to a scale effect that would increase the usage of both capital and labor.

29f. Regulations usually allow the firm a normal rate of return over its costs. As a result it has no incentive to control costs. If the firm pays higher wages, workers will be happier and the best new workers can be hired, making life smoother for the mangers of the firm, and the firm’s rate of return will not be affected.

30a. At W = $4, L = 120. See the line ab in Figure 3-11 for a plot of the original demand curve.

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Answers to Chapter 3

*30b. The subsidy is 50 percent of the difference between the target wage ($8) and the actual wage ($4). Therefore, the subsidy is $2 for each eligible worker. The effective cost to the firm of a new worker is $4 - $2 = $2. *30c. Since the effective cost of new labor is $2, the firm should be willing to hire out to L = 140. It is as if the firm is moving to the employment level associated with point e while the wage remains at $4. The intersection of the $4 wage and the new employment level creates the point f. Repeating this process for wage rates other than $4 creates the line segment dg. The new demand curve in its entirety would be the line bdg.

Figure 3-11.

*30d. At a wage of $4, the new demand curve is flatter (the slope as it appears on the graph changes from -0.1 to -0.067). The curve would be even flatter if the percentage of the subsidy increased to 75 percent. Point f would lie further to the right at L = 150 (and the slope would become -0.057). *30e. The total payment would be $2 times the number of new hires (20) for a total of $40.

If the subsidy applied to all workers, the payment would be $2 times 140 for a total of $280. *30f. If the original demand were steeper, the subsidy would have a smaller effect on employment. If the demand were steeper, point e would lie to the left of its current position. Since the employment level associated with point e determines the employment level associated with point f, point f would lie to the left of its current position. *30g. Targeted programs like this do not always work as well as the model predicts because there may be a stigmatizing effect associated with being eligible for the subsidy. The employer may feel there is something wrong with a worker who needs the government’s help to be hired, and so judge the worker’s marginal revenue product to be even lower than it actually is. If the employer devalues the employee’s worth as much as the subsidy reduces the employer’s cost of hiring this worker, there may be no increase in employment.

314

ANSWERS TO CHAPTER 4 Review Questions 1. Answer b. ii =

%E i −5.25 = = −1.5. %Wi 3.5

2. Answer b. ii =

%E i  %E i = ( ii )(%Wi )  %E i = ( −.5)(3.5) = −1.75. %Wi

3. Answer c. The expression for ii simplifies to ii =

E i Wi 7 = ( −5) = −1.4. Wi E i 25

4. Answer b. Expenditures on labor fall from $175 to $160, a change of -$15. If demand is elastic, expenditures on labor always fall as the wage rises.

5. Answer d. According to the Hicks-Marshall laws, demand is less elastic when it is difficult to substitute capital for labor (answer a), product demand is less elastic (answer b), and the supply of capital is inelastic (answer c).

6. Answer d. The demand curve facing an individual firm will always be more elastic than the market demand curve since from the point of view of any individual firm, consumers have many substitution possibilities. If consumers do not like the prices at one airline, they can often choose another. But from the point of view of the market as a whole, the only alternatives to air travel are the train, bus, or automobile, each considerably more time consuming for long trips.

7. Answer d. When labor and capital are used in fixed proportions, they can not be substituted for one another. Holding all else constant, the smaller the substitution effect of a wage change, the more inelastic the demand for labor.

8. Answer a. Letting (t) stand for teenagers and (a) for adults

at =

%E a 1 = = -0.2. %Wt -5

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Answers to Chapter 4

9. Answer a. If the cross-wage elasticity is negative, a rise in the price of teenage labor should reduce adult employment. Since teenage labor will also be reduced, teenagers and adults are gross complements.

10. Answer c. Adults and teenagers will be gross complements if the scale effect associated with the rise in teenage labor dominates the substitution effect. Answers a and b make for a large substitution effect, while d makes for a small scale effect. When the cost of teenage labor accounts for a large share of total costs, a rise in teen wages will lead to a large increase in the marginal cost of production. The larger the increase in marginal cost, the larger the reduction in output and the more employment in both categories of labor will fall.

11. Answer d. As long as the labor demand curve is downward sloping, an increase in the minimum wage should move the firm up the demand curve, resulting in a lower employment level. The only way the actual level of employment can increase is if the curve also shifts out at the same time the movement along the curve is taking place. In this case, the employment increase would have been even larger had the minimum wage not been imposed.

12. Answer b. Because the share of total costs attributable to low-wage workers varies across firms, increases in the minimum wage affect some firms more than others, and this can lead to significant changes in the relative prices of the goods sold by these firms.

These relative price changes, in turn, can cause changes in consumer buying patterns (intersectoral shifts in demand) and result in some firms actually seeing an increase in the demand for their product. The scale effect of this demand increase can lead to employment increases for some firms even though their costs are higher. Consequently, looking at the employment effects on individual firms may give a misleading impression of the overall employment effects of the minimum wage. For this reason, it is better to look at the employment effects on broader groupings of firms serving many different industries (e.g., the retail sector of the economy).

13. Answer d. In addition to the demand shifts, technological change makes for a more elastic labor demand because product demand will become more elastic as the number of substitution possibilities for consumers increase.

14. Answer b. A reduction in the price of capital stimulates the demand for labor only if there is a large-scale effect associated with the price decrease. A more elastic product demand contributes to a large-scale effect.

15. Answer c. While some industries and jobs are eliminated through technological change, the efficiency and competition it promotes tends to open up new consumption and employment possibilities. The increased productivity and technological change has helped to bring about higher real wages.

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Answers to Chapter 4

Problems 16a. The slope is -2. For every one unit change in W, L changes by 2. This slope is the same for a wage change between $20 and $21 as it is for a change between $5 and $6.

(Note that the slope as it appears on the graph is actually -0.5. Notice that when W is plotted on the vertical axis and L on the horizontal, the slope as it appears on the graph is actually W/L. 16b.  ii =

E i Wi . Wi E i

For a change in the wage from $5 to $6, 5 ii = (-2)40 = -0.25.

For a change in the wage from $20 to $21, 20 ii = (-2)10 = -4.

16c. While the slope remains constant as the wage increases, note that the absolute value of the elasticity gets larger. See Figure 4-5 for a plot of this curve.

Figure 4-5.

16d. When the wage rises from $5 to $6, the firm’s total expenditures on labor rise from $200 to $228, a change of +$28. But when the wage rises from $20 to $21, total expenditures fall from $200 to $169, a change of -$31.

16e. When demand is inelastic, increases in the wage lead to increases in total expenditures. When demand is elastic, increases in the wage lead to decreases in total expenditures.

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Answers to Chapter 4

16f. The slope is now -80, and the elasticity is 5 ii = (-80)1600 = -0.25.

Changing the units in which labor is measured, in this case from number of workers to number of hours, changes the slope of the relationship but not the elasticity.

16g. Elasticity is preferred to the slope as a measure of responsiveness because it is insensitive to changes in the units used to measure W and L. Defined as the ratio of two percentage changes, elasticity is a unit-free measure of responsiveness. Also, along a linear demand curve, slope is constant but elasticity is not. Thus elasticity shows the change in responsiveness at different prices (wages) whereas the slope does not. *17a. As the wage changes from $5 to $10, the slope decreases in magnitude from -4 to -1. (Note that the slope as it appears on the graph changes from -0.25 to -1. Since W is plotted on the vertical axis and L on the horizontal, the slope as it appears on the graph is actually W/L. *17b. As the wage changes from $5 to $6, elasticity remains constant at -1. Any demand curve that can be written in the form L = KW, where K is any constant, has a constant elasticity equal to . *17c. See Figure 4-4.

Figure 4-4.

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Answers to Chapter 4

18a. Demand 1 is more elastic at any given price. For example, at P = $20, demand 1 yields QP = (-1)(20/16) = -1.25, while demand 2 yields QP = (-0.5)(20/16) = -0.625.

18b. Use the MR=MC rule to find the optimal output. With demand 1, optimal output is reduced from 10 to 6, while with the more inelastic demand 2, optimal output is reduced from 10 to only 8.

18c. The scale effect would be larger with the more elastic product demand (demand 1).

Holding all else constant, the larger the scale effect, the more elastic the long-run labor demand.

19a. According to this study, as the wage of teenagers falls (because of the youth subminimum), the quantity of teenagers demanded increases and the quantity of adults demanded decreases. Since the quantity demanded of teenagers and adults moves in opposite directions, teenagers and adults are gross substitutes and the cross-wage elasticity would have a positive sign.

19b. For teenagers and adults to be gross substitutes, the substitution effect must dominate the scale effect.

19c. If teenagers and adults are gross substitutes, then the demand for adults would shift left as the teenage wage falls.

Applications 20. The total income flowing to labor is the wage multiplied by the quantity of labor hired.

When demand is elastic, small percentage increases in the wage cause large percentage reductions in the quantity of labor demanded. With the quantity of labor demanded falling faster than the wage is increasing, total income falls as the wage increases.

21a. An airline pilot is a job that requires rather specialized knowledge, and so it is difficult to substitute other types of labor for the pilots. It is also rather difficult to substitute any kind of capital for the pilots, although running fewer flights with larger planes is one way to do this. Firms that try this latter approach, however, may require new planes. The supply of such planes is likely to be inelastic, since planes are complex items not quickly produced. In the airline industry, the labor costs associated with pilots are a small share of total costs, with fuel being one of the largest. Finally, before deregulation, the number of competitors was tightly controlled, making the product demand facing individual firms more inelastic.

Garments workers, on the other hand, are unskilled labor, and so it is relatively easy for firms to find other labor to substitute. Also the firm can probably hire as much or as little of this substitute labor at a constant price. It does not have to worry about the price of the substitutes being bid up significantly. Garment work like cutting and sewing fabric is labor intensive and overseas competition tends to make for elastic product demand.

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Answers to Chapter 4

21b. Airline deregulation has tended to increase competition, making product demand more elastic. As the product demand becomes more elastic, so does labor demand.

Similarly, reducing tariffs and import quotas on textiles and apparel should increase product demand elasticity and make the demand for garment workers even more elastic.

22a. Plan B should have the least impact on employment since it involves a change in the price of capital. As C increases (holding output constant), there is a tendency for the firm to substitute labor for capital. There will also be a scale effect pushing both labor and capital down, but this scale effect is also present in Plan A and Plan C. Plan A has a substitution effect that will reinforce the reduction in L coming through the scale effect, not counteract it as in B. Plan C has no substitution effect.

22b. Plan A would lead to a large reduction in employment if there were a large substitution effect and a large scale effect associated with the increased labor cost. There would be a large substitution effect if it were easy to substitute capital for labor and if the supply of capital were elastic. There would be a large scale effect if labor costs were a large share of total costs and if the product demand were elastic.

Plan B would lead to a large reduction in employment if there were a small substitution effect and a large scale effect associated with the capital price increase. There would be a small substitution effect if it were difficult to substitute labor for capital and if the supply of labor were inelastic. There would be a large scale effect if capital costs were a large share of total costs and if the product demand were elastic.

Plan C is a direct increase in the marginal cost of production. It reduces labor only through a scale effect. This scale effect would be large if the product demand were elastic.

23a. At W = 4, the original employment level would have occurred where 4 = 25 - 0.5L  L* = 42.

When W increases to 6, employment occurs where 6 = 25 - (1/3)L  L* = 57.

23b. Without the minimum wage, employment would have occurred where 4 = 25 - (1/3)L  L* = 63.

Therefore, even though employment increased from 42 to 57, it would have increased to 63 had it not been for the minimum wage. (Similarly, one could argue that it would have fallen from 42 to 38 had it not been for the demand shift).

24a. A better indicator of a country’s standard of living would be its per capita output and consumption levels.

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Answers to Chapter 4

24b. At the same time that technology destroys jobs, it also opens up new opportunities.

Instead of automatically becoming farmers, young people are now free to become doctors, teachers, engineers, computer programmers, and so on.

24c. Making plant closings more difficult is like banning farm machinery in that both policies are attempts to stop the transfer of resources out of obsolete or inefficient uses into new and more efficient uses. Some of these new uses may not be currently envisioned.

321

ANSWERS TO CHAPTER 5 Review Questions 1. Answer d. This is the best response since it is the broadest true statement. Answers a and c are too broad since these categories include some costs that are not also quasi-fixed.

Answer b gives an example of quasi-fixed costs, but there are others.

2. Answer a. The hourly wage is not a quasi-fixed cost because the total amount paid varies directly with hours worked (and thus with output). Defined benefit plans obligate the firm to make certain payments to retirees. All retirees with a certain number of years of service may receive the same amount, regardless of how many hours they actually worked for the firm, and thus this is likely to be a quasi-fixed cost. Both defined benefit and Social Security programs have elements that are quasi-fixed and elements that do vary with hours worked. Defined contribution plans are usually based on an employee’s total earnings, and hence their cost will be partially a function of how many hours the retiree worked for the firm. Social Security contributions are a percentage of total earnings, provided the earnings are less than some maximum amount. *3. Answer d. Given the benefits are prorated based on hours worked, these contributions do not qualify as quasi-fixed costs, but rather will vary both as the number of workers changes and as hours change.

4. Answer c. The total cost of training includes the explicit costs of training (3,000) plus the implicit opportunity cost of the trainees time (3,500 - 2,000 = 1,500), for a total cost of 4,500.

5. Answer c. MEH = (wage + variable benefits per hour) x number of workers = [10 + (50/40)]500 = 5,625.

6. Answer b. MEH = [(1 + overtime premium)wage + variable benefits per hour] x number of workers = [(1.5)10 + (50/40)]500 = 8,125.

7. Answer c. MEM = weekly wages + weekly employee benefits and quasi-fixed costs = [10(40) + 200] = 600.

8. Answer a.

MEM 600 MEH 8,125 = = 12  = = 13.

MPM 50 MPH 625

The firm should increase M and decrease H to bring about an equality. As M increases, MPM will fall, increasing the left side of the equation. As H decreases, MPH will rise, decreasing the right side of the equation.

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Answers to Chapter 5

9. Answer d. Another possibility is that there will be a decrease in the straight-time wage to the level needed to keep total compensation unchanged. *10. Answer d. Such a law would increase both MEM and MEH. Without knowing the specific ME and MP figures, an increase in both ME values leads to an ambiguous change in the cost-minimization equation. *11. Answer a. Such a law would raise the ME of part-time workers, causing the firm to substitute full-time workers for part-time workers. Even though part-time workers may still be cheaper than full-time workers, a change in the relative cost of each type of input should bring about a change in the input mix.

12. Answer a. This law would increase quasi-fixed costs, thus raising the MEM but not the MEH associated with part-time workers. The ratio of ME to MP for the M input would rise, forcing the firm to decrease M and increase H to restore the costminimization equality. There would be fewer part-time workers employed, but those that were still employed would be working longer hours.

13. Answer a. While the effects of this law on the employment/hours mix would be different from the version where benefits are prorated, the laws would have very similar effects on the mix of part-time and full-time workers. Again, as in question 11, the law would increase the ME of part-time workers, causing the firm to substitute full-time workers for part-time workers.

14. Answer a. The present value of the bonus is the 250,000 received in the current period plus the discounted value of the future payments.

250,000 +

250,000 250,000 250,000 + + = 918,253.

1.06 (1.06) 2 (1.06) 3

15. Answer b. As the interest rate falls, dollars received in the future are not discounted as much, hence the gap between the post-training wage and the marginal product does not have to be as large for the firm to recover the full value of its training investment.

16. Answer d. If workers paid entirely for the training in the initial period (as is the case with general training) the wage during training would have to be much lower, and then there would be no gap between the wage and marginal product in future periods to protect workers from temporary layoffs. The present value of the total compensation package is unaffected, however, by the way in which the training costs are recovered.

17. Answer d. If the firm had to pay the entire cost of training during the initial period then they would have a bigger investment to recover in future periods, causing a bigger gap between the wage and the marginal product. If the gap grows so large that the wage slips below the worker’s inherent marginal product, the worker will have an incentive to quit. In either case, however, the firm recovers in present value terms the entire training investment.

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Answers to Chapter 5

18. Answer c. Whether the firm can attract workers to its training program and keep them will depend on how the present value of the entire compensation stream compares with what can be earned elsewhere. To recover its training costs, however, the firm must pay the workers less than their marginal product at the firm.

19. Answer d. When a firm invests a large sum in its workers, it should be expected to try and recover those investments or take steps to minimize the size of the investment.

Thus large investments are consistent with a large gap between the wage and the marginal product, as well as statistical discrimination and internal labor market strategies.

20. Answer d. If the firm attributes shorter job tenures to women, it will probably try to pay them less so as to recover the hiring and training investments over the shorter period.

If for some reason they must pay the same, the firm will either invest less in its women workers or simply not hire them in the first place.

21. Answer b. In a monopsonistic labor market, the firm faces an upward-sloping supply curve for labor because either it is the only firm in the market, or because mobility costs limit the willingness of workers to leave if other firms offer higher wages.

22. Answer b. Higher mobility costs mean that workers are less likely to leave. Thus a given percentage change in the wage will lead to a relatively smaller change in the quantity of labor supplied (than if mobility costs were lower), and the supply of labor will be relatively less elastic. *23. Answer d. If a monopsonist faces a market supply of labor W = a + bL, then the MEL will equal a + 2bL. The reason that the MEL lies above the wage is that when the firm faces an upward-sloping market supply curve, to attract additional workers it must pay a higher wage, but this higher wage applies to all workers previously hired at the lower wage (assuming it pays a single wage to all workers). This means that the cost of an additional worker to the firm is more than just the wage paid to that worker. The intercept is the same, however, because hiring just one worker does not require any wage changes.

24. Answer d. Setting a minimum wage above the monopsony wage creates a horizontal segment to the marginal expense of labor curve. If this segment lies below the point where the original MEL intersects the MRPL, the optimal employment level will rise. If it intersects the MRPL above that point, employment will fall. It is also possible for the minimum wage to be set exactly at the level where the original ME L intersects the MRPL. In that case, there would be no change in employment.

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Answers to Chapter 5

Problems 25a. The typical worker is employed for 2,000 hours and earns $25,000. The firm must contribute 5 percent of this, or $1,250, to the fund. For each additional worker hired (with the same hours and wage), the firm’s contribution will go up by $1,250. However, if existing workers were required to work one hour longer per week (50 per year), earnings would rise to $25,625 and hence the firm’s contribution would also rise to $1,281.25. Since the cost varies with the number of workers and with the number of hours worked, it is not a quasi-fixed cost.

25b. Holding hours and the wage base constant, if the typical worker earned $25 per hour then the contribution would be a quasi-fixed cost. Each worker would earn $50,000 and the firm would contribute $2,500 for each employee. However, if the employees worked more hours and increased their earnings, the firm would not have to increase its contribution. On the other hand, given the typical workweek and wage at this firm, a wage base of only $25,000 would also transform this contribution into a quasi-fixed cost.

26a. The cost of checking new hires for legal residency (and the fines levied if a violation is detected) would represent an increase in hiring costs, and hence an increase in quasi-fixed costs. This raises MEM and will lead the firm to substitute a longer workweek for more workers.

26b. An increase in quasi-fixed costs raises MEM and hence the relative cost of employing additional workers. This induces a substitution of hours for workers.

However, it will also raise the marginal cost of production, which in turn should lead the firm to choose a lower output level. This lower output level triggers a scale effect in which the firm will have an incentive to cut back on its use of both workers and hours.

Therefore, whether the workweek actually increases depends on whether the substitution effect dominates the scale effect (whether hours and employment are gross substitutes).

27. The inequality suggests that if the firm produced one less unit of output by using fewer workers, its total cost of production would go down by 2. If the firm then proceeded to produce that same unit of output using a longer workweek, its total cost of production would only rise by 1.5. In other words, the firm could produce the same total output at a lower cost by changing it mix of employment and hours. If the firm can produce the same output at a lower cost with a different input mix, it could not have been at the optimal mix of workers and hours.

28a. The post-training wage will be set at 240.

(MP0 - W0) + (MP1 - W1) + …+ (MP15 - W15) = Z. Assuming for simplicity W1 = … = W15 = W, then 200 - 150 + 15(250 - W) = 200  15W = 3600  W = 240.

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Answers to Chapter 5

Under this plan, workers pay for 50 of the 200 in training initially, and then the firm recovers 10 per month over the next 15 months. Workers will find this position attractive since the total payment stream over the entire length of employment is greater than what they could have earned elsewhere based on their inherent marginal product.

150 + 15(240) = 3750 > 16(225) = 3600.

28b. The firm would have to recover its full 200 in training expenses over the 15 posttraining periods. This implies a wage of 236.67. While this is still above the worker’s inherent marginal product, the protection the firm has against quits has shrunk. The more the workers pay for their training in the initial period, the more protection the firm has against quits.

28c. There would be no gap between the post-training wage and the marginal product.

Workers want the firm to bear some of the initial cost so that there is a gap, and hence some protection from temporary layoffs.

28d. This would reduce the post-training wage to 235 and increase the gap between the wage and the marginal product to 15.

28e. The firm can recover its costs over 5 periods if MP0 - W0 + MP1 - W1 + … + MP5 - W5  Z. Given the constraint W0 = … = W5 = 225, then 200 - 225 + 5(250 - 225) = 100 < Z = 200.

Therefore, the firm could not recover its training costs. The shortest time of recovery (n) can be determined by solving the equation 200 - 225 + n(250 - 225) = 200, which implies n = 9 months (after training).

28f. The inherent MP sets a lower bound for the wage in the post-training periods. To find the highest this boundary could be, solve the equation 200 - 150 + 15(250 - MP*) = 200, which implies the maximum MP* equals 240.

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Answers to Chapter 5

29a. The post-training wage will be set at 402.5.

MP0 − W0 +

MP1 − W1 535 − W1 = 150 = Z  400 − 375 + 1+ r 1.06

 535 - W1 = 132.5  W1 = 402.5.

29b. Although the inherent MP is not given in the problem, the lowest it could be is 400, the marginal product during training. Using this value as a lower bound, the firm’s training program is not attractive since the present value of the total compensation stream is less than what can be earned elsewhere.

402.5 400 375 + 1.06 = 754.72 < 400 + 1.06 = 777.36.

30a. The firm more than recovers its training investment on a present value basis.

1800 − 1600 +

2500 − 2200 2800 − 2600 + = 661  Z = 500.

1.06 (1.06) 2

30b. This training program is not likely to persist since other firms could offer the workers the same kinds of specific training opportunities at higher wages and still make a profit.

31a. Since this is general training, the firm will offer a wage of W0 = MP0 - Z = 5.50 - 3 = 2.50 during training. In the post-training periods the wage will equal the marginal product of 9.

31b. Although it would appear a post-training wage of 7.5 would enable the firm to recover its general training investment, such a wage could not be sustained since the typical worker’s marginal product of 9 will be observed by all firms. Other firms would be willing to bid up to 9 for these workers.

31c. Since the training period wage could not fall to 2.50, the firm would have to cut back the amount of training it offers to only 1.50. If this is not possible, then either no training will be offered, or the workers will not be hired. *32a. The optimal employment level (L*) occurs where W/P = MPL (P represents the price of the firm’s output). Substituting the given information yields 40/2 = 50 - 2L*  2L* = 30  L* = 15.

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Answers to Chapter 5

*32b. Employing the W/P = MPL rule again yields 40/1 = 50 - 2L*  2L* = 10  L* = 5.

Assuming no training investment, the firm cuts employment from 15 to 5 when the product price falls. *32c. At L = 15, MPL = 20. If the firm sets W at only 20 and the product price is 2, then at that employment level the MP exceeds the real wage (MPL = 20 > 10 = W/P). If the product price now falls to 1 (say, because the demand for the product falls), the gap will be eliminated, but W/P will now be exactly equal to the MPL and there will be no need to change the employment level. The gap that existed between the wage and the marginal product insulated the workers from the reductions in employment that usually accompany reductions in P. Applications 33a. Robin would be offered a post-training wage of 15,122.

MP0 − W0 +

 11,000 − 10,500 +

MP1 − W1 MP2 − W2 + = Z, 1+ r (1 + r ) 2 16,000 − W1 17,000 − W2 + = 3,000.

1.06 (1.06) 2

Assuming for simplicity W1 = W2 = W, then 16,690 -1.06W + 17,000 - W (1.06)(16,000 - W) + (17,000 - W) = 2,500 = 2,500  2 1.1236 (1.06)

 33,960 - 2.06W = 2,809  2.06W = 31,151  W = W1 = W2 = 15,122.

33b. The program is attractive since the present value of the total compensation stream exceeds that associated with the alternative offers.

10,500 +

15,122 15,122 + = 38,225 1.06 (1.06) 2

11,500 +

11,500 11,500 + = 32,584.

1.06 (1.06) 2

is greater than

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33c. Ann would be offered a lower post-training wage of 13,350.

11,000 − 10500 +

16,000 − W1 = 3,000  16,000 − W = 2,650  W = 13,350.

1.06

33d. The firm’s training program should be attractive since the present value of the total compensation stream is more than what can be earned elsewhere.

10,500 +

13,350 = 23,094 1.06

11,500 +

11,500 = 22,349.

1.06

is greater than

33e. Assuming the firm must pay Ann the higher wage, then they would not be able to recover the 3,000 training investment over her shorter job tenure. As a result, either Ann would not be hired or the firm would not invest as much in her training.

34a. The subminimum wage should increase the likelihood teens would receive on-thejob training of all types, but especially general training. In the training investment model discussed in this chapter, the minimum wage serves as a floor beneath which the wage can not fall, but in so doing, it sometimes results in a gap between the wage and the marginal product that is too small for the firm to recover its training investment. (Recall problem 25e.) This situation is most likely to arise in the case of general training because general training must be recovered during the training period, and so often necessitates a large gap between the wage and the marginal product. This in turn may necessitate a wage so low that it is below the minimum wage.

34b. Using the example given in the Summary section of this chapter, suppose instead the training is general and there is a minimum wage of 425. The firm would like to set a wage of 400 during period zero, but would be prohibited from doing so. The firm would be unable to recover its training investment, and as result, the worker would not be hired or less training would be offered. A subminimum wage of, say 390, would allow the firm to hire the worker and offer the full amount of training.

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Answers to Chapter 5

35a. Using the cost-minimization framework, subsidizing training costs should lead to a reduction in the MEM term, setting off adjustments that would increase the number of workers demanded. (It would also result in a different mix of workers, with a higher percentage of workers from disadvantaged groups being hired.) Holding output constant, as the number of workers demanded increases, the number of hours worked by existing employees will probably go down, unless other inputs like capital are adjusted downward instead. This reduction in hours would be called a substitution effect, and it takes place because workers are now relatively cheaper than they were before. A complete analysis should also allow for the possibility of output changing. An increase in output is to be expected here since a decrease in MEM will drive down the MC of production and lead to an increase in output. As output increases, typically both employment and hours rise.

This increase in the demand for both inputs would be called a scale effect. If the scale effect dominates the substitution effect, hours could actually increase. In such a situation, hours and workers would be called gross complements in the production process.

35b. Since the program is targeting employer expenditures on training, assume that the training being offered is firm-specific. (Recall that with general training the worker typically pays for the training in the initial period.) As mentioned in the answer to 31a, the program should result in an increase in the number of workers from disadvantaged backgrounds being hired. For those disadvantaged workers that would have been hired and trained anyway, protection against temporary layoffs is reduced since there is now likely to be a smaller gap between the post-training wage and the workers’ marginal product. The wage should exceed the workers’ inherent marginal product by more than before, however, providing the firm more of a buffer against quits. For those workers that would not have been hired and trained except for the program, job stability is clearly increased since they now have a job where the post-training wage will be set such that MP* < W < MP. *36a. MRPL = MR*MPL. K = 3  Q = 3L  MPL = 3.

MR = 64 - 2Q = 64 - 2(3L) = 64 - 6L. MRPL = (64 - 6L)3 = 192 - 18L. *36b. In this problem, the marginal product of labor is constant, it does not diminish as L increases. This assumption is made to make the algebra of the problem simpler. *36c. If W = a + bL, then MEL = a + 2bL  MEL = 6L.

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Answers to Chapter 5

36d. Profit maximization occurs where MRPL = MEL. 192 - 18L = 6L  L* = 8.

36e. W* = 3(8) = $24, Q* = 3(8) = 24, P* = 64 - 24 = $40, Profit = PQ - WL - CK = 40(24) - 24(8) - 5(3) = $753.

36f. Wmin = 30  MEL = 30 (provided L < 10)  profit maximization occurs where 192 - 18L = 30  L* = 9.

In this case, the minimum wage leads to an increase in employment opportunities.

Wmin = 66  MEL = 66 (provided L < 22)  profit maximization occurs where 192 - 18L = 66  L* = 7.

In this case, raising the minimum wage too high leads to a decrease in employment opportunities.

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ANSWERS TO CHAPTER 6 Review Questions 1 Answer d Individuals can also affect their hours through working more than one job, vacations, and leaves of absence.

2 Answer d Typically when one observes indifference curves crossing on a graph, for example in Figure 6-3, they represent the preferences of different individuals If they pertain to the same person, than the point of intersection simultaneously yields two different levels of happiness, which violates the basic notion that the person can consistently rank different combinations of leisure and income. Steep indifference curves indicate a high value for leisure, since the person requires a large amount of income to offset a small sacrifice of leisure.

3 Answer a The wage rate is reflected in the slope of the constraint Note that nonlabor income is $200 and the optimal number of hours to supply is 100.

4 Answer d When indifference curves are drawn with a convex shape, it ensures that when one moves from an extreme combination (one where there is a lot of one good but not much of the other) to one where the goods are more evenly consumed, a higher indifference curve will be attained In other words, the convex shape of the indifference curves is a way to make the statement that people prefer variety to extremes.

5 Answer c The objective of the consumer is not to maximize income or leisure but to find that combination of income and leisure that is consistent with the budget constraint and leads to the highest level of utility Since higher indifference curves represents higher levels of utility, maximizing utility can be thought of as trying to get on the highest attainable indifference curve Note that it is impossible for both leisure and income to be maximized at the same point.

6 Answer d When this condition holds, a window of opportunity exists for the individual to attain a higher level of utility by moving to a point involving less than the maximum leisure time. Very steep indifference curves can result in a corner solution.

7 Answer c When work is viewed as something good, leisure implicitly becomes something bad Leisure is bad here when it exceeds 350 hours: when one gets more of it, income must go up, not down, to keep the person at the same level of satisfaction This creates the upward slope to the indifference curves.

8 Answer c Usually when the budget constraint has a flat segment, representing a guaranteed income, the optimum occurs at the point of maximum leisure But because after a point, leisure is viewed as bad, the optimum occurs at 50 hours of work. The

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Answers to Chapter 6

market wage is $4, with an implicit tax of 100 percent on the first $400 of earnings, zero thereafter.

9 Answer b For a person working zero hours, an increase in the wage can not lead them to reduce hours even further. So, although there is theoretically an income effect--if the person makes any changes, her income will rise--in practical terms it must be dominated by the substitution effect.

10 Answer a If leisure were an inferior good, then the income effect associated with the wage increase would actually cause the person to cut back on leisure This, together with a positive substitution effect, would ensure work hours would go up.

11 Answer d Typically, goods do not switch from being normal to inferior, but even if they did, the curve described in answer c could never turn back, since leisure being inferior guarantees that portion of the curve would be upward sloping.

12 Answer a Hours supplied should go up because such a change creates a pure substitution effect The lower marginal tax rate is like an increase in the wage, but the assumption that the total taxes paid by workers remains constant means that income remained constant.

13 Answer a A lump sum payment unrelated to earnings is an increase in nonlabor income that shifts the budget constraint out parallel to the old constraint, thus creating a pure income effect.

14 Answer b Scheduled benefits unrelated to earnings create a parallel shift of the constraint Hence, the opportunity cost of leisure remains the market wage rate, and so an incentive to work is preserved.

15 Answer d The maximum subsidy (S) is $600, and the breakeven income (S/t) is $1,200 Therefore, the value of t must be 0.5 With an implicit tax rate of 0.5, the initial subsidy will be completely “taken away” by the time earnings reach $1,200.

16 Answer d The new optimum occurs at L = 350 (H = 50) The actual subsidy equals S - t(WH) = $600 - .5($200) = $500.

17 Answer b The substitution effect is the movement from the point (L = 247, Y = $990) to the point (L = 350, Y = $700).

18 Answer b The income effect is the movement from the point (L = 200, Y = $800) to the point (L = 247, Y = $990).

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Answers to Chapter 6

19 Answer b As the implicit tax rate increases, the effective wage rate decreases, lowering the opportunity cost of leisure, and reducing work incentives for most individuals An exception to this tendency is exhibited in problem 30.

20 Answer d While reducing the implicit tax rate tends to preserve work incentives, it extends the reach of the program (potentially to everyone if t = 0) As more people are eligible for the program, the cost of the program tends to go up.

21. Answer c. The lowest income recipients actually face an above-market wage, creating a substitution effect in favor of working, working against the income effect allowing more leisure. Without knowing about preferences, one cannot predict the net response. For higher income eligibles, either a zero implicit tax, or a positive implicit tax on earnings exists, so there is nothing to counteract the income effect, and a substitution effect may even reinforce it, reducing work effort.

22. Answer d. Many who work for minimum wages do not live in low-income households, and although their impact on work incentives may be positive (they are theoretically ambiguous), they may result in reduced hours because of employer cutbacks. As noted in the text, subsidies given to employers to hire low-income workers have not been very successful, and in some cases appear to have worsened the target population’s chances of finding employment by identifying them as potential problem employees.

Problems 23a See the solid line in Figure 6-9.

Figure 6-9.

23b See the dashed line in Figure 6-9.

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Answers to Chapter 6

23c Increased appreciation for leisure relative to income tends to make the indifference curves steeper. It takes larger amounts of income to compensate for a given sacrifice of leisure.

24a See the solid line in Figure 6-10.

Figure 6-10.

24b See the dashed line in Figure 6-10.

25a Full income (WT + V) for the original budget line is $2,700 Noticing that V = $300 and T = 400, the original wage was $6 Similarly, after the wage decrease the new level of full income is $1,500, which implies a wage of $3, given the same values of V and T. 25b The income effect is the movement from the point (L = 225, Y = $1350) to the point (L = 177, $Y = 1061), a decrease of 48 leisure hours The substitution effect is the movement from the point (L = 177, Y = $1061) to the point (L = 250, Y = $750), an increase of 73 leisure hours.

25c The two points would be (W = $6, H = 175), and (W = $3, H=150) The curve is positively sloped The substitution effect is stronger than the income effect in 28b.

26a Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is L* =

 WT + V .  + W

Substituting the values that apply before the injury yields L = 8 (H = 8), Y = $40, and U = 320.

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Answers to Chapter 6

26b If all the income is replaced after an injury, then L = 16 , Y = $40 and U = 640, a higher level of utility than that attained while working.

26c To keep the worker just at U = 320, solve the equation (16)(Y) = 320 This implies Y = $20 Therefore, to keep utility constant, only 50 percent of the original income needs to be replaced This whole analysis, of course, assumes that all leisure time is identical That is, leisure time obtained through injury yields the same utility as leisure time taken while healthy This may not be the case, for example, if the injury is painful or limiting.

27a Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is L* =

 WT + V .  + W

(Note that both  and  = 1 in this example.) Substituting the values that apply before the welfare program, the original optimum is 200 leisure hours (200 work hours) With t = 1, the effective wage, given by the expression (1-t)W, becomes zero and while we cannot divide by zero, the optimum occurs at the maximum of 400 leisure hours (zero work hours) With t = 0.5, the effective wage rate is $2 Combining this with $500 in nonlabor income yields an optimum of 325 leisure hours (75 work hours) With t = 0, the effective wage remains the market wage of $4 Combining this with the nonlabor income of $500 yields an optimum of 262.5 leisure hours (137.5 work hours) Summarizing, t = 1 implies H falls by 200, t = 0.5 implies H falls by 125, and t = 0 implies H falls by 62.5.

27b An implicit tax rate of zero preserves work incentives the best since the opportunity cost of leisure remains the market wage Hours of work still fall under such a program because of the income effect of the subsidy, but there is no reinforcing substitution effect if implicit taxes do not reduce the effective wage rate.

28a The breakeven income occurs at the value S/t So for constraint acdb we have 350/t = 350, which implies t = 1 For the constraint aceb we have 350/t = 1400, which implies t = 0.25 Note that when we can view the breakeven point graphically, the tax rate can be calculated as S/B = t, or in the two cases here, 350/350 = 1 and 350/1400 = 0.25.

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Answers to Chapter 6

28b For these preferences, t = 1 provides the strongest work incentives. The reason for this somewhat unusual result is that when t is reduced, the reach of the program (as illustrated by the breakeven point) is expanded dramatically In this case, the person would not even have been affected by the program with the high implicit tax rate The lower rate, however, enables the person to be eligible for the program and experience the income and substitution effects it creates.

29a See Figure 6-11 The breakeven point occurs at L = 1,600 (H = 1,200) and Y = $6,000.

Figure 6-11.

29b Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is L* =

 WT + V .  + W

Substituting the values that apply before the program is enacted yields an optimum of L = 1,400 (H = 1,400) and Y = $7,000 This is point a in Figure 6-11 The level of utility (denoted by U1) is 9,800,000.

29c Using the graph as a guide, it appears likely that the individual will be pulled into the program, even though they are currently above the breakeven point The optimal point appears to be the corner of the constraint which occurs at L = 2,000, Y = $6,000 Notice that the level of utility at this point is 12,000,000 This represents an improvement over the original point The optimum is identical to that which would have been achieved if benefits were simply cut off once earnings reached $4,000 No one that values both leisure and income would want to locate along the horizontal segment of the constraint when moving to the corner of the constraint is possible.

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Answers to Chapter 6

Applications 30a See Figure 6-12 The breakeven point occurs at L = 175 (H = 225), Y = $900 The value of S/t = 200/0.4 = $500 in this case represents the additional income needed to reduce the subsidy to zero once the person qualifies for the program Note that in this case, however, the person does not qualify for the program immediately, but rather works 100 hours, and hence earns $400, before the usual type of income maintenance program begins.

Figure 6-12.

30b Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is L* =

 WT + V .  + W

For a = 0.65, b = 0.35, the optimal combination before the program was L = 260 (H = 140), Y = $560 This is point a in Figure 6-12 After the program, the person should end up at the corner of the new constraint (point d) Since the corner point has coordinates L = 300 (H = 100), Y = $600, this represents a reduction in work hours of 40.

For  = 0.75,  = 0.25, the optimal combination before the program was L = 300 (H = 100), Y = $400 This is point b in Figure 6-12 After the program, the person should also end up at the corner of the new constraint (point d) There will be no reduction in work hours.

For  = 0.85,  = 0.15, the optimal combination before the program was L = 340 (H = 60), Y = $240 This is point c in Figure 6-12 After the program, the person should also end up at the corner of the new constraint (point d) This represents an increase in work hours of 40.

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Answers to Chapter 6

30c While some people will reduce their work hours due to the income and substitution effects such programs can create, the possibility of such individuals dropping out of the labor force is very remote Also, some individuals will actually increase their hours just enough to cross over the threshold and qualify for the program’s maximum benefit Such thresholds seem like a sensible way to preserve at least some minimal work incentives.

31a See Figure 6-13 The original earnings constraint is line ab. Under this EITC, the maximum subsidy first occurs where earnings equal $9,000 This occurs where L = 1,500 (H = 1,500) This is point c in Figure 6-13 The level of total income (including the government payment) will be Y = $11,700 (point d) The maximum subsidy continues to be received until earnings = $12,000 (point e). This occurs where L = 1,000 (H = 2,000). Factoring in the subsidy, total income is $14,700 at L = 1,000 (point f). The breakeven point occurs when earnings equal $18,000 (point b). Once the person has reached point e, an additional $6,000 in earnings at an implicit tax rate of 0.45 just eliminates the $2,700 subsidy ($6,000 x 0.45 = $2,700). To achieve the additional $6,000 in earnings, the person must increase work hours (reduce leisure) by 1,000 hours.

Figure 6-13.

31b. To the right of point d, the individual is accumulating income according to the formula income = WH + .3(WH), which makes the effective wage rate (the absolute value of the slope of the constraint) (1.3)(W) which equals 7.8. To the left of point f, the effective wage rate is (1-t)W, where t = 0.45 This means that the absolute value of the slope is 3.3.

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Answers to Chapter 6

31c A person originally at point g will experience both an income effect and a substitution effect. The substitution effect will push the person in the direction of more work, while the income effect will tend to counteract this. At low levels of work hours, however, the income effect tends to be relatively small, and so it is likely that the substitution effect will dominate the income effect and the person will work more.

31d A person originally to the left of point c will tend to reduce work hours. The extent of the reduction depends on whether the person originally worked more or less than 2,000 hours. If the person worked more than 1,500 hours but less than 2,000 hours, he will experience just a pure income effect. If the person worked in excess of 2,000 hours, he will experience reinforcing income and substitution effects. Note for H > 2,000, the position of the constraint moves out at the same time that it becomes flatter. This creates a strong incentive to work less, and many workers are likely to end up near point f. *32a See Figure 6-14.

Figure 6-14.

*32b The 40 percent marginal tax rate applies after $1,000 in total income is reached With nonlabor income of $200, that income level is reached when L = 200 (H = 200) This is point a in Figure 6-14 The tax reduces total income by 20 percent to a total of $800 (point b) The effective wage rate (the slope of the constraint) is now (1-t)W, where t is the marginal tax rate To the right of point b, the slope is (1-.2)4 = 3.2 To the left of point b, the slope is (1-.4)4 = 2.4. *32c Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is L* =

 WT + V .  + W

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Answers to Chapter 6

Substituting the appropriate values leads to an optimum of L = 225 (H = 175), Y = $900 (point c) before the tax After the tax, the level of nonlabor income falls to $160 and the effective wage rate is 3.2 Substituting into the L* expression again yields L = 225 (H = 175), but Y is now lower at $720 There is no change in labor supply since the income and substitution effects of the tax change have exactly canceled one another This combination is point d The person has paid $180 in taxes, making for an average tax rate of $180/$900 = 20 percent. *32d What is the value of Y on the after-tax constraint when H = 400 H = 400 implies Y = $1800 When total income is $1800, the person pays $200 on the first $1,000 he earned, plus $320 on the next $800, for a total after tax income of $1,280 If WT + V = $1,280, and W is $2.4 and T is 400, the implicit value of V is $320. *32e Making the appropriate substitutions into the L* expression yields L =112.5 (H = 287.5), Y = $1,350 before the tax program (point e) After the tax program, substitute W = $2.4 and V = $320 into the L* expression to find L = 133.33, (H = 266.67), Y = $960 (point f) Hours of work are reduced modestly because of the stronger substitution effect of the higher marginal tax rate The total tax paid is 20 percent of $1,000 plus 40 percent of $350, for a total of $340 Note that this is not the difference between $1,350 and $960, since the $960 reflects the lower level of work hours that the tax induced The average tax rate is $340/$1,350 = 25.19 percent. *32f Significantly higher marginal tax rates can result in appreciable reductions in the work hours of higher-income individuals.

33a Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is L* =

 WT + V .  + W

With both fixed monetary and time costs of working it is as if V is only $100 and T is 370 hours This leads to an optimum at L = 197.5 (H = 172.5) and Y = $790 This yields a utility level of 156,025 This does exceed the utility associated with not participating in the labor force since the combination L = 400,Y = $200 yields a utility level of 80,000.

33b Telecommuting would return V to $200 and T to 400, leading to an optimum at L = 225 (H = 175) and Y = $900 Utility would now be 202,500 In this example, telecommuting leads to higher levels of leisure, work, income, and utility.

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ANSWERS TO CHAPTER 7 Review Questions 1. Answer d. In the household production model, income is assumed to be spent on market purchased goods and services. Time spent in home production yields commodities that the individual or family consumes, and leisure is also a consumption good. Thus three types of goods enter the utility function, market goods, household goods, and leisure.

2. Answer a. Each indifference curve represents a tradeoff between income (market goods) and household production time (time spent producing household goods or consuming leisure).

3. Answer a. The magnitude of the slope is given by the wage rate, and the height of the constraint at the maximum amount of time available equals the level of nonlabor income.

4. Answer c. The income effect of the wage increase creates an incentive to spend more time in household production (and leisure consumption), while the substitution effect creates an incentive to spend less time in household production activities.

5. Answer d. An increase in the wage increases the opportunity cost of both household production and leisure time, creating an incentive to reduce both. On the other hand, for any given amount of work (except zero hours) an increase in the wage leads to an increase in income. This allows an individual to buy more of all goods, including leisure and any commodities produced at home. The greater the demand for household produced commodities, the greater the incentive to spend time in home production.

6. Answer c. If a were true, household production time would have decreased. If b were true, leisure time would have decreased.

7. Answer d. In addition, for women’s total market work hours to have increased, the net effect on market work hours resulting from a must have been strong enough to overcome the net effect on work hours resulting from b.

8. Answer a. When time and goods are easily substitutable, the substitution effect of a wage change tends to be large. When time and goods are used complementarily or in fixed proportions, the substitution effect of a wage change tends to be small.

9. Answer c. A household’s total production will be maximized when the spouse with the lowest net gain from market work stays home. For example, suppose spouse A can earn $12 per hour in the market and produce the equivalent of $6 per hour at home, while spouse B can earn $15 per hour in the market and produce the equivalent of $10 per hour at home. Even though spouse B can earn more in the market, the net gain to the household of having B work is only $5, while the net gain to having A work is $6. For 343

Answers to Chapter 7

every hour A works and B stays at home, the household produces the equivalent of $22, while having B work and A stay at home would result in only $21.

10. Answer d. This condition assures that the household will attain at least the same level of utility as before the extra hour of work.

11. Answer c. If the wife’s increase in work hours increases the husband’s marginal productivity at home, the net gain to the husband from working will decrease and the incentive to substitute household production for market work will increase.

12. Answer d. If the husband’s marginal productivity at home does not decrease because of the health problem, the drop in the wage will make him relatively more productive at home, increasing his incentive to work at home. If the husband’s time at home is a substitute for the wife’s, this would decrease her marginal productivity at home and increase the net gain associated with her market work.

13. Answer d. The expected wage E(W) is given by the equation E(W) = W where  is the probability of finding a job and W is the wage of the job. During a recession p falls, reducing the expected wage of the unemployed person. The change in the expected wage lowers the expected gain from job search. This lowers the opportunity cost of time at home and creates a substitution effect that can cause the person to stop allocating any time to job search activities.

14. Answer d. The reduction in the effective wage and the increase in family income creates reinforcing income and substitution effects that will cause more total time to be allocated to household production. However, it is at least possible that with more total time devoted to household production, the husband’s household marginal productivity may increase so much that the wife’s net gain from market work may exceed his. This would create a situation where she would be the one to work for pay, provided the family continues to have an incentive to supply hours to the market.

15. Answer b. Although the other factors would also tend to increase the labor force participation rates of married women, those factors have been changing rather steadily, and hence could not explain the large increase observed after age 30.

16. Answer c. If the path of wages is anticipated, workers can form an estimate of lifetime wealth. Then, as anticipated wage changes occur, there will be no change in the estimate of lifetime wealth and no income effect will be experienced. Higher wages do, however, change the opportunity cost of leisure, resulting in a substitution effect in favor of more hours of work.

17. Answer d. If lifetime benefits remained constant as the retirement age increased, remaining lifetime earnings would rise at a constant rate as the retirement age increased.

In terms of Figure 7-1 from the Summary section, the budget constraint connecting points a through f would now be a straight line rather than a concave curve. Although point a would remain the same, the rest of the curve would rotate outward slightly and 344

Answers to Chapter 7

straighten as the vertical intercept rose from $195,000 to $220,000. This would create opposing income and substitution effects. The retirement age would decrease only if the increase in the demand for leisure resulting from the change in the position of the constraint (the income effect) dominated the increased incentive to work coming from the higher effective wage rate (the substitution effect).

Problems 18a. Notice that the isoquant for family 2 is drawn with less convexity than the one for family 1. This means that for family 2, household goods and market goods are traded off at roughly a constant rate. This means that family 2 sees household goods and purchased goods as easily substitutable. On the other hand, the isoquant for family 1 is relatively convex. This means that family 1 sees household goods and purchased goods as not as easily substitutable.

18b. See Figure 7-5. The substitution effect can be observed by allowing the budget constraint to rotate outward in response to the higher wage, and then pulling it back so the family just attains its old level of utility. The movement along the original indifference curve will reflect the family’s response to just the change in the opportunity cost of time, and therefore can be interpreted as the substitution effect of the wage change.

Figure 7-5.

In Figure 7-5, the substitution effect for family 1 is the movement from point c to point e, while the substitution effect for family 2 is the movement from point c to point d. Since family 2 sees time and goods as more substitutable, it is not surprising that the change in the opportunity cost of household time resulted in a larger decrease in household hours.

19a. H = 4  N =12 and Y = ($10)(4) = $40. N = 12 and Y = 40  U = 480.

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19b. Y rises to $80 for an increase of $40.

19c. With H increasing to 8 hours, N falls to 8 hours. To keep U at 480, Y would have to rise to $60. This represents an increase in income of $20.

19d. Since income would only have to rise by $20 to compensate for the decrease in household hours, the increase of $40 that actually takes place will make the family better off.

19e. Under the new ranking formula, the original combination of N = 12 and Y = $40 yields a utility level of (122)(40) or 5760. When H rises to 8 and N falls to 8, Y must rise to $90 to keep U at 5760. This represents an increase of $50. Since the increased work hours only bring in $40, this move would make the family worse off. Given the presence of the child, the extra hour of work makes the family worse off.

19f. If H equals 8, then N equals 8 and Y equals $80. This means that the original level of utility is now 640. If H increases to 9, N decreases to 7 and Y increases to $90. Under this utility function, this combination receives a lower ranking of 630.

19g. Under the new ranking formula, the original combination of N = 8 and Y = $80 yields a utility level of (8)(802) or 51,200. When H rises to 9 and N falls to 7, Y rises to $90, and the new ranking rises to 56,208. Given the new technology, the extra hour of work makes the family better off.

20a. A household’s total production will be maximized when the spouse with the highest net gain from market work is the one that works for pay. Even though the wife is more productive at home than the husband, the net gain to the household of having the wife work is $5, while the net gain to having the husband work is $3. For every hour the wife works and the husband stays at home, the household produces the equivalent of $32, while having the husband work and the wife stay at home would result in only $27.

20b. Yes, since an extra hour of market work allows each to buy at least enough goods and services to compensate for the hour of lost production time at home.

20c. An increase in the wife’s wage would decrease her work hours if the income effect of the wage increase dominated the substitution effect. On the other hand, work hours would increase if the substitution effect of the wage increase dominated the income effect.

Empirical studies suggest that the latter is the more common occurrence for women. The income effect associated with the wife’s wage increase reduces the husband’s incentive to work for pay provided there are no cross effects on the husband’s household marginal productivity or the marginal utility that the husband derives from household consumption.

20d. If the husband and wife are substitutes in household production, an increase in the wife’s work hours will increase her household marginal productivity, creating an incentive for the husband to spend more time in household production and less time in market work.

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Answers to Chapter 7

20e. If the husband and wife are complements in the consumption of household commodities, an increase in the wife’s work hours will decrease the utility the husband derives from the additional consumption of household commodities and create an incentive to spend more time in market work.

21a. H = 7  N = 9 and Y = ($5)(7) + $10 = $45. N = 9 and Y = $45  U = 405.

21b. H = 0  N = 16 and Y = $10. N = 16 and Y = $10  U = 160. *21c. The return to taking an hour away from household production activities to look for work is the expected wage E(W) = W where  is the probability of finding a job. *21d. One hour of job search yields an expected payoff of (0.5)($5) = $2.50, which raises the expected income to Y = $2.50 + $10 = $12.50. The level of utility associated with N = 15, and an expected value of Y = $15 is (15)(15) = 225. When compared to the utility associated with not looking for a job (U = 160), one hour of job search is a good move.

When a person is unemployed but looking for a job, he is a member of the labor force. *21e. One hour of job search now yields an expected payoff of (0.1)($5) = $0.5, which raises the expected income to Y = $0.50 + $10 = $10.50. The level of utility associated with N = 15, and an expected value of Y = $10.50 is (15)(10.50) = 157.5. When compared to the utility associated with not looking for a job (U = 160), one hour of job search is not a good move. When a person drops out of the labor force because of the reduced probability of finding a job, she is categorized as a discouraged worker. *21f. One hour of job search yields an expected payoff of (1/3)($2) = $0.667, which raises the expected family income to Y = $0.667 + $10 = $10.667. The level of utility associated with N = 15, and an expected value of Y = $10.667 is (15)(10.667) = 160.

Since the utility associated with not looking for a job (U = 160) is the same, the person will be completely indifferent about looking for a job.

Applications 22a. See Figure 7-6. The substitution effect can be observed by allowing the budget constraint to rotate outward in response to the higher wage (line ad), and then pulling it back (line ef) so the individual just attains his or her old level of utility. The resulting movement along the original indifference curve will reflect the individual’s response to just the change in the opportunity cost of time, and therefore can be interpreted as the substitution effect of the wage change. In Figure 7-6, there is no response to the change in slope since the optimum remains at point c. The substitution effect is zero.

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Answers to Chapter 7

Figure 7-6.

22b. See Figure 7-7.

The substitution effect can be observed by allowing the budget constraint to rotate outward in response to the higher wage (line ac), and then pulling it back (line de) so the individual just attains his or her old level of utility. The resulting movement along the original indifference curve will reflect the individual’s response to just the change in the opportunity cost of time, and therefore can be interpreted as the substitution effect of the wage change. In Figure 7-7, the individual moves from point a to point e in response to the change in slope. The substitution effect is a reduction in household work of the full 400 hours available.

Figure 7-7.

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22c. Figure 7-3 is a better model of the choice between market work and leisure because the tradeoff between income (purchased goods) and leisure that underlies the choice is inherently one where the substitution possibilities are limited. Purchased goods and leisure are usually utilized in a complementary manner.

22d. Figure 7-4 is a better model of the choice between market work and household production time because the tradeoff between purchased goods and household production time that underlies the choice is one where goods and services can be readily substituted for household time.

22e. If purchased goods and household production time are highly substitutable, Figure 7-7 shows that wage increases can be associated with very large substitution effects that lead to household production time being reduced dramatically in favor of market work.

Since women have traditionally been responsible for most household production activities, it seems likely that as their wages have increased over time, they may have experienced these rather large substitution effects that could easily dominate any income effect associated with the wage increase. For men, who have traditionally been primarily consumers of household production, the wage increases would create primarily an income effect that would lead them to consume, and perhaps help supply, more household production.

At the same time, Figure 7-6 shows that wage increases may be associated with very small substitution effects from the point of view of the labor/leisure choice. For this choice, the income effect will almost surely dominate the substitution effect leading to more leisure and less market work. This should probably be true for both men and women. However, since the increase in market work that comes from the substitution away from household production will be so large for women, it could easily overcome the tendency towards less market work that comes out of the choice between market work and leisure. Given this strong tendency to reduce household work, it seems very clear that women could increase their leisure time and at the same time still increase their market work substantially. For men, however, the income effect appears likely to dominate the substitution effect in the context of both choices, thereby leading to more leisure and household production, and less market work.

23a. The curve is concave because lifetime Social Security benefits do not remain constant as the retirement age increases. Yearly benefits increase with retirement age, but not enough to overcome the reduced number of years over which the benefits will be received, so that older retirees are penalized with lower lifetime benefit levels.

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Answers to Chapter 7

For the points a through f in Figure 7-1 to lie along a straight line, yearly Social Security benefits would have to be set at the levels listed in Table 7-3.

Table 7-3.

Retirement age

Yearly social security

Lifetime social security

Lifetime earnings

Total lifetime income

65 66 67 68 69 70

8 8.57 9.23 10 10.91 12

120 120 120 120 120 120

0 20 40 60 80 100

120 140 160 180 200 220

Plotting the retirement age against the total remaining lifetime income figures in the last column of the table would then yield a straight line. Point a would retain its current position and the vertical intercept (point f) would increase to $220,000.

23b. The rotation of the constraint described in the answer to 23a would create opposing income and substitution effects. The retirement age would decrease only if the increase in the demand for leisure resulting from the change in the position of the constraint (the income effect) dominated the increased incentive to work coming from the higher effective wage rate (the substitution effect). Using the same ranking formula as in the Example, Table 7-4 was constructed.

Table 7-4.

Retirement age

Leisure years (L)

Lifetime income (Y)

Utility ranking (U = LY)

65 66 67 68 69 70

15 14 13 12 11 10

120 140 160 180 200 220

1,800 1,960 2,080 2,160 2,200 2,200

Table 7-4 shows that the optimal retirement age increases to 69 (or 70), indicating that the substitution effect of the change dominated the income effect. (If it were possible to retire at half-year increments, the optimal retirement age would be 69.5 since 11.5 remaining years and a remaining income of $210,000 would yield a ranking of 2,415.)

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Answers to Chapter 7

24a. See the line adefb in Figure 7-8. The person receives no benefits when he or she works 1,610 hours (1,390 hours allocated to household production) and earns a total of $32,200 (point f).

Figure 7-8.

24b. See the line adegb in Figure 7-8. The person receives no benefits when he or she works 2,160 hours (840 hours allocated to household production) and earns a total of $43,200 (point g).

24c. For a person working 1,000 hours (point h) the reduction in the implicit tax rate would create counteracting income and substitution effects. The person would receive a higher benefit, creating an income effect which would reduce the incentive to work.

However, the effective wage would also rise, creating a substitution effect which would increase the incentive to work. For a person working 1,800 hours (point i), the reduction in the implicit tax rate would make the person eligible to receive benefits. This in turn would create reinforcing income and substitution effects. The person would receive a higher benefit, creating an income effect which would reduce the incentive to work. In addition, the effective wage would also be reduced, creating a substitution effect which would further decrease the incentive to work.

24d. Reducing the rate at which benefits are scaled back increases the amount of benefits paid out and so most likely would require increased payroll taxes on all those working.

For a worker like the one at point h, the increase in taxes should roughly offset the increase in benefits so that lifetime wealth will remain unchanged. The payroll tax, however, decreases the effective wage during the working years, while the reduction in the implicit tax rate increases the wage after retirement. With expected lifetime wealth constant, this should lead the person to reduce market work during their younger years and increase market work after retirement.

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ANSWERS TO CHAPTER 8 Review Questions 1. Answer a. Worker utility is a function of both the pecuniary and nonpecuniary aspects of the job. However, with the nonpecuniary characteristics held constant, the level of utility will be determined by the level of monetary compensation.

2. Answer c. The whole point of a compensating wage differential is to make sure that even firms with undesirable working conditions can obtain workers. It will also be true that workers who are indifferent about the adverse conditions will work for the higher paying firm, but this will occur even before the equilibrium compensating differential is reached. Compensating differentials do not represent so much an incentive to improve conditions as they do a way firms can avoid making improvements in their working conditions.

3. Answer b. The compensating differential framework assumes that people choose the wage/risk combinations that best suit their preferences. This results in those doing dangerous work being better paid than those in comparable jobs working under safer conditions. While those that choose dangerous jobs will generally be less averse to risk, the model in no way assumes that danger is a good. Also, the model explicitly assumes that people do have other employment opportunities.

4. Answer b. A compensating differential represents the payment needed to attract the borderline or marginal worker. There will always be some workers who would work under the adverse conditions for less than the equilibrium differential, and some workers who probably could never be induced to work under the adverse conditions.

5. Answer d. It is important to realize that the theory only predicts higher wages will be associated with less desirable conditions if all the other things that influence wages are held constant. In answer c, wages are the same even though some workers are experiencing more desirable conditions. This does not contradict the theory, however, since these workers are more highly skilled. They normally would be paid more than their less skilled counterparts. All that is important is that here the more desirable conditions still exert a dampening effect on wages.

6. Answer a. The theory assumes workers try to maximize their utility, not their level of compensation.

7. Answer c. Indifference curves are typically drawn downward sloping since a “good” appears on each axis. In this case, however, a “bad” (risk of injury) appears on the horizontal axis. While b may be true, it does not impact the shape of the indifference curves, which only reflect worker preferences.

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8. Answer d. The slope of the indifference curve indicates the willingness of the person to give up wages for a given reduction in risk. As one moves up a given indifference curve, the slope increases and so the willingness to pay for a given risk reduction increases.

9. Answer a. Isoprofit curves represent all the wage/risk combinations that yield a certain profit level. Since making the workplace safer is costly, the firm stays at the same profit level only if it reduces the wage.

10. Answer d. The slope of the isoprofit curve indicates the rate at which a firm must reduce wages for a given reduction in risk. As one moves up a given isoprofit curve, the slope decreases and so the rate at which the firm must reduce wages for a given risk reduction is lower. If the firm can reduce wages at a lower rate for a given risk reduction, that risk reduction must be less costly.

11. Answer b. Since the isoprofit curves shown in Figure 8-3 are assumed to be wage/risk combinations associated with zero economic profits, the offer curve also represents actual wage/risk offers consistent with zero economic profits, not positive economic profits.

12. Answer d. In the hedonic theory of wages, workers like B that experience undesirable conditions do so voluntarily as part of a mutually beneficial arrangement between themselves and firm Y. 13. Answer d. By forcing risk exposure down to 4 deaths per 10,000 workers, person B will be forced to a lower indifference curve. The reduction can be minimized by switching to employer X (i.e., moving to point a), but this will still represent a lower level of utility for B. 14. Answer c. When imperfect information exists, Figure 8-3 may no longer be an accurate depiction of the matching process between employers and employees. Such imperfect information often leads to a window of opportunity for regulation to make workers better off provided the worker’s willingness to pay for a certain risk reduction does not exceed the cost. If it does, the person will actually end up on a lower indifference curve because of the mandated risk reduction.

15. Answer d. Estimates of the benefits of a regulation typically focus on the current willingness to pay values of those directly affected by the regulation. This is a fairly narrow perspective that is often criticized for the reasons listed in responses a through c.

16. Answer a. As income tax rates increase, the benefits of receiving compensation in the form of wages decreases, and so the willingness to give up wages for a given increase in employee benefits should increase. This increased willingness to pay shows up as an increase in the slope of the indifference curve.

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17. Answer b. Answer a would be true if it stated that taxes and insurance contributions were based on a percentage of the firm’s cash payroll. Answer c is a true statement but does not relate to the slope of the firm’s isoprofit curve.

18. Answer b. The hedonic wage theory of employee benefits is based on the same assumptions as the hedonic wage theory relating to risk of fatal injury. Workers (not firms) are assumed to have complete information and are assumed to be mobile enough to have access to various employment opportunities. Although workers being free to determine their own mix of wages and benefits would make it easier for workers to achieve their optimal mix, it is typically the firms that set the compensation mix.

Workers must then match themselves with the firms that best satisfy their preferences.

19. Answer d. When workers have steeper indifference curves, the optimal compensation mix will include a higher proportion of employee benefits. Workers have steeper indifference curves, in turn, when they are willing to give up a significant amount in wages for a given increase in benefits. This willingness is usually displayed by older workers with higher incomes, since the tax advantages associated with receiving compensation in the form of benefits are likely to be more substantial. Younger workers are typically more in need of discretionary income to facilitate the purchase of things like homes and automobiles.

20. Answer d. The mandated provision of benefits, like mandatory risk reduction, only increases worker well being if worker willingness to pay for the benefit exceeds the cost to the firms of providing it.

21. Answer a. The unconstrained choice of 200 leisure hours may involve a job with a layoff since layoffs are one way for a worker to obtain more leisure time. Two hundred work hours may constitute a part-time or full-time job depending on the time period being considered and the work hours that are customary for that occupation. Since the choice is unconstrained, however, any layoff implicit in this level of hours will not be considered an undesirable characteristic and so need not be accompanied by a compensating differential.

22. Answer a. To attain an income of $500 when only working 80 hours requires a wage of $500/80 or $6.25. Since the original wage was $4, the new wage reflects a compensating differential of $2.25.

23. Answer d. The vertical intercept of the budget line represents the level of income attained if the person works the maximum number of hours. (This is often called the level of full income.) If the wage is $6.25 and the maximum number of work hours is 400, the maximum level of income is ($6.25)(400) or $2,500.

24. Answer a. The person experiences a utility level of 10 half of the time, and a utility level of 30 the other half of the time, so the average level of utility is 20.

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25. Answer d. A job that involves 250 hours all of the time will yield a utility level between 20 and 25 all of the time, which means that the average level of utility will exceed the average level associated with the uncertain schedule. This preference for the certain situation is called risk aversion. The only way the uncertain schedule could yield the same average level of utility would be if the wage associated with this job was higher.

Problems 26a. The lack of alternative offers means that person A ends up on the indifference curve A1 that goes through point a instead of being able to reach a higher indifference curve.

Given the shape of A’s indifference curve, it appears A’s maximum utility would be attained near point c. To reach point c, however, A would have to be able to move and work for employer X. 26b. Such a regulation would make the immobile person A better off by allowing A to attain the level of utility associated with point b.

26c. The regulation would make person B worse off by forcing B to point c, a point associated with a lower indifference curve. The regulation, however, would be even worse if B was constrained to work for employer Y since that would require a movement to point b.

27a. The optimal level of risk is that level associated with point c (4 deaths per 10,000 workers). The wage rate, however, would fall from somewhere between $10 and $11 to $8.

27b. The lowest level of risk is that associated with point d (approximately 1.6 deaths per 10,000 workers).

27c. No, person A would not be in favor of such a regulation since A perceives that he or she is on indifference curve A3. In this case, however, movement to point e does also lead to a lower actual level of utility.

27d. Under perfect information and mobility, person A should choose point c where the wage is $8 and the risk of fatal injury is 4 deaths per 10,000 workers.

27e. No, regulation to any risk level lower than 4 deaths per 10,000 workers would make a fully informed and mobile worker worse off.

28a. Person A would be willing to see the wage reduced from $8 to just under $6 (from point a to point c).

28b. The cost of reducing risk can be seen in the wage reductions necessary to keep the firms competitive. In this case, the wage must fall from $8 to $4 (from point a to point b) for a cost per hour of $4.

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Answers to Chapter 8

28c. No, since the cost ($4) exceeds the worker’s willingness to pay (slightly over $2), the regulation fails a benefit/cost test. When this happens, note that the worker will be forced to a lower indifference curve.

28d. The slope of the dashed line is -1. At point a, the tradeoff between wage and risk is such that every one unit reduction in risk must be accompanied by a one dollar reduction in the wage.

28e. Based on the rate of change at point a, one would predict that person A would be willing to give up $3 in wages for a reduction in risk from 4 deaths per 10,000 to 1.

28f. The extrapolation overstates A’s willingness to pay for risk reductions. This occurs because the extrapolation ignores the convexity of A’s indifference curves. This convexity reflects a decreasing willingness to pay for risk reductions as the workplace becomes safer. This means that benefit/cost studies of risk reductions may be slightly biased in favor of finding that the benefits exceed the costs.

29a. Such a weighting occurs when the spending flexibility that wage income provides is more important than the tax advantages of receiving compensation in the form of employee benefits.

29b. Originally E = $40 and W = $60  U = (40)(60)2 = 144,000.

29c. To keep utility constant as E rises by $20 to $60, the wage can fall to W=

144,000 60

= $48.99.

This means the person is willing to give up $11.01 in wages for the $20 increase in benefits. However, since every $1 increase in benefits costs the firm 75 cents, a $20 increase in benefits costs the firm $15. Since the willingness to pay for the increased benefits is lower than the cost, the change in the compensation mix would make the worker worse off.

29d. Originally E = $40 and W = $60  U = (40)(60) = 2,400.

To keep utility constant as E rises by $20 to $60, the wage can fall to 2,400 W = 60

= $40.

This means the person is willing to give up $20 in wages for the $20 increase in benefits.

However, since every $1 increase in benefits costs the firm 75 cents, a $20 increase in benefits costs the firm $15. Since the willingness to pay for the increased benefits is

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greater than the cost, the change in the compensation mix would make the worker better off.

30a. Originally L = 200 and Y = $400  U = (200)2(400) = 16,000,000.

See the indifference curve labeled U1 in Figure 8-10. The original budget line is the line ab and the original optimum is point c.

Figure 8-10.

30b. To find the income level needed to keep utility constant, solve the equation (250)2(Y) = 16,000,000  Y = $256.

See point e in Figure 8-10. At L = 250, however, the person only earns $200 (point d).

30c. If leisure increases to 250 hours, then work hours decrease to 50. To earn $256 when H is only 50, the wage must rise to 256 W = 50 = $5.12.

Since the original wage was $4, this new wage represents a compensating differential of $1.12. The budget line consistent with this new wage is line bf in Figure 8-10. *30d. If, at the original equilibrium, the person saw leisure and income as perfect complements, the original indifference curve would be represented by curve U1' in Figure 8-10. Therefore, to keep utility constant as leisure increases to 250, income would have to stay at $400 (point g). This would require a wage of $400/50 or $8. This means the compensating differential is now $4. This new wage is represented by the dashed budget line connecting points b and g in Figure 8-10.

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*30e. The change in preferences raised the compensating differential that is required.

With the new preferences, the extra leisure that is forced upon the worker has no value, whereas with normal downward-sloping indifference curves it does. So to keep utility constant, income (and hence the wage) must be higher in the perfect complement case. *31a. When work hours (H) = 5, then Y is $25 and U is 5. If U is always equal to 5, then the average level of utility is also 5. *31b. The average work hours is given by the equation 1 1 Average Hours = 2 (2) + 2 8 = 5. *31c. When H = 2, Y = $10. When H = 8, Y = $40. The average level of utility is given by the equation 1 1 Average U = 2 10 + 2 40 = 4.74. *31d. The worker will prefer job A, the job with the certain schedule since the average level of utility is higher. *31e. The compensating differential can be inferred from the wage that is necessary to make the average level of utility from job B equal the average level of utility from job A. This wage can be found by solving the equation 1 1 2W + 2 2 8W = 5  2.121 W = 5  W = $5.56.

Since the original wage was $5, the compensating differential for the less desirable schedule is 50 cents.

Applications 32a. The law would force the non-union worker (person A) away from the point a to point c. This point would be associated with a lower indifference curve.

32b. Person A will now try to move from point c to point b since b will be associated with a higher level of utility. The problem is that all the B workers will still be at point b as well. With all the workers preferring firm U, the firm will be able to be more selective in its personnel decisions and so will end up with the most skilled and productive workers among this general class of workers.

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Answers to Chapter 8

32c. Although the wage will be the same for all workers, the more skilled and productive workers at firm U will also be enjoying better working conditions than those workers at firm NU. This situation is consistent with theory of compensating differentials. More productive workers typically will be paid more, so here the better working conditions are still exerting a dampening effect on the wage.

32d. The argument about the effects of the minimum wage is identical to that observed in this problem. A higher minimum wage should cause firms to move up along their isoprofit curve, offsetting the increased wage costs with reductions in costs obtained by increasing the pace of work and decreasing other desirable conditions and benefits such as job training. Among all the firms paying the minimum wage, workers will seek out those with the best conditions. Those firms can then be more selective in their personnel decisions. The result will be that the least skilled workers will end up working at the minimum wage firms offering the least desirable working conditions. *33a. In Table 8-1, UA and UB represent the levels of utility attained by persons A and B under each of the 4 possible scenarios. The utilities were computed as follows.

Safe for A/Safe for B  UA = 200 + 200 + 0 = 400, UB = 200 + 200 + 0 = 400.

Unsafe for A/Safe for B  UA = 300 + 0 + 200 = 500, UB = 200 + 200 - 250 = 150.

Safe for A/Unsafe for B  UA = 200 + 200 - 250 = 150, UB = 300 + 0 + 200 = 500.

Unsafe for A/Unsafe for B  UA = 300 + 0 + 0 = 300, UB = 300 + 0 + 0 =300.

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Answers to Chapter 8

Table 8-1.

Person B Person A \ Safe conditions Unsafe conditions

Safe conditions

Unsafe conditions

UA = 400 UB = 400 UA = 500 UB = 150

UA = 150 UB = 500 UA = 300 UB = 300

*33b. Regardless of person B’s choice, person A always does better by choosing the unsafe conditions. Similarly, regardless of A’s choice, person B always does better by choosing the unsafe conditions. *33c. Forcing the workers to the safe conditions makes each worker better off. *33d. Norms and standards play an important role in shaping our behavior and influencing our level of satisfaction. While a fifty degree day seems delightful if it occurs in January, that same temperature seems uncomfortably cold in July. It is not so much the absolute temperature that is important but what we are accustomed to. In much the same way, material satisfaction depends on the amount of goods one has relative to the amount needed or desired. These needs and desires in turn are largely determined by the way in which one observes other members of the society living. As the obligations and expectations of individuals change, the goods they consume change and people's perceptions of what they need change. For example, the average family in the United States today does not consider itself wealthy even though they live in a way only the wealthy did 200 years ago. Our consumption standards are not those of the colonial days but those of a much more complex society. In addition it is important to recognize that concern about relative standing may be instrumental in helping to achieve certain absolute goals. In general, any winner-take-all competition or auction system makes it imperative for people to be concerned about relative standing. When viewed in this way, it seems clear that concern about relative income can be something perfectly consistent with the assumption of rational consumers.

34a. The premise of the proposed change is essentially the theory of compensating differentials presented in this chapter. Regulations to reduce risk force costly adjustments upon firms, and the result is lower wages. When individual’s earn lower incomes, their spending on health care may be reduced, leading to more illness and earlier deaths. While it may sound insensitive to refer to a tradeoff between wages and risk, the fact is that safety can not be achieved without cost. This forces workers to balance the desire for more safety against their desire for more income.

34b. Benefit computations often do not take into account the benefits from increased safety that would accrue to people not directly affected by the regulation, including those

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Answers to Chapter 8

workers who will be employed in helping to make the workplace safer. Also, the computations typically take worker willingness to pay for increased safety as a given.

This ignores the convexity of indifference curves as well as changes in preferences and attitudes such regulations can bring about over time. Also, one could argue that regulations leading to increased health and safety will help to raise productivity and income since healthier and safer workers may work harder and have better morale.

35a. Increased administrative costs should rotate the isoprofit curve for the firm inward.

For example, in Figure 8-11, the firm initially is willing to tradeoff $500 in wages for $750 in benefits (line ab). However, if the benefits become more costly to administer, the firm may be willing to tradeoff $500 in wages for only $500 in benefits (line ad).

Figure 8-11.

35b. An increase in administrative costs should lead to a reduction in employee benefits.

In Figure 8-11 the level of benefits falls from $300 to $200 (point c to point e).

36a. Taxing health care benefits should lead to a flattening of the indifference curves in the hedonic wage model as the willingness to give up wages for additional dollars of benefits should decrease. This is shown in Figure 8-12 as a change in the shape of the indifference curves from U1 to U1'.

36b. Allowing firms to deduct only part of their health care expenses would increase the cost of providing benefits relative to the cost of providing wages. This should lead to steeper isoprofit curves for firms. For example, in Figure 8-12, the isoprofit curve is shown rotating from line ab to line ad. Previously, the firm could tradeoff, say, $500 in wages for $750 in benefits. With the change in policy, however, the firm may be able to tradeoff $500 in wages for only $500 in benefits.

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Answers to Chapter 8

Figure 8-12.

36c. Taken by itself, the flattening of the indifference curve should lead to more wages and fewer benefits. The steepening of the isoprofit curve should lead to fewer benefits (and perhaps more wages). Taken together, the prediction would be for fewer benefits and more wages. This is illustrated in Figure 8-12 as a movement from point c to point e.

In this movement, benefits decrease from $300 to $100 and wages increase from $300 to $400.

37a. Firms make changes such as these so that they can attract the type of workers they feel will be best for the firm. In this case, offering more work at home and family leave policies means that the firm is strategically trying to attract older workers with families.

Perhaps they feel these workers will be more reliable, dependable, and productive, and that they will stay with the firm for longer periods.

37b. While such compensation packages will be attractive to many workers, the provision of such benefits will be costly and will cause the firm to reduce wages below what they would otherwise be. Mandating such a move for all workers would make workers who preferred to take more of their compensation in the form of wages worse off.

38a. This unemployment insurance payment will allow the worker to attain point e (L = 250, Y = $256) in Figure 8-10. No compensating differential will be required.

38b. By not having to pay the compensating differential of $1.12 on the 50 hours the person works, the firm saves $56. However, since the firm has paid only $30 into the fund, the unemployment insurance program effectively subsidizes this firm by $26.

Firms subsidized in this way will tend to thrive and grow, and so the program is promoting the growth of firms that rely on temporary layoffs.

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ANSWERS TO CHAPTER 9 Review Questions 1. Answer d. Other benefits include a more stable employment situation, more interesting and challenging work, and access to occupations with more prestige and more desirable working conditions.

2. Answer d. The costs associated with education include direct expenses, foregone, earnings, and psychic losses.

3. Answer d. While discounting will also adjust for differences in purchasing power if the discount rate includes a premium for expected inflation, it is also possible to adjust for inflation using a price index for different years. Even if all the benefits are expressed in real terms, it would still be necessary to discount future benefits.

4. Answer a.

$1,000 = $558.39.

(1 + 0.06)10 5. Answer a. Substituting B = $10,000, r = 0.06, and T = 40 into the annuity formula yields 1 1− (1 + 0.06) 40 PVB = $10,000  PVB = $150,462.97 0.06 6. Answer b. Setting the present value of the benefits equal to the costs



$2,500 2,500 = $2,000  (1 + r ) 2 = 2 (1 + r ) 2,000

 1 + r = 1.25  r = 0.118  r = 11.8%.

7. Answer c. An increase in the retirement age effectively increases T, the length of time over which the benefits to education can accrue, raising the present value of the benefit stream. On the other hand, an increase in r would lower the present value of the benefit stream. The higher wages and decreased aptitude associated with high school graduates will tend to raise the costs of additional educational investments by increasing the forgone earnings and raising the psychic costs of education.

8. Answer b. Even if the value of B was falling for most individuals, an increase in T could more than compensate, thus raising the present value of the benefit stream.

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Answers to Chapter 9

9. Answer a. The net gain from education is greatest at 12 years. The net gain, represented by the distance between points a and b, equals $1,000,000 and is greater than that attained at any other education level. For example, at 14.5 years, the net gain is zero, while at 16 years the net gain is only $200,000 (the distance between points e and d). At 20 years of education, the costs actually exceed the benefits.

10. Answer c. At 16 years, the net gain is $1,600,000 (the difference between points e and c), while at 12 years the net gain is only $1,000,000. At 14.5 the net gain is something less than $1,000,000 because additional costs have been incurred, but no additional benefits. Likewise, at 20 years, there are additional costs but no added benefits, leaving net benefits less than $1,600,000.

11. Answer c. Since only the higher-productivity individuals (the type B individuals) will have an incentive to attain 16 years of education, this level of achievement will be an effective way to distinguish between types of workers. The reason the low-roductivity individuals voluntarily choose the lower education level is because of the higher costs they face for attaining a given level of education.

12. Answer b. The socially optimal level of education to use as a screening device would be that level just slightly past point f (14.5 years). This is the lowest threshold that firms could set and still have type A workers choose less than the threshold amount and type B workers above the threshold amount. In a world where education’s only value is as a signal, it does not make sense from the point of view of society as a whole to devote any resources to education beyond that level needed to maintain the signaling function.

13. Answer d. Answers b and c account for the steepening of the age-earnings profile, while answer a accounts for the flattening of the profile as age increases.

14. Answer b. Age-earnings profiles steepen when an individual receives more on-thejob training. On-the-job training, in turn, is more likely to be acquired by those for whom the costs of training are lower, holding all else constant. Those who have completed higher levels of schooling have shown that they can learn more quickly which implies that the cost of educational investments will be lower for these individuals.

15. Answer d. Steepening of the age-earnings profile is usually attributable to on-thejob training. Such training becomes a better investment for women as their worklives increase (T increases).

16. Answer b. The higher wages attained by those completing higher levels of education are, for the most part, the benefits to investing in human capital. However, these benefits must be weighed against the costs. For the investment to be worthwhile, not only must the internal rate of return be positive, but it must also exceed the person’s discount rate.

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Answers to Chapter 9

17. Answer c. High-bility people typically earn more than lower-bility people, holding all else constant. Since education and ability are positively correlated, measures of the rate of return to education that ignore ability may attribute all of the earnings gap to education itself, when in fact some of the difference is due to the higher ability of the more educated person.

18. Answer d. For those who actually made the investment, the return may be understated since they probably would have been a worse than average worker in the unskilled profession. On the other hand, for those who did not make the investment, the potential return is overstated since they may be a worse than average worker in jobs requiring greater skill.

19. Answer a. If a certain level of education already has signaling value, higher levels of education may actually destroy the signaling value of education. Answer b, far from being a sign of wasted resources, represents a situation where the level of education has reached it optimal social level. Answer c is a sign that the investment is acceptable since the investor will earn just a normal rate of return.

20. Answer b. The initial shortage is the difference between the quantity demanded off the new demand curve (28) and the quantity supplied (18).

For readers wishing to derive these answers more precisely, note that the equations underlying questions 20-24 are Demand 1: LD = 30 - W, Demand 2: LD = 40 - W, Supply: LS = 1.5W. 21. Answer b. With the quantity of labor supplied fixed at 18, the wage must rise to $22 to clear the market.

22. Answer d. When the labor supply plans of all workers have been realized, the surplus will be the difference between the quantity supplied and quantity demanded at the wage of $22.

23. Answer a. With the quantity of labor supplied now at 33, the wage must fall to $7 to clear the market.

24. Answer d. The magnitude of the slope of the demand curves (as it appears on the graph) is one, while the slope of the supply curve is two-thirds. If workers had rational expectations there would be no boom-and-bust cycle. If workers were adapting their expectations based on the past behavior of wages, the cycle would tend to diminish.

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Answers to Chapter 9

25. Answer b. Indifference curves represent the education and wage combinations that keep worker utility constant at a particular level, not what firms have to do to attract workers. In this case, since higher wages accompany higher levels of education, the implicit message is that higher levels of education are perceived by workers as a bad since they are costly. Therefore, in order to keep workers at the same level of utility the wage, a good, must rise. Note that with this kind of preference structure, workers prefer movements towards combinations that involve a higher wage and less education.

26. Answer d. An isoprofit curve is a constraint from the firm’s point of view. It represents what the firm is willing and able to pay workers with different levels of education, not what workers demand. If the firm perceives that workers with higher levels of education are more productive, either because education makes them more productive or because it identifies workers who are inherently more productive, it should be willing and able to pay them a higher wage and still stay at the zero (normal) profit level.

27. Answer d. The steeper the indifference curve, the more averse the person is to additional years of education. On the other hand, the steeper the isoprofit curve, the more the firm is willing to pay for additional years of education. The matching of person B with firm Z suggests that the person least averse to additional schooling is matched with the firm most willing to pay for additional education. Since each individual is free to choose from the combinations offered by both firms Y and Z, the implicit assumption must be that A and B are mobile enough to be able to accept either employment opportunity. Such a matching process also typically assumes that worker are accurately informed about the wage and education combinations offered by the different firms.

Problems 28. Substituting B = $3,000, r = 0.06, and T = 10 into the annuity formula yields a total present value of benefits equal to 1− PVB = $30,000

1 (1 + 0.06)10  PVB = $22,080.26 0.06

The total cost of the investment is the $2,000 for tuition and books plus $20,000 in lost earnings for a total cost of $22,000. The costs need not be discounted since they all occur in the current year (year 0). Since the present value of the benefits exceeds the present value of the costs, this is a good investment.

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Answers to Chapter 9

*29a. Setting the present value of the benefits equal to the present value of the cost yields





$2,000 $2,000 + = $3,500 1+ r (1 + r ) 2

2,000 + 2000 r + 2000 = 3,500 (1 + r ) 2

 4,000 + 2,000r = 3,500(1 + r)2  4,000 + 2,000r = 3,500(1 + 2r + r2)  3,500r2+ 5,000r - 500 = 0  35r2 + 50r - 5 = 0.

Applying the quadratic formula yields r=

−50  50 2 − ( 4)(35)( −5)  r = 0.0938 or 9.38%.

2(35)

29b. Since the internal rate of return exceeds the interest rate on alternative investments, the training program is a good investment for the worker.

29c. Any discount rate that is less than or equal to the internal rate of return would still make this a worthwhile investment. A person may have a higher discount rate than the market interest rate if he or she is very present-oriented. For example, a person may discount future benefits at a very high rate because of a fear that they may not live long enough to enjoy the benefits.

29d. Since older workers have a shorter time period over which to reap the benefits of the investment, the present value of the entire benefit stream will be lower, holding all else constant. Also, since older workers typically receive a higher wage than younger workers, the earnings that they forgo during training are higher, raising the cost of the investment. The tendency of on-the-job training to diminish with age leads to a flattening out of the age-earnings profile, thus contributing to its concave shape.

30a. Since the costs occur in the current period they are not discounted. The present value of the benefits equals

PVB =

$6,000 $2,000 + = $11,000.40.

1 + 0.06 (1 + 0.06) 2

Therefore, the present value of the benefits exceeds the present value of the costs by $1,000.40.

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Answers to Chapter 9

30b. Substituting r = 0.06 and p = 0.04 into the formula for the real interest rate (i) yields i=

0.06 − 0.04 = 0.01923 or 1.923% 1 + 0.04

30c. To convert nominal values to real values, divide the nominal value by the price index and multiply the result by 100. This yields Real cost in year 0 = 10,000, Real benefit in year 1 = 5,769.23, Real benefit in year 2 = 5,547.34.

30d. Since the costs occur in the current period they are not discounted. The present value of the real benefits equals

PVB =

5,769.23 5,547.34 + = 11,000.40.

101923 .

(101923 . )2

Therefore, the present value of the benefits exceeds the present value of the costs by 1,000.40 in real terms.

30e. Comparing the answers to 30a and 30d suggests that discounting nominal values by the market interest rate is the same as converting nominal values to real and then discounting by the real interest rate. Because the market interest rate adjusts to reflect anticipated inflation, it is not necessary to deflate future benefits by the anticipated price indices.

31a. For those who have actually made the educational investment, selection bias leads to an understatement of the true return, which suggests that the upper end of the range of estimates is more appropriate. On the other hand, for those who have not made the investment, selection bias tends to overstate the rate of return that is possible on educational investments.

This suggests that the lower end of the range of estimates would be more appropriate.

31b. Selection bias and ability bias are both examples of the omitted variable problem discussed in the appendix to Chapter 1. Selection bias is a problem that stems from a failure to account for the comparative advantage people have in different occupations.

For example, someone who successfully completes a college education probably has a set of interests and abilities that would not be well utilized in a work environment suitable for the typical high school graduate. That is presumably part of the reason the person chose to attend college in the first place. Therefore, simply comparing the average earnings of high school and college graduates understates the benefits to the person choosing to attend college. Such a simple comparison does not account for the fact that

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the person would probably have not been as successful as the typical high school graduate had he or she not attended college. If one could control for the different aptitudes and interests of each individual, there would be no selection bias. The problem is that these differences are very difficult to observe and measure and so in some studies their effects go unaccounted for. In the same way, ability bias is simply a failure to control for the differences in ability that occur between those achieving different levels of education. Since ability is difficult to define and measure, it often goes unaccounted for.

To do so, however, overstates the return to education provided individuals attaining higher levels of education also have more general ability. The increase in wages earned by the more educated and more able workers is all attributed to education if measures of ability are not also included in the analysis.

32a. For a type A person, the net benefit from 12 years of education is $1,000,000 (distance ab), while the net benefit from 16 years of education is $800,000 (distance ed).

The optimal level of education is 12 years.

32b. For a type B person, the net benefit from 12 years of education is $1,000,000 (distance ab), while the net benefit from 16 years of education is $1,200,000 (distance ec). The optimal level of education is 16 years.

32c. Since only type B workers have an incentive to acquire 16 years of education, that level of education could be used to distinguish high productivity workers from lowproductivity workers.

32d. Figure 9-10 shows the new wage schedules given the decrease in the hiring standard.

Figure 9-10.

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Note that type A individuals will now have an incentive to attain 14 years of education since the net gain of $1,400,000 (distance ed) exceeds the $1,000,000 return on 12 years of education (distance ab). Type B individuals will also have an incentive to attain 14 years of education since the net gain of $1,600,000 (distance ec) exceeds the $1,000,000 return on 12 years of education. Since both types of workers would have an incentive to acquire 14 years of education, that threshold would be an ineffective signal of worker productivity.

32e. Figure 9-11 shows the new wage schedules given the increase in the hiring standard. Note that type A individuals will now have an incentive to attain only 12 years of education since the net gain of $1,000,000 (distance ab) exceeds the $200,000 return on 18 years of education (distance ed). Type B individuals will also have an incentive to attain just 12 years of education since the net gain of $1,000,000 exceeds the $800,000 return on 18 years of education (distance ec). Since both types of workers would have an incentive to acquire just 12 years of education, that threshold would be an ineffective signal of worker productivity.

Figure 9-11.

33a. Equilibrium  LD = LS  10 - 0.5W = 0.5W  W* = $10  L* = 5.

The initial equilibrium is represented by point a in Figure 9-12.

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Figure 9-12.

33b. Equilibrium  LD = LS  12 - 0.5W = 0.5W  W* = $12  L* = 6.

The new equilibrium is represented by point e in Figure 9-12.

33c. With the quantity of labor supplied fixed temporarily at 5, the market clears where 12 - 0.5W = 5  W* = $14.

This outcome is represented by point b in Figure 9-12.

33d. With the wage rising to $14, an incentive will be created for the quantity of labor supplied to increase to LS = 0.5W = 0.5(14)  LS = 7.

This outcome is represented by point c in Figure 9-12.

33e. With the quantity of labor supplied fixed temporarily at 7, the market will clear at 12 - 0.5W = 7  W* = $10.

This outcome is represented by point d in Figure 9-12.

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33f. With the wage at $10, there will be an incentive to supply labor to the point where LS = 0.5W = 0.5(10)  LS = 5.

This outcome is represented by point a in Figure 9-12.

33g. The market is not moving closer to the market clearing values associated with the demand curve D2. Rather, the market continues to cycle around the true equilibrium value.

33h. The cycle will not converge to the true equilibrium since the magnitude of the slope of the demand curve (as it appears on the graph) is the same as the slope of the supply curve. For this model to converge, the demand curve must be flatter than the supply curve.

34a. Provided person B were willing and able to switch to employer Z (i.e., move from point a to point b), the 4-year increase in education would result in a wage increase of slightly over $4.

34b. Given the initial indifference curve B1, the person would require an increase in the wage of just over $2 to undertake the costs of an additional four years of education. This difference of just over $2 represent the difference in the wage between points a and c.

34c. The additional years of education would be a good investment for person B since the benefits exceed the minimum necessary to keep utility constant. The result is an increase in utility as B moves from point a to point c, and from indifference curve B 1 to indifference curve B2. On the other hand, person A is already at his or her optimum wage and education combination. Any increases in education beyond point a will result in a lower level of utility since the increases will result in a smaller increase in the wage than is necessary to compensate person A for the increased costs.

Applications 35. The simplest explanation is that enrollment rates were rising, despite the cost increases, because the benefits of a college education were also rising. (According to the article, male college graduates earned on average 23.8 percent more than high school graduates in 1979, but by 1986 the difference had risen to 39.2 percent. For women, the difference rose from 27.9 percent to 40.5 percent over the same period.) Human capital investment decisions are made by comparing costs and benefits.

36. This explanation is very plausible and highlights the uncertain nature of the benefits associated with educational investments. Decisions about particular educational investments are based on expectations of future earnings, formed largely through contacts with friends, family, neighborhood acquaintances, and other role models. It seems very plausible that given the small percentage of women with graduate degrees in business in

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the early 1970s, that information on future career and earnings prospects would have been relatively hard to come by. Recent experiences suggest that the initial estimates made by many women of the benefits of an M.B.A. degree may have been overly optimistic. As this information has circulated to younger women, it apparently has had the dampening effect on enrollment rates that the human capital investment framework would predict. *37a. The parameter r could be estimated using least squares regression analysis.

Letting S be the independent variable, ln YS the dependent variable, and ln Y0 the constant (or intercept) term, an estimate of r could be derived by fitting a least squares regression line to cross-section data on schooling and earnings. *37b. A large number of variables that can influence earnings have been left out of this model. For example, the amount of ability, on-the-job training, experience, and employee benefits a person receives all influence earnings. However, these omitted variables only bias the estimate of r if they are correlated with the level of education. For example, some measure of individual ability must be included in the regression (making this a multiple regression analysis). Since education and ability are most likely positively correlated, failure to include a measure of ability would bias the estimate of r upward. *37c. Unless the regression included a good measure of individual interests and aptitudes, the estimate would suffer from selection bias. The estimate of r would overstate the rate of return that could be expected by someone who has not invested in additional years of schooling, and would understate the return attained by those who already have invested in additional years of schooling. *37d. The rate of return would be 8.4 percent. r=

ln 35,000 − ln 25,000 = 0.084 4

*37e. Education would be a good investment provided this rate of return exceeded the rate of return available on other comparable investments.

38a. For a type A person, the net benefit from 12 years of education is $1,000,000 (distance ab), while the net benefit from 16 years of education is $1,400,000 (distance ed). The optimal level of education is 16 years.

38b. For a type B person, the net benefit from 12 years of education is $1,000,000 (distance ab), while the net benefit from 16 years of education is $1,600,000 (distance ec). The optimal level of education is 16 years.

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Answers to Chapter 9

38c. Since both types of workers have an incentive to acquire 16 years of education, that level of education could not be used to distinguish high-productivity workers from lowproductivity workers. Lowering the cost of education has increased the incentive to invest in education, but in so doing it has taken away education’s signaling value, thus eliminating the social benefit society derives from education in this model.

38d. Grade inflation may lower the cost of education perceived by individuals, particularly the psychic costs, by reducing the difficulty and anxiety associated with schooling. As shown in the previous questions, however, lowering the cost of education can destroy the ability of education to function as an effective signal of the most productive individuals.

39a. The law would force person A to move from point a to point b. This would force person A to a lower indifference curve. Person B would not be affected.

39b. If person A is restricted to employer Y, the law would force person A to move from point a to point c. This would lead to a greater reduction in utility than in the previous problem. Person B would not be affected.

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ANSWERS TO CHAPTER 10 Review Questions 1. Answer c. Note that answer a ignores the possibility of psychic costs or benefits as well as the timing of costs and benefits. Answer b does not address the costs of mobility.

2. Answer b. The present value of the benefit stream is PVB =

100,000 100,000 100,000 + +  PVB = $267,301.

1+.06 (1+.06) 2 (1+.06) 3

Assuming there are no other benefits associated with the move, and the costs of moving all occur in the current period, the total costs could not exceed this amount.

3. Answer c. Access to information about job opportunities is easier for educated workers to obtain since they tend to participate in regional and national labor markets.

This reduces the costs associated with mobility. Older workers have too little time to recover the costs of mobility and their psychic costs tend to be high. Psychic costs may also be high for married couples, and if both spouses work, it may be difficult for both to find good job matches.

4. Answer d. Education, not age, tends to determine whether a person participates in a local or national labor market.

5. Answer b. Age tends to be more closely connected to the psychic costs of moving while education influences the cost of obtaining information about employment opportunities.

6. Answer b. When the earnings distribution is compressed in the sending country, human capital investments by skilled workers have little payoff, and so these workers may seek out an environment where they can reap the rewards of their investments.

7. Answer a. Given the low standards of living from which many immigrants come, an earnings level even close to that of native-born Americans means that their investment in mobility has resulted in a very high stream of benefits. Individual outcomes, of course, depend on the individual circumstances. The evidence does not necessarily demonstrate that immigrants are more productive than native-born workers, however, since such a relationship may simply result from a failure to account for change in the productive quality of immigrants over time.

8. Answer a. Note that the human capital investment framework utilizes expectations of future benefits and costs. Given incomplete information and uncertainty about future events, it is easy to see how mistakes could be made in evaluating mobility investments.

Even though migration appears to be a good investment on average, that does not mean

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that it will be a good investment for all individuals. Regarding family mobility decisions, evidence indicates that while family income rises, one of the spouses may see their earnings fall.

9. Answer a. Note that while traditionally viewed as something voluntary, quits can also be seen as a form of employer-induced mobility since the firm did not raise the wage high enough to keep the worker.

10. Answer b. Quit rates decrease when the probability of quickly finding another job decreases. This happens when the unemployment rate and layoff rate rise. Such a situation is considered a loose labor market in the sense that many job seekers exist at the same time there are fewer jobs.

11. Answer c. Mobility investments, including quits, are less likely for older workers since the benefits accrue for a shorter time (the value of T is lower). The lower quit rates, in turn, translate into longer job tenures for older workers.

12. Answer a. The costs of quitting are likely to be higher since changing jobs frequently requires a change of residence given that there are fewer job opportunities in rural areas. Note also that if rural residents did have lower discount rates this would tend to increase the likelihood of voluntary turnover since the present value of the future benefit stream would be higher.

13. Answer b. If immigration was prohibited, the market equilibrium would result in the employment of 8 native-born workers at a wage of $8. With immigration, total employment is 12 at a wage of $4. Native-born workers fill 4 of those jobs, while immigrants fill the other 8.

14. Answer c. The total real income of native-born workers falls from 64 (area dbi0) to 16 (area efh0) for a decrease of 48.

15. Answer d. Total profits increase from 32 (area abd) to 72 (area ace) for an increase of 40.

16. Answer c. Total output increases from 96 (area abi0) to 120 (area acj0) for an increase of 24. *17. Answer b. At any given employment level, immigrants should be willing to give up the difference between the wage they actually receive and the minimum they would be willing to accept in return for supplying that quantity of labor. This latter value can be read off the immigrant supply curve at any given employment level. Summing up these differences for the eight units of labor supplied by immigrants yields area eg0 (or equivalently, area fc0) which is the area of economic rent. It has a value of 16.

Immigrants could pay just up to this amount and still have some incentive to supply labor in this market.

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18. Answer d. It is not necessary that immigrants be denied all government assistance, rather they must pay more in taxes than they receive in subsidies so that there is a net transfer of income from immigrants to native workers. Denying all assistance would also accomplish this, but denying it just to illegal immigrants would not be sufficient since illegal immigrants are only a small subset of the total immigrant work force.

19. Answer d. Note that Figure 10-2 is a single-market analysis and so ignores the effects of immigration on other markets.

20. Answer d. Assuming workers can change jobs costlessly (that is, they are highly mobile), wages in competitive labor markets are determined by workers’ human capital characteristics and working conditions. Without mobility, workers would not be able to leave undesirable jobs in search of better opportunities (either higher wages or better working conditions). Even if there were perfect mobility, wage differentials would still exist if employers had jobs with different working conditions, and workers had different preferences regarding wages and working conditions.

21. Answer a. When some workers find it costly to change jobs, the supply curve facing a typical firm may be upward sloping and the monopsony model may be useful in predicting firm behavior, especially the firm’s response to a government-enforced minimum wage.

Problems 22a. The benefits of the move are the increases in combined salary for each year. The present value of the benefit stream is PVB =

3,000 5,000 7,000 + +  PVB = $13,157.51.

2 1+.06 (1+.06) (1+.06) 3

The costs of $10,000 need not be discounted because they occur in year 0. Therefore, the present value of the benefits exceeds the present value of the cost and the investment is worthwhile.

22b. Assuming there are no other benefits associated with the move, and the costs of moving all occur in the current period, the total costs could not exceed $13,157.51.

22c. Although the psychic costs of leaving friends, family, coworkers, and familiar surrounding will be greatest initially, such feelings will continue into the future and can intensify in the future. For example, the events connected to the illness or death of an aged parent can be very stressful when they have to be handled from a long distance.

22d. The benefits of moving may extend well beyond monetary improvements in employment opportunities. The opportunity to leave problems behind and experience new challenges and people are very important to some families. Migration to new areas

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of the country may also allow for lifestyle changes or access to leisure activities that yield more enjoyment. *22e. The first year wage in the new job (call it W) must be high enough to just keep the present value of the benefits equal to the present value of the costs 

W − 80,000 5,000 7,000 + + = 10,000 1.06 1.06 2 1.06 3



W − 80,000 = −327.32 1.06

 W - 80,000 = -346.96  W = $79,654.04.

22f. It is unlikely that both spouses would gain equally. Evidence suggests while family income rises because of migration, one of the spouses may actually see his or her income decline because of the move.

23a. Table 10-3 shows the marginal product of labor schedule for market A.

Table 10-3.

Labor Market A

Labor Market B

Labor

MPL

Labor

MPL

1 2 3 4 5

12 8 5 3 2

1 2 3 4 5

17 13 10 8 7

23b. See Figure 10-5.

23c. The area under the marginal product schedule consists of the area of the 5 rectangles that can be seen in Figure 10-5. The height of each rectangle is the marginal product, while the width is one unit  Area = 12(1) + 8(1) + 5(1) + 3(1) + 2(1).

Note that this computation is the same as summing the marginal product values. Note that the area equals 30, the total output associated with 5 units of labor in market A. 378

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23d. See Table 10-3.

Figure 10-5.

23e. The wage rate will be 5 in market A and 10 in market B. The total output from this allocation of labor will equal 65 (25 + 40).

23f. Given the higher wage rate in B, workers would be expected to migrate from A to B. If one worker migrates so that now A has 2 workers and B has 4, the total output increases to 68. If an additional worker migrates, however, output falls to 67. There would not be an incentive for the second worker to migrate, however, since after the first worker migrates, the marginal product, and hence the real wage, equals 8 in both markets.

The output of this economy is maximized when labor is allocated in such a way that the marginal product is equal across the markets.

24a. If immigration were totally prohibited, the market clearing wage and employment level would occur where LD = LN  20 - 2W = 2W  W* = 5  L* = 10.

See point b in Figure 10-6. Allowing immigrants to enter this labor market would create a total supply curve given by the equation LT = LN + LI  LT = 2W + W  LT = 3W.

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Given the two groups of workers, the market clearing wage occurs where LD = LT 20 - 2W = 3W  W* = 4  L* = 12.

See point c in Figure 10-6. Substituting this wage back into the supply equations for each group reveals that the employment of native-born workers will be 8 (point g) and the employment of immigrants will be 4 (point f). Therefore, immigration has reduced native employment from 10 to 8. Note that this reduction of 2 is less than the number of immigrants employed.

Figure 10-6.

24b. Real income for native-born workers has fallen from 50 (area dbj0) to 32 (area egi0) for a total reduction of 18.

24c. Total profits increase from 25 (area abd) to 36 (area ace) for an increase of 11.

24d. Total output increases from 75 (area abj0) to 84 (area ack0) for an increase of 9. *24e. Immigrants should be willing to give up area ef0 (or equivalently, area gc0) which equals 8, the area of economic rent. *24f. Native-born workers have lost 18 in income but the firms have gained 11 in profits and immigrants have earned 8 in economic rent. So, for example, if the increased profits of 11 plus 7 of the “surplus” earned by immigrants were transferred to the native-born workers, their income would be the same as before immigration. The other two groups are also the same or better off than before immigration.

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24g. This problem is a single-market analysis and so ignores the effects of immigration on other markets. For example, the wage reduction brought about by immigration in this market will help to put downward pressure on consumer prices The income earned by immigrants will also translate into increased demand for products. The scale effect that this creates will lead to employment and wage gains for those categories of labor that are gross complements with the labor in this market. Also, the change in employment opportunities that occur in this market may create a situation where native-born workers will migrate away from the geographic areas experiencing the influx of immigrants.

Applications 25. This example does not contradict the notion that mobility is an investment undertaken when the present value of the benefits is expected to exceed the present value of the costs. In this case, the choice is no longer between the $60,000 salary and the $50,000 salary. Rather the choice is between the $50,000 salary and whatever the best opportunity is in the New England area. Perhaps because of the increased unemployment in this area, the only other alternative was a $40,000 salary. Given that scenario, it is easier to see the payoff to mobility. *26a. If women are perceived to have shorter work lives because of traditional child rearing responsibilities, firms may feel that there is not sufficient time to recover their investment in firm-specific training. As a result, women may not be hired for jobs involving training or may be offered less extensive training opportunities. *26b. When a firm invests in firm-specific training for the worker, it tries to recover the investment in the post-training periods by offering a real wage that is less than the worker’s marginal product but above what the worker can get elsewhere. If no such training is offered, there will not be a gap between the wage the worker is receiving and his or her alternative offers. In this situation, the worker has little incentive to stay with the firm. Eliminating general training opportunities does not create the same kind of change since workers pay for the cost of general training in the form of lower wages during the training period. As a result, the real wage and the marginal product (which in this case also represents the worker’s alternative offers) are already equal in the posttraining period. Eliminating general training would not change the relationship between the wage the worker receives and the worker’s alternative offers.

27a. Recall from problem 24 that the market clearing wage was 4 if immigration was allowed and 5 if it was not. In either situation, a minimum wage of 6 will be binding.

27b. Substituting W = 6 into the demand equation yields LD = 20 - 2(6) = 8.

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See point a in Figure 10-7.

Figure 10-7.

27c. Substituting W = 6 into the equation for the total supply curve yields LT = 3(6) = 18.

See point c in Figure 10-7. Of these 18, 12 are native-born workers (point b) and 6 are immigrants.

27d. There is no way of determining how the 8 jobs will be split between immigrants and domestic workers. It could be that all 6 immigrants will be hired along with 2 natives, or perhaps only 8 natives will be hired, or anywhere in between. Native workers may have an advantage over immigrants, because of proficiency with the language and other local knowledge. On the other hand, an unscrupulous employer might try to exploit immigrants-especially if they lack legal status and hence would be afraid to complain--by paying them less than the minimum wage that would be demanded by native-born workers.

27e. When the minimum wage is binding, native workers will replace immigrants on a one-to-one basis. For example, suppose the 8 available positions were filled by 4 illegal immigrants and 4 native-born workers. Under the 1986 law, the 4 illegal residents could not be hired and so the firm would hire native-born workers for all 8 positions. Note that this relationship only holds when the minimum wage is set above the intersection of demand and the supply of native-born labor. Note that in problem 25 where there was no minimum wage, eliminating the 4 immigrants that were hired would only increase nativeborn employment by 2. (The cost of determining whether workers are legal residents is an example of a quasi-fixed cost.)

27f. Such an amnesty program could increase the flow of immigrants by raising the potential benefits associated with immigration. Those contemplating illegal entry may be

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encouraged by the hope that a similar amnesty program would be offered in the future.

(Also, once the immigrants become U.S. citizens, immediate family members are eligible to enter the country as well.)

27g. The expansion of welfare eligibility increases the chances that immigration will lead to a reduction in the aggregate income of native-born workers. For the native-born population not to be hurt by immigration, it is necessary that immigrants pay more in taxes than they receive in government assistance. *28a. Since the 20 year old will be from group C, the 40 year old from group B, and the 60 year old from group C, the cross section will consist of the points (20,10), (40,13), and (60,16). The points are connected by the dashed line labeled E in Figure 10-8. Note that these three points imply that each additional 20 years of experience increases the logarithm of earnings by 3. This translates into a rate of return of 0.15 per year. *28b. The estimated rate of return will give a misleading impression. Even though the growth rate of immigrant earnings is the same as that of native-born workers (r was set at 0.1 for all workers), the cross section estimate yields a rate of increase of 0.15 for immigrants. Given this steeper estimated age-earnings profile for immigrants, it would be tempting to conclude that immigrants are more productive than native-born workers. *29a. Since the 20 year old will be from group C, the 40 year old from group B, and the 60 year old from group C, the cross section will consist of the points (20,14), (40,14), and (60,14). The points are connected by the dashed horizontal line labeled E in Figure 10-9.

Note that these three points imply that additional years of experience do not change immigrant earnings. This translates into a rate of return of zero.

Figure 10-8.

*29b. The key to eliminating the bias in the estimated age-earnings profile is to control for quality differences in immigrants over time. It is the omission of this variable that causes the bias. Instead of performing a simple least squares regression with the 383

Answers to Chapter 10

logarithm of earnings on the left side of the equation and time spent in the country on the right, it is necessary to perform a multiple regression where both time spent in the country and some measure of immigrant ability are included as independent variables.

Simple regression would be appropriate only if panel data on immigrant earnings were available. Panel data is collected by following the fate of a particular group of immigrants over time. *29c. All three biases are examples of the omitted variable problem discussed in the appendix to Chapter 1. The problem of cohort quality change is almost identical to the problem of ability bias discussed in Chapter 9. In each case, ability differences are not controlled for. However, since ability and the remaining explanatory variable (education in Chapter 9, age in Chapter 10) are correlated, the effects of the ability differences are attributed to the other variable, thus biasing the true relationship. Selection bias is also an omitted variable problem that stems from failure to account for hard-to-measure aptitudes and interests for particular occupations. In the same way, the bias resulting from cohort quality change arises in large part because such differences are difficult to observe and measure.

Figure 10-9.

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ANSWERS TO CHAPTER 11 Review Questions 1. Answer c. Although it would be possible for even non-union employers and employees to draw up formal employment contracts that precisely specify the obligations of each party in a way that would be legally enforceable, such agreements would be costly to form and would limit the flexibility of employers in responding to new situations. As a result, most employment contracts take the form of implicit and incomplete understandings. These characteristics, however, also make employment contracts difficult to enforce.

2. Answer a. Answers b to d are the characteristics that create the necessity for selfenforcing contracts.

3. Answer d. Employment contracts that are implicit and incomplete can be very vague and difficult to enforce. These problems are compounded when information is asymmetric since the likelihood of being able to successfully cheat on the employment contract increases.

4. Answer d. When employment contracts contain precise promises, formal financial penalties may be helpful in assuring compliance. When contracts are not precise, compliance becomes a matter of contracting with the “right” person. How can you tell the kind of person with whom you are contracting? Information about an individual’s characteristics can often be inferred through choices individuals make. For example, in Appendix 9A, it was shown that under certain conditions, different levels of education can serve as reliable signals of individual ability. While that information might be acquired through better interviewing and screening of applicants, b (and hence d) is a better answer.

5. Answer b. When the workers’ marginal revenue product exceeds the alternative offers, the employment relationship can be said to generate a surplus that is capable of making each party better off--even when it is not divided evenly. It is the fear of losing one’s share of the surplus that assures compliance. Firm specific training is only one example of an investment that generates such a surplus.

6. Answer d. While close supervision and pay for performance are not feasible options for all firms, fair treatment is a principle that can be adopted at any firm to help increase productivity.

7. Answer c. Although most workers are concerned about their treatment relative to others in the firms, they also place some value on seeing the group as a whole succeed.

The more workers are willing to work for group success, the less likely they are to shirk.

8. Answer d. Under output-based pay, external factors can have a significant effect on the pay received in any one period. The fluctuations in income, in turn, produce lower average levels of utility if the worker is risk averse. Answer c essentially repeats the question.

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Answers to Chapter 11

9. Answer d. Output-based pay leads to higher levels of pay because of quality differences between workers, risk averse preferences, and the productivity increases caused by the pay scheme.

10. Answer a. Firm profits are more stable under an incentive-pay scheme. If workers do not exert their best efforts and output falls, the compensation per worker also falls, helping to lower costs below what they would be under time-based pay. This additional cost reduction would help to offset losses in revenue caused by the lower output.

11. Answer b. Group incentive-pay plans are more likely when it is difficult to measure individual output. When employees work interdependently in teams, it is difficult to decide how much of the group’s output is attributable to each member. Answers a and c would make group incentive-pay less likely.

12. Answer b. Stock prices can fluctuate considerably over time due to factors beyond an executive’s control. This variability in earnings would be viewed as an undesirable job characteristic by an executive having risk averse preferences. Note that when executives are employed under these terms, evidence suggests that the stock market performance of the firm is superior to that of other firms. Incentives for managers to emphasize short-run profits tend to be created only when pay is tied to short-run measures of profitability, not to the firm’s stock market performance.

13. Answer c. Saying that individual output is highly correlated with individual effort is the same as saying that external factors do not play a significant role in determining output. It is in these situations that merit-pay plans have the most potential for motivating workers. Unfortunately, such situations are relatively rare. While relative rankings of workers help to create a sense of fairness and acceptance for the outcomes, if rankings are subjective and not based on readily identifiable individual performance that can be observed by all, they will typically be very unpopular among those being rated.

14. Answer d. Although it would seem in the firm’s interest to set the wage so as to keep as much of the surplus as possible, the higher turnover and reduced motivation that may result can actually lead to increases in the firm’s total costs.

15. Answer a. The tendency of workers to undercut rivals and invest time trying to win over supervisors is more a function of how the pay is based rather than the level of pay.

Such problems are especially likely when merit-pay raises are based on a supervisor’s ranking of a worker’s relative performance.

16. Answer b. This is the most specific correct answer. Answers a and d are really subsets of answer b. The situation in c would make an efficiency wage strategy impossible.

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17. Answer d. If output were easily measurable, the firm could use an individual incentive-pay plan to increase worker motivation, and paying an efficiency wage would not be necessary. Efficiency wages are most likely when the firm anticipated a long-term attachment with the worker and other ways of increasing effort (e.g., increased supervision) are not feasible.

18. Answer c. Setting the present value of the underpayment equal to the present value of the overpayment yields

5+

W − 20 W − 20 5 10 = 2 +  2 = 1.32 2 3 1+.06 (1+.06) (1+.06) (1+.06) 2

 W2 = (1.32)(1.06)2 + 20  W2 = 21.48.

19. Answer c. Note that the firm just breaks even over the time period since at the end of period 3, the present value of the total compensation just equals the present value of the marginal product values. If workers continue to be paid more than they contribute, the firm will eventually go out of business. On the other hand, if workers left before period 3 was complete, the firm would have made positive economic profits.

20. Answer d. If the firm develops a reputation for treating the losers poorly, it will not be able to attract enough entrants to make the tournament possible. Also, since the winner will be the one with the best relative performance, some effort may be diverted to undercutting rivals instead of enhancing the interests of the firm. The willingness of the firm to tolerate “deadwood” is one of the factors that make such tournaments possible.

Problems 21a. If the owners cooperate, the workers attain a higher level of utility by shirking. If the owners shirk, the workers again attain a higher level of utility by shirking.

21b. If the workers cooperate, the owners attain a higher level of utility by shirking. If the workers shirk, the owners again attain a higher level of utility by shirking.

21c. The employment contract is not self-enforcing since both parties have an incentive to shirk (i.e., not exert their best efforts). Note that when both parties shirk, however, they each end up with a lower level of utility than if they both cooperated.

21d. Knowing that the other party plans to shirk does not change the outcome. Each party perceives it to be in their self-interest to shirk regardless of the decision made by the other.

21e. Note that the payoffs from cooperation have all been increased, while the payoffs from shirking have all been reduced. Perhaps this occurred because each party developed a sense of loyalty to the group, and so feels bad when cheating on the employment contract.

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21f. The employment contract is now self-enforcing. Regardless of the choice made by the owners, workers attain a higher level of utility by cooperating. Similarly, regardless of the choice made by workers, owners attain a higher level of utility by cooperating. *22a. To make the compensation per worker (Y) under the profit sharing scheme equal to what the workers can attain elsewhere, the guaranteed wage and the profit sharing parameter must be set such that Y in long-run equilibrium equals the market clearing wage of $9. Substituting the appropriate values into the expression for Y yields Y = 7+

1 (38)(20) − (7)(20) − (9)(20) 11 20

 Y = 7+

1 440 1 = 7 + 22 = 9.

11 20 11

*22b. Since the compensation per worker will be more variable under profit sharing, risk averse workers will prefer a time-based wage. They will require a compensating differential to work at firms offering profit sharing. In other words, Wg and s must be set in such a way that they yield a compensation per worker slightly above $9. *22c. Substituting the long-run equilibrium values into the marginal revenue and marginal product expressions yields MR = 58 - 2(20) =18, MPL =

1 20 1 = .

2 20 2

Substituting these values into the marginal expense of labor expression yields ME L = 7 +

1 [(18)(.05) − 7] = 7.18.

11

*22d. Since MRPL = 9 > 7.18 = MEL, the firm has an incentive to increase employment. *22e. Substituting L = 21, K = 20 into the production function yields Q = 21 20 = 20.494

 P = 58 - 20.494 = 37.506. *22f. Substituting into the profit pool expression yields  = (37.506)(20.494) - (7)(21) - (9)(20)   = 768.648 - 147 - 180 = 441.648.

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*22g. Compensation per worker (Y) falls from 9 to 1 441.648 Y = 7 + 11 21 = 7 + 1.912  Y = 8.912.

Since the compensation per worker is less than what workers can attain elsewhere, the firm would not be able to retain 21 workers. *22h. Although profit sharing will not lead to a higher level of employment in this example, it should lead to a more stable employment relationship because a gap exists between what the marginal worker contributes to the firm ($9) and what the marginal worker costs the firm ($7.18). If the MRPL falls because of a decline in the demand for the product, but stays above $7.18, the firm does not have an incentive to lay off workers.

Although workers do not have any incentive to quit the firm, the firm does not really have any protection against quits since the compensation per worker is just comparable to what workers can attain elsewhere (plus a compensating differential if workers are risk averse).

23a. At a wage of $50, 9 workers would be needed to produce 36 units of output since each worker only produces 4. Total labor costs will be ($50)(9) = $450. At a wage of $100, only 4 workers will be needed since each worker produces 9. As a result, total labor costs fall to $400. Since total revenue should be the same in each case, paying the higher wage will actually increase profits.

23b. This move would be consistent with an efficiency wage strategy. Whether $100 could actually be considered the efficiency wage depends on whether further increases in the wage continue to increase profits. If they do, then $100 is not the efficiency wage.

24a. Setting the present value of the underpayment equal to the present value of the overpayment yields

3+



W − 16 2 1 + = 4 4 2 1.06 (1.06) (1.06)

W4 − 16 = 5.78  W4 = (5.78)(1.06) 4 + 16  W4 = 23.29.

4 (1+.06)

Given this value of W4, note that both the marginal product and wage schedules yield identical present values of 52.27 even though the marginal product values sum to 60 and the wage values sum to 61.29. The underpayment (6) must be less than the overpayment (7.29) to compensate workers for the time value of money.

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24b. A necessary condition for such a deferred payment scheme is a long-term relationship between workers and the firm. Internal labor market strategies promote long-term attachments by filling upper-level positions with workers from within the firm.

24c. A deferred payment scheme is thought to increase productivity for two reasons.

The first is that such a scheme will appeal mainly to those types of workers who anticipate staying with the firm and working hard enough to avoid being fired before the deferred compensation is completely recovered. Thus such a scheme may be a way for a firm to attract workers with above average commitment and motivation. The second reason is that such a scheme provides an incentive for all employees to work hard since the penalty for shirking and being fired can be very large. Knowing that workers have less incentive to shirk, the firm can devote fewer resources to supervision.

24d. The prohibition of mandatory retirement means that the firm can not prohibit workers from staying past period 4. In this example, workers who stay past period 4 will receive a deferred payment that exceeds, in present value terms, the earlier underpayment (assuming the firm can not lower the wage to older workers). This means that firm will not be able to earn even a normal profit.

Applications 25a. Under such a “piece-rate” scheme, doctors have an incentive to see many patients quickly. The fear is that doctors provided with this type of incentive may not provide quality care to all patients, particularly those that need a great deal of attention.

25b. A flat fee system may help to keep costs down by taking away the incentive to provide excessive treatment.

25c. The fee must be set in such a way that it provides long-run compensation consistent with what the doctors can earn elsewhere. If the compensation elsewhere involves more certainty, a compensating differential will also be required to make the more variable income stream yield the same level of utility as the certain one.

25d. The advantage of such an incentive-pay plan is that it should make doctors more accountable to their patients, provide an incentive for them to keep careful records, and give those who work hard a chance to get ahead. Such plans also tend to appeal to those who have above-average ability and motivation. On the other hand, the plans may cause doctors to focus excessively on the aspects of the doctor-patient relationship asked about in the questionnaire. Also the systems may be perceived as unfair since often patients are not in a position to understand the quality of the care they are receiving. Differences in pay can also cause resentment because of concern about relative standing. The questions used in measuring quality should ultimately be things that are under the doctor’s control and not influenced by external factors. Also, the questions should relate to qualities that further the organization’s overall objectives (e.g., providing quality care at a reasonable cost).

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25e. The incentive-pay plans should work better with those who have private practices.

Since the doctors do not interact with one another, differences in pay will not generate resentment due to concern about relative standing or status.

25f. To the extent that performance ratings are influenced by external factors, merit-pay plans may create little incentive for the doctors to exert extra effort. If the performance ratings are based on relative success, doctors may be less cooperative with one another and divert extra effort into ingratiating themselves with their supervisors.

25g. If measures of individual output can not be constructed, it may make sense to base a portion of an individual’s pay on the group success. Since most HMOs are non-profit organizations, however, some measure of success other than profits must be used. For example, the extent to which the organization can keep costs down may be an alternative measure. Such group incentives may be relatively ineffective, however, if the efforts of the typical doctor have little influence on the attainment of the goal. In those situations, individual’s have an incentive to free ride on the efforts of others.

25h. While time-based pay is preferred by workers with risk-averse preferences, it provides little incentive for individual’s to exert their best efforts and so may require increased supervision.

26a. The idea behind an efficiency wage strategy is that if workers are receiving more than they can earn elsewhere, they will avoid shirking so as to reduce the risk of being fired and losing the surplus they are accumulating. If a worker is planning on leaving the job anyway, the fear of being fired is not an effective deterrent to shirking. Also, workers with broader career concerns are less likely to shirk since being fired may affect opportunities at other firms. If workers are not likely to shirk, there is little reason to pay an efficiency wage.

26b. The argument that large firms are more likely to pay efficiency wages stems from the fact that large firms present employees with a wide variety of job options and so there is likely to be a longer-term attachment between employer and employee. Such longterm attachments increase the likelihood of efficiency wages. The highly interdependent production processes at large firms also require that firms take steps to stop shirking. To the extent that monitoring worker effort is more costly at a large firm, efficiency wages may be an effective alternative to motivate workers to exert their best efforts.

27. Layoff policies that do not protect those with longer job tenures inhibit the use of deferred payment schemes. Workers will not be willing to be paid less than their marginal product early in their career if they are likely to be laid off during the period when they are receiving the deferred payment.

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Answers to Chapter 12

ANSWERS TO CHAPTER 12 Review Questions 1. Answer b. Although answer a is a true statement, the wage gap could be the result of differences in productive characteristics (premarket differences). Labor market discrimination focuses on differences in labor market payoffs to productive characteristics. Answer c is also a true statement but such segregation could be voluntary (i.e., represent premarket choices).

2. Answer d. Differences in any of the factors might justify differing wages between male and female employees.

3. Answer a. Holding occupation constant takes away its affect on wages, making it impossible to see the impact that restricting employment opportunities has on women’s relative wages.

4. Answer b. Note that some of these differences may not be measurable or observable, making it impossible to hold them constant. Also, the current values of these productive characteristics may have been influenced by past discrimination. Answer d describes the goal in measuring wage discrimination.

5. Answer a. The observed wages are represented by points a and b.

6. Answer b. Since some current labor market discrimination may take the form of occupational segregation, it is important not to control the occupation. Given the occupational differences, women would earn $10 (point d) if they had the same experience as men. That leaves a gap between men’s and women’s wages of $10 (the difference between points b and d).

7. Answer c. When measuring wage discrimination, all premarket factors, including occupation, must be held constant. This leaves the gap between point b and c ($6) unexplained.

8. Answer d. Assuming women’s employment options are limited to the low-paying sector because of discrimination, this leads to a reduction in wages of $4, even if women had the same experience as men. Occupational segregation can be represented by the gap between points c and d.

9. Answer d. Note that if women experienced wage discrimination in the past, some of the premarket differences could be attributable to discrimination. Hence, holding them constant would understate the effect of discrimination on wages.

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Answers to Chapter 12

10. Answer c.

S= ½ (|75-10| + |25-90|) = 65.

11. Answer d. Prejudiced employers will act as if the marginal product of blacks has been shifted down. If black and white wages are equal this will lead to a reduction in employment for blacks. If blacks and whites are hired in the same numbers, blacks will be paid less since their marginal product will be subjectively devalued.

12. Answer a. If the employers prejudice causes a reduction in employment, this reduces the area under the marginal product curve. Recall that this area represents output (real income) to the firm. If the firm reduces wages paid to blacks instead of black employment, note that the lower wage would lead a nondiscriminating firm to an even higher employment and output level. See problem 26 for numerical examples of these points.

13. Answer d. By segregating blacks away from customer contact positions, the firm can avoid losing prejudiced customers. On the other hand, allowing blacks in such positions may be worth it if they are more qualified, and hence more productive, than whites. This higher productivity presumably makes up for the lost customers. Since self employment takes away the possibility of employment prejudice, an earnings gap between equally productive black and white entrepreneurs points to customer prejudice.

14. Answer d. Prejudiced white employees would have to be paid a compensating differential to work in an integrated group. This creates a window of opportunity for a firm to lower costs and increase profits by substituting less expensive black workers for whites.

15. Answer c. Firms use statistical discrimination as a way to identify the most productive workers while avoiding the cost associated with a careful investigation of each worker. The more diverse a group becomes in their productive characteristics, the less reliable is group affiliation as an indicator of productivity. Statistical discrimination does not stem from prejudice or monopoly power.

16. Answer b. The notion of noncompeting groups is a plausible one if firms exercise monopsony power over women and minorities. The problem is that theories do not give any reason for the lack of competition. The theories fit the facts, but are based on assumptions and premises that seem difficult to support.

17. Answer b. Firms do not necessarily create prejudice in the monopoly power models, but they are assumed to profit from its existence. However, such scenarios are unlikely to persist since there will be strong incentives for individual firms to cheat on the agreement.

18. Answer c. Disparate treatment occurs if individual workers are intentionally treated differently with respect to wages and employment opportunities because of the demographic group to which they belong.

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Answers to Chapter 12

19. Answer d. Although word-of-mouth recruiting may not intentionally disadvantage any group, it can have a disparate impact over time since it can carry forward the effects of past discrimination. The same is true of seniority systems, but such systems are explicitly allowed under Title VII. 20. Answer c. One shortcoming of standards used in calculating the pool of available applicants is the interest people in the targeted groups have in working at the firm.

Because of commuting distance or the mix of compensation offered at a particular firm, all workers in a particular area may not be equally interested in working for the firm. By ignoring worker interest, affirmative action goals may be set beyond the firm’s immediate reach.

21 Answer d. Comparable worth pay systems attempt to make pay a function of the job that is performed, rather than a function of a workers personal characteristics.

22 Answer b. A job score of 100 would lead to $1,500 in earnings for a man. A salary of $1,200 represents only 80 percent of what a man earns. Therefore, the women’s pay represents a 20 percent comparable worth earnings gap.

Problems 23a. Substituting the appropriate values into the wage formulas yields Wm = 3 + 0.5(4) + 0.6(10) + 1 = 12, Wf = 3 + 0.4(3) + 0.5(6) = 7.2 

Wf 7.2 = = 0.6  40% earnings gap Wm 12

23b. Substituting ED = 4, Exp = 10, and OC = 1 into the women’s wage equation yields Wf = 3 + 0.4(4) + 0.5(10) + 1 = 10.6 

Wf 10.6 = = 0.883 Wm 12

23c. After controlling for all premarket characteristics, women still earn 11.7 percent less.

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Answers to Chapter 12

23d. Substituting ED = 4, EXP = 10 into the women’s wage equation yields Wf = 3 + 0.4(4) + 0.5(10) = 9.6 

Wf 9.6 = = 0.8 Wm 12

23e. After adjusting for all productive characteristics except occupation, women earn 20 percent less than men in this example. This gap can be attributed to current labor market discrimination because it reflects different employment opportunities and different labor market payoffs to the various productive characteristics. The occupational segregation costs women an extra $1 in wages and so widens the wage gap by 8.3 percent.

23f. If the premarket differences in education or experience are the result of past discrimination, the estimate of current labor market discrimination understates the influence of discrimination on labor market outcomes. On the other hand, if unmeasurable or unobservable differences exist in the productive characteristics of men and women, the estimate of current labor market discrimination overstates the problem.

23g. Substituting ED = 3, EXP = 6, and OC = 0 into the men’s wage equation yields Wm = 3 + 0.5(3) + 0.6(6) = 8.1 

Wf 7.2 = = 0.89 Wm 8.1

This approach yields a slightly smaller discriminatory wage gap (11 percent) than in 23c.

23h. Half of the women would earn 7.2, while half would earn 8.2, for and average wage of 7.7. Similarly, half of the men would earn 12, while half would earn 11, for an average wage of 11.5. This change in the occupational distribution increases the relative wage of women from 0.6 to 0.67 (7.7/11.5).

24a. See Table 12-3. The number in each occupation can be found by multiplying the percentage male or female (expressed as a fraction) times the total employment. ________________________________________________________________________ Table 12-3.

Occupation #Male #Female Total ________________________________________________________________________ `

A B C D

10 40 50 20 30 50 40 10 50 30 20 50 100 100 200 ________________________________________________________________________

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Answers to Chapter 12

24b. The percentage of the total male or female workers in each occupation can be found by dividing the number of males or females in each occupation by the total male or female population. In this example, the total population is 100 for each sex. The results are presented in Table 12-4. The last column computes the absolute value of the difference between the total male and female percentages in each occupation. ________________________________________________________________________ Table 12-4.

Occupation percent Male percent Female | percentM- percentF| ________________________________________________________________________ `

A B C D

10 percent 20 percent 40 percent 30 percent

40 percent 20 percent 10 percent 20 percent

30 10 30 10 80 ________________________________________________________________________ 24c. The index of dissimilarity is 40.

S = ½ (30 + 10 + 30 + 10) = 40.

This indicates that 40 percent of the women (or men) would have to change occupation in order to make the occupational distribution of women then same as men. For example, 30 percent of the women would have to move from A to C, and 10 percent of the women would have to move from B to D. The main point of this exercise was to show that the index of dissimilarity is computer using the percentage of the total male and female population in each occupation, not the percentage of each occupation that is male and female.

25. Substituting ER = 0.608 and LFPR = 0.776 into the employment rate expression yields 0.614 = 0.776(1-UR)  UR = 0.209 or 20.9 percent.

26a. Profit maximization occurs at that level of employment where the marginal product of labor equals the real wage W = MPl  15 = 25 – 0.5L

 L * = 20 for each group.

This equilibrium is shown as point c in Figure 12-4.

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Answers to Chapter 12

Figure 12-4.

Ignoring the cost of capital, profit is represented by the area under the marginal product curve and above the wage line. Thus the employment of 20 blacks result in a profit (p) denoted by the area of triangle acg. This area has a value of

 = ½ (20)(10) = 100. *26b. A prejudiced employer acts as if the marginal product of blacks is 5 units less than whites at any given employment level.

W = MPl  15 = 25 – 0.5L – 5

 L* = 10 for blacks.

The new employment of blacks is represented by point e. White employment remains at 20. Profit from black employment is now given by the area of trapezoid abeg which has an area of

 = ½ (10)(5) = (10)(5) = 75. *26c. To keep black employment at 20 requires that the wage fall to W = MPl  W = 25 – 0.5(20) – 5  W * = 10 for blacks.

This equilibrium is denoted by point f. Profit from black employment is now given by the area of the trapezoid acfh which has an area of

 = ½ (20)(10) + (20)(5) = 200.

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Answers to Chapter 12

*26d. At W = 10, an unprejudiced employer would hire blacks up to the point where W = MPl  10 = 25 – 0.5L  L* = 30 for blacks.

This equilibrium is represented by point d. Profit from back employment is now given by the area of the triangle adh which has an area of

 = ½ (30)(15) = 225.

Therefore, whether the prejudiced employer adjusts wages or employment, the prejudiced employer can always earn a higher profit.

27a. The market clearing relative wage will be 0.5 and 10,000 women will be employed.

This equilibrium is represented by point d in Figure 12-5.

27b. The increase in the number of non-discriminating employers together with the worsening of discriminatory preferences creates the new market demand curve shown as line aec in Figure 12-5. This new demand curve leads to an increase in the relative wage and an increase in employment. The new equilibrium is point f.

28a. A job score of 600 would lead to $50,000 in earnings from a man. Therefore, the women’s salary reflects a $10,000 comparable worth earnings gap.

28b. A salary of $40,000 represents only 80 percent of what a man earns. Therefore, the woman’s salary represents a 20 percent comparable worth earnings gap.

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Answers to Chapter 12

Applications 29. Demographic groups that earn more than the U.S. average may still experience discrimination. Recall that wages can be thought of as a function of an individual’s personal productive characteristics and the payoff that each characteristic brings in the labor market. Even though the payoffs may be reduced because of the group an individual belongs to, if the person has highly productive characteristics, the wage that is actually received may still be well above average. To measure the discrimination, one could estimate what Russians would earn if they had the same productive characteristics as native born white Americans. If the estimate reveals Russian would earn less, this would be evidence supporting the hypothesis of discrimination.

30a. Substituting the appropriate values into the wage formulas yields Wm = 8 = 0.75(12) + 2(1) = 20,

Wf = 8 + 0.5(8) = 12



Wf 12 = = 0.6  14 percent earnings gap.

Wm 20

30b. Substituting EXP = 12, OC = 1, and Z = 1 into the women’s wage equation yields Wf = 8 + 0.5(12) + 2(1) = 17 

17 Wf = = 0.85 Wm 20

30c. After controlling for all premarket characteristics, women earn 15 percent less than men.

30d. After Substituting EXP = 12, and OC = 1 into the women’s wage equation yields Wf = 8 + 0.5(12) + 2(1) = 16



Wf 16 = = 0.8.

Wm 20

30e. After controlling for all pre-market characteristics except attitude, women appearing to be experiencing a 20 percent discriminatory earnings gap.

31a. Profit maximization requires that firms pay a real wage equal to the marginal product of labor in each sector

 Wa = 40, Wb = 70 = Wc.

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Answers to Chapter 12

31b. Total output = 390 + 240 + 240 = 870.

31c. The real wage would equal 60 in each sector.

31d. Total output = 3(300) = 900. the new distribution of labor is optional since the marginal product of labor is equal across the sectors. This means that there is no way to reallocate labor and get a higher output.

32a. A 20 percent turnover rate in a firm with 1,000 employees means that the firm must replace 200 workers annually. If 20 percent of the new hires are black, the firm will be hiring 40 blacks annually. Provided the turnover rate applies equally across all demographic groups in the firm, 20 percent of the 100 black workers will leave the firm for a total loss of 20 black workers.

32b. If 20 blacks leave the firm during the first year and 40 are hired, there will be a net gain of 20. Therefore, at the end of year 1, there will be 120 black workers. This represents 12 percent of total employment, up from 10 percent at the start of the year.

32c. the computations in Table 12-5 shows that 16.7 percent of total employment will be black after 5 years of affirmative action. _____________________________________________________________________ Table 12-5.

Year 3

1 2 4 5 # Loss 20 24 27 30 40 New Hires 40 40 40 40 40 Net Gain 20 16 13 10 8 Total 120 136 149 159 167 Percent 12 13.6 14.9 15.9 16.7 Black ________________________________________________________________________ 32d. An increase in turnover would reduce the number of years needed to achieve the goal. For example, if the turnover rate increased from 20 percent to 30 percent, 300 new workers would be hired in year 1, 60 of whom would be black. At the same time, 30 blacks would leave the firm in year 1, for a net gain of 30. When the turnover was 20 percent, the net gain in year 1 was only 20 black workers.

400

ANSWERS TO CHAPTER 13 Review Questions 1. Answer c. Note that bargaining often takes place simultaneously with a number of employers. The AFL-CIO is largely a political action group. It is not involved directly in the collective bargaining process.

2. Answer c. It is perfectly legal for employers to explain to employees why joining a union is not in their best interest, but they can not threaten or discriminate against those that do.

3. Answer a. The replacement of striking workers is legal. Answers c and d are examples of unfair labor practices.

4. Answer a. Workers with short job tenures are less likely to join unions since many of the things unions bargain for (seniority rules, job security arrangements, pensions) are of little benefit to someone who does not expect to stay with the firm.

5. Answer b. Increased employer resistance raises the cost of union organizing activity and shifts the supply curve to the left.

6. Answer a. Although the Reagan administration’s replacement of striking air traffic controllers is often cited as an action of the federal government that contributed to the decline of unions, this action was taken under existing federal law and did not represent new legislation against unions. Growing female participation in the labor force was probably more of a factor in the first half of this period than it has been in the second half.

7. Answer c. Every point on the demand curve is a point of profit maximization. To stay at the same profit level as one moves to alternate levels of employment, wages must fall to keep profits at the specified level. Note that profits fall as the firm is forced up its labor demand curve by higher union wages.

8. Answer c. If it is possible to make someone better off without hurting anyone else, then it makes sense to move away from the current combination. An efficient contract has been reached only when these kinds of moves are no longer possible. Note that the firm’s profits serve as a constraint on the union’s ability to maximize utility.

9. Answer d. A rapidly growing product demand should translate into a growing demand for labor that can be used to mask the adverse employment effects of union wage increases. An inelastic supply of substitute inputs reduces the incentive of a firm to substitute other inputs for labor. Note that a highly elastic product demand leads to a more elastic labor demand.

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Answers to Chapter 13

10. Answer d. According to the Hicks Marshall laws presented in Chapter 4, all of these factors should lead to a more elastic labor demand.

11. Answer d. All of these factors limit the firm’s ability to substitute other inputs for union labor and so make the demand for labor more inelastic.

12. Answer c. Occupational licensing laws restrict entry into a profession and so limit a firm’s ability to find substitutes for union labor.

13. Answer d. The Hicks bargaining model predicts that settlements will be made in advance when both parties are aware of how the other’s bargaining position will change over time and that the union is not using the strike to strategically enhance its bargaining power in future negotiations. See Figure 13.6 in the text for an example of a union resistance curve that is not always downward sloping.

14. Answer d. Note that wait unemployment can cause the relative wage advantage to understate or overstate the absolute union wage effect.

15. Answer c. Expected earnings in each sector are equal when WUFU = WNFN  FU =

WN 1 FN  FU = (1) = 0.8.

WU 1.25

16. Answer d. All factors that can influence wages must be held constant before the relative union wage advantage can be identified.

17. Answer d. Limits on the substitution of capital for labor mean that the firm may not be able to produce using the most efficient combination of inputs. Note that empirical evidence associates unions with lower quit rates, which would likely increase productivity.

18. Answer b. If unions allow workers to communicate more effectively with management, workers may be able to resolve problems without quitting. Lower quit rates lead to longer job tenures.

19. Answer a. Person A should voluntarily accept only those shares that yield a higher level of utility than the level that is expected to result from arbitration. Note that if the person is risk averse, the expected, or average, utility from arbitration will be less than the utility level associated with the average arbitration settlement.

20. Answer a. The contract zone, like the contract curve in the efficient contract model, is where the parties should move in order to make themselves better off.

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Answers to Chapter 13

21. Answer d. Increasing the arbitrator’s range of possible outcomes and/or increasing the curvature of the utility function lowers the average utility associated with the arbitrated outcome. The lower the average utility associated with the arbitrated outcome, the lower the share that will be needed from a voluntary settlement to make any individual better off.

Problems 22a. Substituting W = $10 into the original demand yields an employment level of 80.

Substituting W = $15 into the new demand equations yields an employment level of 90.

22b. If the wage had remained at $10, the demand shift would have increased employment to 100. Alternatively, one could argue that without the demand shift, the increase in the wage would have reduced employment to 70. Either approach suggests that the union wage increase reduced employment by 10 relative to what it could have been.

23a. See Figure 13-3.

Figure 13-3.

23b. Profit maximization occurs at the employment level where MRPL = MEL  40 - 4L = 4L  L* = 5.

L* = 5  W* = 2(5) = 10.

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Answers to Chapter 13

23c. The firm now faces a fixed MEL of $16 and so profit maximization occurs where 40 - 4L = 16  L* = 6.

See point a in Figure 13-3. In this case, the higher wage is associated with a higher employment level.

23d. Employment is maximized at the point where the labor supply curve intersects the MRPL curve. See point b in Figure 13-3.

40 - 4L = 2L  L* = 6.67.

L* = 6.67  W* = 2(6.67) = 13.33.

24a. For a firm that sells its output in a perfectly competitive market MRPL = (P)(MPL)  MRPL = 5(10 - L) = 50 - 5L. This curve appears as the line labeled D in Figure 13-2 in the Applications section.

24b. Profit maximization  MRPL = W  50 - 5L = 15  L* = 7.

See point a in Figure 13-2.

L* = 7  Q* = (10)(7) - (0.5)(49) = 45.5.

24c.  = PQ - WL   = (5)(45.5) - (15)(7) = $122.5. *24d. To find the isoprofit curve expression, find those combinations of W and L that yield a profit level of $122.50. Substituting the production function and the price of output into the profit expression yields 122.5 = (5)(10L - 0.5L2) - WL  122.5 = 50L - 2.5L2 - WL  WL = 50L - 2.5L2 - 122.5  W = 5 − 2.5L −

122.5 .

L

*24e. See the isoprofit curve labeled I3 in Figure 13-2.

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Answers to Chapter 13

24f. Profit maximization  MRPL = W  50 - 5L = 30  L* = 4.

See point b in Figure 13-2.

L* = 4  Q* = (10)(4) - (.5)(16) = 32.  = PQ - WL   = (5)(32) - (30)(4) = $40.

25a. Equilibrium in the union sector  30 - 0.5W = W  W* = 20.

W* = 20  L* = 20.

Equilibrium in the non-union sector  60 - 2W = W  W* = 20.

W* = 20  L* = 20.

25b. An increase in the union wage from $20 to $22 represents an absolute wage effect of 10 percent. Note that the increase in the union wage reduces the quantity of union labor demanded to LDU = 30 − 0.5(22) = 19, while the quantity of labor supplied increases to LSU = 22.

Together this creates a labor surplus in the union sector of 3 units.

25c. The new supply curve in the union sector becomes LSU = W − 3,

while the supply curve in the non-union sector becomes LSN = W + 3.

The supply shift in the union sector is just enough to eliminate the unemployment in that sector. The increase in supply in the non-union sector creates a surplus in that sector at

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Answers to Chapter 13

the original wage of $20. However, since the wage is free to adjust in the non-union sector, the market will clear where 60 - 2W = W + 3  WN* = $19 and LN* = 22.

Note that after the spillover adjustment is complete, the union wage ($22) exceeds the non-union wage ($19) by $3 for a relative wage advantage of 15.8 percent.

25d. Since there is no unemployment in either sector after the spillover, expected earnings equal $22 in the union sector and $19 in the non-union sector. This should lead to a movement of some workers back to the union sector.

25e. The unemployment rate in the union sector will be UR =

2 = 0.095 2+9

 FU = 1 - 0.095 = 0.905  WUFU = (22)(0.905) = $19.9.

In the non-union sector, the market will clear where 60 - 2W = W + 1  WN* = $19.67 and LN* = 20.67.

Since there is no unemployment in the non-union sector, expected earnings equal $19.67.

Wait unemployment is rational here since workers should continue to flow back to the non-union sector as long as expected earnings there are greater than in the non-union sector.

25f. The unemployment rate in the union sector will be UR =

3 = 0.136 3 + 19

 FU = 1 - 0.136 = 0.864  WUFU = (22)(0.864) = $19.

In the non-union sector, the market will clear at the original wage and employment levels  WN* = $20 and LN* = 20.

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Answers to Chapter 13

Since there is no unemployment in the non-union sector, expected earnings equal $20.

This suggests that the optimal amount of wait unemployment in this example is under 3 workers. As a result the wage in the non-union sector will be less than $20. If the nonunion wage is less than $20, then the relative union wage advantage will overstate the absolute wage effect of the union.

26a. Equilibrium in the union sector  24 - 0.5W = 1.5W  W* = 12.

W* = 12  L* = 18.

Note that in this example the demand shift does not raise the wage but it does eliminate the excess supply associated with the union wage.

26b. Equilibrium in the non-union sector  36 - 2W = 2W  W* = 9.

W* = 9  L* = 18.

In the nonunion sector, the demand decrease lowers the wage from $10 to $9 and decreases employment from 20 to 18.

26c. Ignoring any wait unemployment effects, the relative wage advantage of 33 percent overstates the absolute union wage effect of 20 percent.

27a. SA = 0.5  UA =

0.5 = 0.707.

27b. SA = 0.25  U A =

2.5 = 0.5.

SA = 0.75  UA =

.75 = 0.866.

27c. Expected utility from arbitration is 1 1 (0.5) + (0.866) = 0.683 2 2

Since receiving a share of 0.5 with certainty yields a higher level of utility (.707) than receiving a share of 0.5 on average (0.683), the person exhibits risk averse preferences.

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Answers to Chapter 13

27d.

SA = 0.683  SA = 0.47.

A share of 0.47 received with certainty yields the same level of utility that can be expected from arbitration.

27e. Since the shares must add to one, the maximum share B could receive is 0.53.

27f. Since B has the same preferences as A, the minimum share B would accept is 0.47 and the maximum A could receive is 0.53.

27g. The contract zone consists of those shares between 0.47 and 0.53.

27h. SA =

1  UA = 3

2 1 = 0.577, and SA =  UA = 3 3

2 = 0.816, 3

Expected utility from arbitration is 1 1 (0.577) + (0.816) = 0.697 .

2 2 SA = 0.697  SA = 0.486

The contract zone consists of those shares between 0.486 and 0.514. Notice that a smaller spread between the arbitrator’s settlements reduces the contract zone. Assuming the size of the contract zone is directly related to the probability of a voluntary settlement, the chances for a voluntary settlement have been reduced.

Applications 28. This paradox can be resolved by noting that wages are only a part of total compensation. Evidence suggests that public sector unions have had a larger effect on employee benefits than on wages since employee benefits are not as readily observed and their full costs can often be deferred. As a result, is not clear that public sector unions have had a smaller effect on the total compensation of their members.

29a. Point b is not efficient since it is possible to make one party better off without hurting the other. For example, by moving to point c, the union is better off and the firm is still at the same profit level. On the other hand, moving to point d increases firm profits while leaving the union at the same level of utility.

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Answers to Chapter 13

29b. Each point along the line cd is a point of tangency between a union indifference curve and a firm isoprofit curve. However, the outcomes are not necessarily equitable.

Points closer to c are better for the union and worse for the firm, while points closer to d are better for the firm and worse for the union. Regardless of which party gains the most, all the points along cd are better than point b.

29c. While there may be few explicit agreements on employment, Chapter 11 pointed out that provisions of an employment contract are often implicit.

30a. In the asymmetric information model, union leaders, through their involvement with management during the bargaining process, may become well informed about the firm’s true financial position and the maximum wage offer the firm can make. If this offer is less than what the membership expects, union leaders may recommend a strike even though they know it will not change the firm’s wage offer. Such a strike will gradually serve to moderate the members’ wage demands while at the same time allowing the union leaders to appear to be strong and decisive leaders.

30b. Perhaps the firm would have been more receptive to productivity bargaining.

Under this type of bargaining, the union and employer explicitly agree to certain increases in compensation contingent on work rule changes and productivity increases.

31a. Workers will be demanded up to the point where the real wage equals the marginal product of labor. Therefore, a real wage of 25 translates into an employment of 6 workers in each sector. Output in each sector will be 225 for a total output of 450.

31b. A wage increase to 35 in the union sector should reduce employment to 4 and output to 170.

31c. An employment of 8 in the non-union sector should drive the wage down to 15 and increase output to 260.

31d. Total output after the labor spillover is 430 compared to 450 before the union wage increase. The allocation of labor is not optimal since the marginal product of labor is higher in the union sector than in the non-union sector.

31e. Assuming no spillovers, output would be 170 in the union sector and 225 in the non-union sector for a total output of 395. This represents a decline of 55 units from the original level.

31f. A collective voice is necessary since many improvements in the workplace can be likened to public goods. A public good is something that no one can be excluded from once it is provided. A good example is national defense. If workplace changes are like public goods, individuals may not come forward to bring about change, reasoning that if they wait for someone else to come forward, they will share in the benefits without bearing the costs.

Individuals may also not come forward out of fear of retaliation by the firm.

409

ANSWERS TO CHAPTER 14 Review Questions 1. Answer a. u=

U 15 = = 010 . .

U + E 15 + 135

2. Answer a. The degree of economic hardship is clearly influenced by the percentage of the population that is employed, and yet the unemployment rate does not provide a reliable guide to how the employment rate is changing. If the labor force participation rate is growing fast enough, the employment rate will rise even if the unemployment rate is rising.

3. Answer c. The proportions can also be viewed as transition probabilities--in this case, the probability of moving from unemployment to employment during the month.

4. Answer a. As people flow from e to n, the numerator of the unemployment rate stays constant, but the denominator decreases, raising the entire fraction.

5. Answer d. Labor markets are inherently dynamic, resulting in continual flows between the various labor market states. Because information is imperfect, it may take workers and firms some time to match up.

6. Answer b. An increase in the replacement rate should increase unemployment benefits and lower the marginal cost associated with job search.

7. Answer b. A higher reservation wage means that more low-wage offers are ruled out, thus raising the expected wage.

8. Answer d. Structural unemployment results in a mismatch of workers and jobs in different occupations and geographic areas.

9. Answer a. Advance notice of a plant closing gives the workers time to consider geographic changes or human capital investments that will allow them to be employed in other sectors of the labor market.

10. Answer c. The unemployment associated with efficiency wages is similar to the phenomenon of wait unemployment discussed in Chapter 13.

11. Answer b. The supply and demand model suggests that unemployment (a surplus of labor) occurs when wages are too high, but the wage curve highlights the fact that high unemployment is associated with low wages.

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Answers to Chapter 15

12. Answer c. When unemployment is high, workers are less likely to shirk, and so firms need not pay a high efficiency wage premium.

13. Answer d. A change in required skills is more likely to result in structural unemployment.

14. Answer a. By collectively not undercutting the prevailing wage, workers may end up with a higher present value of earnings stream.

15. Answer c. An imperfect experience rating system increases the benefits to firms of laying off workers.

16. Answer a. No experience rating means that the tax rate paid by firms would be independent of the number of workers laid off.

17. Answer b. Note that a and c are also true for demand deficient unemployment and yet that does not make such unemployment voluntary.

18. Answer b. New entrants are only one part of the unemployed “pool” every month.

19. Answer d. Teenagers and blacks traditionally have above-average unemployment rates. Therefore, if their proportions in the labor force fall, the unemployment rate should fall. An increase in women does not counteract this trend because the unemployment rate for women now tends to be closer to that for men.

20. Answer a. This relationship was originally known as Okun’s law.

Problems 21a. u = 20/250 = 0.08.

21b. lfp = 250/400 = 0.625.

21c. e = 230/400 = 0.575.

21d. Substituting u = 0.1 and e = 0.575 into e = lfp(1 - u)  0.575 = lfp(0.9)  lfp = 0.639.

Therefore, given that the unemployment rate rose to 0.1, the labor force participation rate must rise to 0.639 (an increase of 1.4 percentage points) if the employment rate is to remain constant.

417

Answers to Chapter 15

22a. Sector A: 20 - W = W  WA* = $10  LA* = 10.

Sector B: 40 - 2W = 2W  WB* = $10  LB* = 20.

22b. Because of the time needed to make job matches, there will still be some positive rate of unemployment even when markets are in equilibrium. This is the idea behind frictional unemployment.

22c. Substituting W = 10 into the supply and demand equations  LDA = 15 − 10 = 5 and LSA = 10.

Therefore, there are 5 workers unemployed in sector A. Solving for the new equilibrium in sector B Sector B: 45 - 2W = 2W  WB* = $11.25  LB* = 22.5.

22d. If the 5 unemployed workers were subtracted from the supply in A and added to the supply in B, a new equilibrium would occur where Sector A: 15 - W = W - 5  WA* = $10  LA* = 5.

Sector B: 45 - 2W = 2W + 5  WB* = $10  LB* = 25.

22e. The costs of occupational and geographic mobility restrict these adjustments.

22f. If the adjustments could not be made, the unemployment could be classified as structural.

23a. The area of the distribution to the left of 50 is (50 - 10)(0.02) = 0.8. Therefore, if any offer in that range is acceptable, the person has an 80 percent chance of receiving a job offer.

23b. Note that if WR were set at $10, the probability of getting a better offer is 80 percent. On the other hand, if the reservation wage were set at $50, the probability of getting a better offer is zero (given the skill level of this individual). Hence, for reservation wages between $10 and $50 the probability (P) of getting a better offer can be written as P=

50 − WR .

50

418

Answers to Chapter 15

23c. Since the average wage in the interval between WR and $50 can be written as (WR+50)/2, this wage would represent a gain (G) over WR of G=

WR + 50 W + 20 − 2 WR 50 − WR − WR  G = R G= .

2 2 2

23d. Multiplying G by P yields the expected gain from additional job search (EG)

EG = (P)(G) =

50 − WR 50 − WR (50 − WR ) 2  EG = .

50 2 100

23e. Assuming for simplicity that the marginal cost of an additional period of job search is constant at $1, the optimal value for the reservation wage occurs where

(50 − WR ) 2 = 1  WR = 50 − 100 = $40.

100 23f. Note that by setting a reservation wage of $40, the individual deliberately reduces his or her chances of a job offer from 0.8 to (50 - 40)(0.02) = 0.2 (from 80 percent to 20 percent). The dramatic reduction occurs because of the low marginal cost associated with additional periods of job search.

23g. A reservation wage strategy is a deliberate and purposeful restriction of the probability of flowing from unemployment to employment. If everyone does this, it lowers Pue in the stock flow model and so raises the unemployment rate.

Applications 24a. Since the person now has the highest skill level, he or she has a 100 percent chance of receiving a job offer.

24b. Note that if WR were set at $10, the probability of getting a better offer is 100 percent. On the other hand, if the reservation wage were set at $30, the probability of getting a better offer is zero (given the skill level of this individual). Hence, for reservation wages between $10 and $30 the probability (P) of getting a better offer can be written as P=

30 − WR .

20

419

Answers to Chapter 15

24c. Since the average wage in the interval between WR and $30 can be written as (WR+30)/2, this wage would represent a gain (G) over WR of G=

WR + 30 W + 30 − 2 WR 30 − WR − WR  G = R G= .

2 2 2

24d. Multiplying G by P yields the expected gain from additional job search (EG)

EG = (P)(G) =

30 − WR 30 − WR (30 − WR ) 2  EG = .

20 2 40

24e. Assuming for simplicity that the marginal cost of an additional period of job search is constant at $2, the optimal value for the reservation wage occurs where

(30 − WR ) 2 = 2  WR = 30 − 80 = $21.06.

40 24f. Note that by setting a reservation wage of $21.06, the individual deliberately reduces his or her chances of a job offer from 1.0 to (30 - 21.06)(0.05) = 0.447 (from 100 percent to about 45 percent).

24g. Note that the increase in skill level has raised the reservation wage substantially, from $11.06 in the Summary section Example problem to $21.06 here. However, note that the probability of a job offer has remained at 0.447. Thus the proportion of people flowing from unemployment to employment should be unchanged.

25a. This firm would face the minimum unemployment insurance (UI) tax rate. Its tax payment for each worker is computed by multiplying the tax rate times the worker’s earnings if the earnings are less than the specified taxable wage base (e.g., $10,000). If earnings exceed the base, the tax payment for the worker is the tax rate times the wage base.

25b. The firm would have contributed less because of the imperfect experience rating of the UI tax rate. This refers to the tendency of the UI tax rate to rise with layoff experience at a lower rate than is necessary to make the employer’s marginal cost of layoff equal to the marginal UI benefits paid out to laid-off workers. Note that the tax rate also has a ceiling so that at some point additional layoffs have no effect on the UI tax rate. The rest of the money paid out to unemployed workers comes from the firms that conducted no layoffs but still paid their UI taxes.

25c. Since low-layoff firms are essentially subsidizing high-layoff firms, the high-layoff firms are more likely to survive and grow, thus increasing the incentive to use layoffs.

More widespread use of layoffs increase the proportion of people flowing from employment to unemployment.

420

Answers to Chapter 15

26a. Earnings = $400, taxes paid = 0.255(400) = $102, after tax earnings = $298 ($7.45 per hour).

26b. UI benefits = $220, taxes paid = 0.18(220) = $39.6, after tax benefits = $180.4 ($4.51 per hour).

26c. The marginal cost of being unemployed is only $117.6 per week ($2.94 per hour).

If UI benefits were subject to Social Security and Medicare taxes, the marginal cost of unemployment would be higher, raising the cost of job search, and lowering the duration of job search unemployment. *27a. PVCut = 9.9 +

5 5 + = 19.07.

1.06 1.06 2

*27b. Expected wage = 0.4(5) + 0.6(10) = 8. *27c. PVWait = 5 +

8 8 + = 19.67.

1.06 1.06 2

27d. On average, the person is better off holding out for the prevailing wage even if it means a spell of unemployment.

421

ANSWERS TO CHAPTER 15 Review Questions 1. Answer a. The distribution can also be described by the percentage of people falling within specified earnings ranges.

2. Answer b. The average (mean) and median earnings are measures of the central location of the distribution.

3. Answer b. The variance is the only dispersion measure listed that would increase if all earnings were multiplied by some constant number.

4. Answer d. The median, standard deviation, and variance would all remain the same.

The coefficient of variation would fall since its numerator, the standard deviation, would be constant while its denominator, the mean, would increase by $1,000.

5. Answer a. According to Table 15.1 in the text, the 80-20 ratio for men rose from 3.08 in 1980 to 3.41 in 2005, a 10 percent increase. Over the same time period, the ratio for women increased by about 6%, from 3.70 to 3.94.

6. Answer c. According to Table 15.1 in the text, real earnings for men at the 20 th percentile fell and the 80th percentile rose over the period 1980-2005. Over this same period, the earnings of women at the 20th and 80th percentiles rose, with the largest increases being at the top of the distribution.

7. Answer d. Mathematically, each of these changes would lead to the distribution of earnings becoming more stretched.

8. Answer c. According to Table 15.2 in the text, the 80:50 ratios increased over this period for both men and women, showing worsening inequality. At the same time, the 50:20 ratios improved for both groups, showing slightly improving inequality.

9. Answer a. These trends are clearly indicated in Table 15.3 of the text. Note the significant increases in the returns to education for both men and women. For women, the average earnings of college graduates relative to high school graduates rose from 1.36 to 1.85 over the period 1980-2005, a 36 percent increase; the increase for males, from 1.41 to 1.91, was 35 percent. Returns to other types of education also generally increased, but not by as much.

10. Answer d. See Table 15.3 in the text. The gain in relative earnings for college educated men is due both to the falling earnings of high school graduates and to rises in their own earning. In contrast, the gain in relative earnings for women were due exclusively to the rising earnings (over 26 percent) of college-educated women; earnings of high school-educated women actually rose slightly over the period..

410

Answers to Chapter 14

11. Answer d. Returns to a college education increased in both periods, but higher returns also encourage entry into the market, so the supply of college graduates also increased. This lowered the return to a college education relative to what it would have been without the increase in supply.

12. Answer b. Note that in Table 15.3 of the text, the ratio of earnings at the 80th and 20th percentiles rose for each male human capital group over the period 1980-2005.

13. Answer d. Note that each of these factors would increase earnings inequality by affecting relative wages.

14. Answer b. If supply shifts had been the cause, the share of aggregate employment accounted for by less-educated workers would have grown. However, just the opposite change took place, supporting the hypothesis of relative demand shifts in favor of moreeducated workers. Explanations related to institutional factors such as the declining share of unionism are flawed for several reasons. For example, union membership has been declining steadily since the mid-1950s, yet the increases in earnings inequality have not occurred until more recently.

15. Answer d. Answer a corresponds to a scale effect favoring more-educated workers, while answer b refers to a substitution effect in favor of more-educated workers.

16. Answer b. Several studies cited in the text suggest that shifts in employment across industries played a relatively small role in raising the relative wage of college-educated workers.

17. Answer d. Recall that when two inputs are gross complements, a reduction in the price of one leads to an increase in the demand for the other. While the rising wage inequality in other countries is consistent with the technological change explanation, the differences in rates have focused attention on factors other than the demand side of the labor market.

18. Answer c. Note that answers a and b together simply assure a decrease in the demand for unskilled labor. Without seniority rule, there would not necessarily be a larger decrease in demand for younger unskilled workers.

19. Answer c. When the Lorenz curves cross, it is possible for the area between each curve and the line of perfect equality to be the same. Since the Gini coefficient is this area divided by 0.5, the same Gini coefficient can be associated with two different Lorenz curves.

20. Answer d. Note that if all earnings increase by the same proportion, the Lorenz curve will be unchanged.

411

Answers to Chapter 14

Problems 21a. The variance is reduced to 1440 and the coefficient of variation is reduced to 0.47.

21b. The variance is now 2080 and the coefficient of variation is 0.57.

21c. Many people would view the first redistribution as bringing about greater equality since it brings the ends of the distribution closer. Note that both measures show a larger decrease for the first redistribution.

21d. In the first case, the 80-20 ratio would fall to 100/40 = 2.5. In the second case, the ratio would actually rise to 120/20 = 6. The response in the first case seems consistent with the reduced inequality. The response in the second case seems to indicate more inequality, even though earnings have been redistributed away from the richest person.

22a. In group A the mean is $80, the variance is 66.67, and the coefficient of variation is 0.10. In group B the mean is $20, the variance is 66.67, and the coefficient of variation is 0.41.

22b. For the entire population, the variance is 966.67 and the coefficient of variation is 0.62.

22c. The mean earnings for group A are still $80, but the variance has increased to 150 and the coefficient of variation has increased to 0.15. The mean earnings for group B are still $20, but the variance has increased to 150 and the coefficient of variation has increased to 0.61.

22d. For the entire population, the variance has increased to 1050 and the coefficient of variation has increased to 0.65. The increased within-group dispersion had increased the inequality measures for the entire group. The increased within-group dispersion is consistent with the earnings patterns observed in the United States. The difference is that the increased within-group dispersion in the United States has also been accompanied by a rise in across-group dispersion as the earnings of more-educated workers have risen relative to the earnings of less-educated workers. In this example, the ratio of average earnings in group A to average earnings in group B remained constant.

23a. C = 1500(0.1) + 0 = 150.

23b. C = 0 + 0.2(500) = 100.

23c. C = 800(0.1) + 0.2(-200) = 40. *24a. Since the mean and the median earnings are both $80,  = 0.

412

Answers to Chapter 14

*24b. This redistribution lowers the variance from 2400 to 2080. Given that the median earnings is now $60, while the mean is $80, and the standard deviation is 45.61,  is computed as 1.32. Since  > 0, the distribution is skewed to the right. *24c. Note that in this example, increased equality was accompanied by increased skewness. This serves as a reminder that dispersion and skewness are separate and distinct characteristics of any earnings distribution. *24d. Recall that an earnings distribution that is skewed to the right means that individuals are bunched at the lower end of the distribution, while a few individuals have high incomes. This type of distribution violates many people’s sense of fairness.

25a. See curve L1 in Figure 15-1.

Figure 15-1.

The coordinates of the points on the Lorenz curve are (0,0), (0.2,0.05), (0.4,0.15), (0.6,0.35), (0.8,0.6), and (1,1). *25b. To find the area under the Lorenz curve, add the areas of rectangles a, b, c, and d, for a total area of 0.23. The remaining triangles have an area of 0.1 since each has a base equal to 0.2 and their height sums to one. Given that the total area under the Lorenz curve is 0.33, the Gini coefficient is given by Gini =

0.5 − 0.33 = 0.34.

0.5

25c. See curve L2 in Figure 15-2. The coordinates of the points on the new Lorenz curve are (0,0), (0.2,0.08), (0.4,0.2), (0.6,0.35), (0.8,0.55), and (1,1). Curve L1 is repeated for comparison purposes.

413

Answers to Chapter 14

Figure 15-2.

25d. Since the Lorenz curves cross, a conclusion about which represents the greater equality is not possible. *25e. Using the same method as before, the area under L2 is computed as 0.336. This yields a Gini coefficient of 0.328, slightly smaller than the previous one. This suggests that the second distribution displays more earnings equality.

Applications 26a. The growing inequality for men took place in the context of falling real earnings along all points in the earnings distribution. Hence, the higher earnings group simply declined less than the rest. For women, real earnings rose along all points on the earnings distribution.

26b. The gain in relative position was largely determined by increasing returns to education.

It is hard to see how this could be construed as the rich exploiting the poor for material gain.

26c. Such supply shifts would have led to an increase in the share of aggregate employment accounted for by low-skilled workers. However, just the opposite happened.

26d. On tests of cognitive achievement, the scores of high school graduates actually rose relative to those of college graduates during the 1980s (even though the scores for both groups were falling). Since the relative quality of labor supplied by high school graduates seemed to be rising, this can not explain the rising wage gap between more- and lesseducated workers.

26e. Union membership as a percentage of the labor force peaked in 1954, and has been declining steadily since then. If this decline were the major factor explaining the increasing returns to education, it would be very difficult to explain why the returns to education dropped significantly during the 1970s. As noted in the text, women have traditionally been less unionized than men, so declining unionization should not have had as much impact on their rate of return from education. That the returns to education for women rose as fast as or faster than those for men during the 1980s does not appear to have any relationship to the decline in unionization.

414

Answers to Chapter 14

27a. I would be willing to pay up to $1 million for A, but nothing for B. 27b. In this example, very slight differences in productivity are translated into very large differences in earnings because of the winner-take-all nature of the contest.

27c. Such contests would increase the within-group dispersion of earnings significantly.

This, in turn, would increase the inequality of the overall population.

27d. According to the hypothesis presented in Chapter 1, concern for relative standing tends to flatten the relationship between wages and productivity. This would tend to reduce the dispersion of earnings both within and across groups.

28a. Originally, the person worked 100 hours at $4 per hour for total earnings of $400. After the welfare program, work hours were cut back to 53.125 for total earnings of $212.5.

28b. This person was not effected by the program. Earnings remained constant at $1,200.

28c. The welfare program increased the dispersion of earnings by leading the lower earnings person to cut back on his or her work hours.

29a. The Lorenz curve is unchanged since the share of earnings going to any particular group has not changed. *29b. See curve L3 in Figure 15-3. The coordinates of the points on the Lorenz curve are (0,0), (0.2,0.08), (0.4,0.2), (0.6,0.4), (0.8,0.64), and (1,1). Curve L1 is repeated for comparison purposes. The new Gini coefficient is 0.27. In this case, both the Lorenz curve and the Gini coefficient reflect increased earnings equality.

Figure 15-3.

29c. The after-tax income distribution tends to be more equal than the earnings distribution because of government transfers to the poor and higher tax rates for the rich.

415

ANSWERS TO CHAPTER 16 1. Answer a. The production possibilities curve has a slope of -5. This tells how much corn must be given up to attain an additional unit of wheat.

2. Answer d. If 1 unit of wheat costs 2 units of corn as the slope of the production possibilities curve indicates, then it is possible to express that same tradeoff as 1 unit of corn for one-half unit of wheat.

3. Answer b. Per capita consumption in the U.S. is 0.4 units of wheat and 2 units of corn. In Canada, per capita consumption is 0.9 units of wheat and 4.8 units of corn.

Canada has the higher real wage rates in this case.

4. Answer d. The limits of the terms of trade are between 2 and 5 units of corn for a unit of wheat, or conversely, between one-half and one-fifth units of wheat for one unit of corn. All the answers fall in this range.

5. Answer c. The new “trading possibilities curve” has a slope of -4. This tells how much corn must be given up to attain an additional unit of wheat.

6. Answer d. After specialization, the U.S. will have 400 units of corn and no wheat (point b), and Canada will have 120 units of wheat and no corn (point v). To get from these points to the final allocations, Canada must have traded 50 units of wheat to the U.S. for 200 units of corn.

7. Answer d. While both countries still fully employ their resources, all farmers in the U.S. now produce corn, while all Canadian farmers produce wheat. Before trade, there used to be some of both in each country. Note however, that per capita consumption levels have risen, indicating higher real wages through the shifting out of the production possibilities curve for each country.

8. Answer c. Lower wages abroad mean that total production costs for U.S. firms (that have overseas facilities) will fall. This decreases firm costs and increases supply (in a competitive market). Thus the price of the final product will fall, and output will increase as quantity demanded rises. At a higher scale of production, firms will demand more of all types of workers, increasing the U.S. demand for labor.

9. Answer a. Lower wages abroad make the ratio of wages to marginal productivity abroad lower than it was previously and encourages substitution of foreign labor for domestic labor. The demand for U.S. labor falls.

10. Answer b. Where foreign labor is a large part of the cost of production, a fall in its price will lead to a large decrease in total costs, which will make the scale effect relatively larger, and thus it is more likely that the demand for labor will increase.

1

11. Answer d. Although empirical studies show mixed results, on average the consensus seems to be that current effects of international trade have reduced employment greatly in some sectors, but since labor is relatively mobile, overall effects have been slightly negative but small.

12. Answer b. A lower wage to marginal productivity ratio will cause firms to consider moving. However, the costs of moving and trading across borders are generally very high, and thus firms are only likely to move if the cost savings is large enough to outweigh the additional costs of relocating production.

13. Answer a. Wage convergence is most likely when workers have similar skill levels and the location of production relative to the end user is not very important, as with telecommunications and many manufactured goods.

14. Answer d. The least-skilled and thus least able to adapt workers are most likely to be displaced by trade. Government assistance to these workers can both help subsidize the cost of necessary human capital investment and can help these workers move to new sectors, thus speeding the efficient reallocation of resources.

15. Answer c. The costs of trade are not limited to affected markets, particularly since workers in other areas may experience increased uncertainty and risk as well as experiencing unpredictable swings in wages.

16a. For the U.S., 1 unit of food costs 0.25 units of clothing. Conversely, 1 unit of clothing costs 4 units of food.

16b. For China, 1 unit of food costs 0.5 units of clothing. Conversely, 1 unit of clothing costs 2 units of food.

16c. The U.S. is the low-cost producer of food, China is the low cost producer of clothing.

16d. In the U.S., workers consume 2.4 units of food and 0.4 units of clothing per person, while in China, workers consume 0.2 units of food and 0.4 units of clothing per person.

16e. The U.S. should specialize in food, China should specialize in clothing.

16f. A unit of food would have to trade for at least 0.25 units of clothing (otherwise the U.S. would not cover its costs), but no more than 0.5 units of clothing (otherwise China could produce the food itself).

16g. After specialization, the U.S. would have 400 units of food and no clothing. China would have 300 units of clothing and no food. Now suppose a trade of 150 units of food for 50 units of clothing was made. The U.S. would end up with 250 units of food and 50 units of clothing. China would end up with 150 units of food and 250 units of clothing.

Per capita consumption levels would rise to 2.5 units of food and 0.5 units of clothing in

2

the U.S., and 0.25 units of food and 0.4167 units of clothing in China. These figures represent an increase in living standards for both countries.

17. Barriers to trade are constructed to avoid the transitional job losses that trade imposes. For example, in this problem even though living standards improve, initially the U.S. would have lost clothing jobs to China. Eventually these would have been made up by new jobs in the food producing sector, but this transition of resources is not always smooth or painless for many workers. To avoid making these kinds of adjustments, countries often look to devices like tariffs and import quotas to preserve existing industries and jobs.

18. Technological change and international trade are similar in that they both cause transitional job losses. With technological change, jobs are lost in the sectors producing outdated products, or through substitutions of capital for labor. Eventually, this labor is reabsorbed into the other expanding sectors of the economy that the technological change and increased efficiency has made possible, but the transition process is not always smooth or painless for many workers.

19a. The costs of trading across borders are significantly higher for many service-related industries. For example, it would not generally be cost effective for a doctor to deliver medical care from another country; the transactions costs involved would simply be too high.

On the other hand, unless the good being produced is unusually difficult or costly to transport, the cost of trading across borders, while significant, is not generally sufficient to make relocation of production facilities undesirable.

19b. Substitution effects are large because clothing production is relatively unskilled labor, and thus the elasticity of substitution between U.S. and foreign workers is large. Domestic workers remaining are likely to have jobs that are substitutes, not complements, to foreign production, and demand for these goods is elastic and thus very responsive to price/cost changes. Thus small changes in either the foreign wage or the domestic wage are likely to cause large changes in domestic employment, with no significant positive scale effects to offset them.

20a. Trade represents a reallocation of resources, not a permanent loss of resources. Jobs will be lost in those areas where Mexico can produce goods more cheaply, but at the same time, opportunities will grow in those areas where the U.S. is the low-cost producer. Because of specialization and trade, living standards (real wage rates) in both countries should rise.

20b. Import quotas do seem to preserve employment in those areas where they apply.

However, if the import quotas result in more monopoly power for domestic firms, the price increases that result may reduce the number of jobs that are really preserved. Also, the reduction in competition may lead the domestic firms to grow sluggish and inefficient, leading to even more job losses in the future.

3

INSTRUCTOR'S MANUAL to accompany

Modern Labor Economics: Theory & Public Policy Fourteenth Edition

By Ronald G. Ehrenberg, Robert S. Smith and Kevin F. Hallock

Leonie L. Stone State University of NY at Geneseo

Copyright Routledge

A NOTE TO THE INSTRUCTOR This Instructor's Manual is intended to summarize the content of the 14th edition of Modern Labor Economics: Theory and Public Policy in a way that explains our pedagogical strategy.

Summarized briefly, we believe that labor economics can be best learned if students are (1) able to see the "big picture" early on, so that new concepts can be placed in perspective; (2) moved carefully from concepts they already know to new ones; (3) motivated by seeing the policy implications or inherently interesting insights generated by the concepts being taught. To this last end, we discuss policy issues in every chapter and, in addition, employ "boxed examples" to demonstrate in historical, cross-cultural, or applied managerial settings the power of the concepts introduced.

The text is designed to be accessible to students with limited backgrounds in economics. We do employ graphic analyses and equations as learning aids in various chapters; however, we are careful to precede their use with verbal explanations of the analyses and to introduce these aids in a step-by-step fashion. To help students in the application of concepts to various issues, we have printed answers to the odd-numbered review questions for each chapter at the back of the book.

We have also endeavored to put together a text that, while accessible to all, is a comprehensive and up-to-date survey of modern labor economics. There are chapter appendices designed to be used with more advanced students in generating additional insights.

In the first part of this Instructor's Manual, we present a brief overview and the general plan of Modern Labor Economics. We then present a chapter-by-chapter review of the concepts presented in the text. In the discussion of each chapter we list the major concepts or understandings covered, and in some cases suggest topics or sections that could be eliminated if time must be conserved. We also present our answers to the even-numbered review questions at the end of each chapter.

An important part of this Instructor's Manual are the suggested essay questions related to each chapter. We present two suggested essay questions for each chapter.

This instructor's manual is a compilation of the work of three previous authors, Robert S. Smith (Cornell University), Robert M. Whaples (Wake Forest University), and Lawrence Wohl (Gustavus Adolphus University), and the current author, Leonie Stone.

TABLE OF CONTENTS

Overview of the Text

4

Chapter 1

Introduction

7

Chapter 2

Overview of the Labor Market

12

Chapter 3

The Demand for Labor

19

Chapter 4

Labor Demand Elasticities

28

Chapter 5

Frictions in the Labor Market

36

Chapter 6

Supply of Labor to the Economy: The Decision to Work

44

Chapter 7

Labor Supply: Household Production, the Family, and the Life Cycle

53

Chapter 8

Compensating Wage Differentials and Labor Markets

63

Chapter 9

Investments in Human Capital: Education and Training

71

Chapter 10

Worker Mobility: Migration, Immigration, and Turnover

79

Chapter 11

Pay and Productivity: Wage Determination within the Firm

86

Chapter 12

Gender, Race, and Ethnicity in the Labor Market

94

Chapter 13

Unions and the Labor Market

104

Chapter 14

Unemployment

114

Chapter 15

Inequality in Earnings

122

Chapter 16

The Labor-Market Effects of International Trade

127

OVERVIEW OF THE TEXT INTRODUCTION/REVIEW: Chapters 1 and 2 Chapter 1 - Introduction Appendix 1A - Statistical Testing of Labor Market Hypotheses Chapter 2 - Overview of the Labor Market Chapters 1 and 2 introduce basic concepts of labor economics. They are written to be accessible to students without backgrounds in intermediate theory, and can, therefore, be used as building blocks when a professor must "begin at the beginning." If the course is being taught to economics majors with intermediate microeconomics as a prerequisite, these chapters may be skipped or skimmed quickly as a review.

An appendix to Chapter 1 introduces the student to econometrics. The purpose of this appendix is to present enough of the basic econometric concepts and issues to permit students to read papers employing ordinary least squares regression techniques. We strongly recommend assigning Appendix 1A in courses requiring students to read empirical papers in the field. We also recommend (in footnote 3 of the appendix) an introductory econometrics text that could be assigned by instructors who wish to go beyond our introductory treatment.

THE DEMAND FOR LABOR: Chapters 3-5 Chapter 3 - The Demand for Labor Appendix 3A - Graphical Derivation of a Firm's Labor Demand Curve Chapter 4 - Labor Demand Elasticities Chapter 5 - Frictions in the Labor Market The demand for labor is discussed first primarily because we believe that the supply of labor is a more complex topic in many ways. Before analyzing the labor/leisure choice and household production, we first introduce students to the employer side of the market. For instructors who desire to cover topics concerned with the decision to work first, however, we note that Chapters 6 and 7, which deals with that decision, are self-contained. Therefore, nothing would be lost if Chapters 6 and 7 were taught ahead of Chapters 3, 4, and 5.

In Chapter 3 the principal question analyzed is why demand curves slope downward. In Chapter 4 we move to a discussion of the elasticity of demand, and analyze the determinants of the precise relationship between wages and employment. The concepts are used to analyze how technological change and foreign trade affect labor demand. Finally, Chapter 5 discusses frictions in the labor market, both from the employee side of the market (monopsony) and from the employer side (quasi-fixed costs, training investments, hiring investments).

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SUPPLY OF LABOR TO THE ECONOMY: Chapters 6 and 7 Chapter 6 - Supply of Labor to the Economy: The Decision to Work Appendix 6A - Child Care, Commuting, and the Fixed Costs of Working Chapter 7 - Labor Supply: Household Production, the Family, and the Life Cycle Chapters 6 and 7 analyze the decision of an individual to work for pay. The traditional analysis of the labor/leisure choice is given in Chapter 6, while in Chapter 7 the decision to work for pay is placed in the context of household production. The essential features of the decision to work for pay are included in Chapter 6. In one-quarter courses or courses in which time is scarce, Chapter 7 could be skipped; however, doing so would eliminate analyses of family labor supply decisions as well as labor supply decisions in the context of the life cycle.

FACTORS AFFECTING THE CHOICE OF EMPLOYMENT: Chapters 8-10 Chapter 8 - Compensating Wage Differentials and Labor Markets Appendix 8A - Compensating Wage Differentials and Layoffs Chapter 9 - Investments in Human Capital: Education and Training Appendix 9A - A "Cobweb Model" of Labor Market Adjustment Appendix 9B - A Hedonic Model of Earnings and Educational Level Chapter 10 - Worker Mobility: Migration, Immigration, and Turnover Once they have decided to seek employment, prospective workers encounter important choices concerning their occupation and industry, as well as the general location of their employment.

Chapters 8 through 10 analyze these choices, with Chapters 8 and 9 focusing on industry/occupational choice and Chapter 10 on the choice of a specific employer and the location of employment. More particularly, Chapter 8 presents an analysis of job choice within the context of jobs that differ along nonpecuniary dimensions. Chapters 9 and 10 analyze issues affecting worker investments in skill acquisition (Chapter 9) and job change (Chapter 10), and both employ the concepts of human capital theory. All three chapters contain appendices of interest to instructors who wish to teach more advanced material.

ANALYSES OF SPECIAL TOPICS IN LABOR ECONOMICS: Chapters 11-16 Chapter 11 - Pay and Productivity Chapter 12 - Gender, Race, and Ethnicity in the Labor Market Analysis Chapter 13 - Unions and the Labor Market Appendix 13A - Arbitration and the Bargaining "Contract Zone" Chapter 14 – Unemployment Chapter 15 -- Inequality in Earnings Appendix 15A - Lorenz Curves and Gini Coefficients Chapter 16 – The Labor-Market Effects of International Trade and Production Sharing 5

Having presented basic concepts and analytical tools necessary to understand the demand and supply sides of the labor market, we now move to analyses of special topics: compensation, discrimination, unions, unemployment, inequality, and international issues. A complete analysis of all these topics requires an understanding of behavior on both the demand and supply sides of the market, and these chapters are built upon the preceding ten. No new analytical tools are introduced in these chapters.

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CHAPTER 1 - INTRODUCTION Because the textbook stresses economic analysis as it applies to the labor market, students must understand the ways economic analyses are used. The basic purpose of Chapter 1 is to introduce students to the two major modes of economic analysis: positive and normative.

Because both modes of analysis rest on some very fundamental assumptions, Chapter 1 discusses the bases of each mode in some detail.

In our treatment of positive economics, the concept of rationality is defined and discussed, as is the underlying concept of scarcity. There is, in addition, a lengthy discussion of what an economic model is, and an example of the behavioral predictions flowing from such a model is presented. The discussion of normative economics emphasizes its philosophical underpinnings and includes a discussion of the conditions under which a market would fail to produce results consistent with the normative criteria. Labor market examples of governmental remedies are provided.

The appendix to Chapter 1 introduces the student to ordinary least squares regression analysis.

It begins with univariate analysis, introduced in a graphical context, explaining the concepts of dependent and independent variables, the "intercept" and "slope" parameters, the "error term," and the t statistic. The analysis then moves to multivariate analysis and the problem of omitted variables.

List of Major Concepts 1. The essential features of a market include the facilitation of contact between buyers and sellers, the exchange of information, and the execution of contracts.

2. The uniqueness of labor services affects the characteristics of the labor market.

3. Positive economics is the study of economic behavior, and underlying this theory of behavior are the basic assumptions of scarcity and rationality.

4. Normative economics is the study of what "should be," and theories of social optimality are based in part on the underlying philosophical principle of "mutual benefit. " 5. A market "fails" when it does not permit all mutually beneficial trades to take place, and there are three common reasons for such failure.

6. A governmental policy is "Pareto-improving" if it encourages additional mutually beneficial transactions. At times, though, the goal of improving Pareto efficiency conflicts with one of generating more equity.

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7. The concept that governmental intervention in a market may be justified on grounds other than the principle of mutual benefit is discussed (for example, government intervention may be justified on the grounds that income redistribution is a desirable social objective).

8. (Appendix) The relationship between two economic variables (e.g., wages and quit rates) can be plotted graphically; this visual relationship can also be summarized algebraically.

9. (Appendix) A way to summarize a linear relationship between two variables is through ordinary least squares regression analysis -- a procedure that plots the "best" line (the one that minimizes the sum of squared deviations) through the various data points. The parameters describing this line are estimated, and the uncertainty surrounding these estimates are summarized by the standard error of the estimate.

10. (Appendix) Multivariate procedures for summarizing the relationship between a dependent and two or more independent variables is a generalization of the univariate procedure, and each coefficient can be interpreted as the effect on the dependent variable of a one-unit change in the relevant independent variable, holding the other variables constant.

11. (Appendix) If an independent variable that should be in an estimating equation is left out, estimates of the other coefficients may be biased away from their true values.

Answers to Even-Numbered Review Questions 2. Are the following statements "positive" or "normative"? Why? a. Employers should not be required to offer pensions to their employees. b. Employers offering pension benefits will pay lower wages than they would if they did not offer a pension program. c. If further immigration of unskilled foreigners is prevented, the wages of unskilled immigrants already here will rise. d. The military draft compels people to engage in a transaction they would not voluntarily enter into; it should therefore be avoided as a way of recruiting military personnel. e. If the military draft were reinstituted, military salaries would probably fall.

Answer: (a) normative (b) positive (c) positive (d) normative (e) positive 4.

What are the functions and limitations of an economic model?

Answer: The major function of an economic model is to strip away real world complexities and focus on a particular cause/effect relationship. In this sense an economic model is analogous to an architect's model of a building. An architect may be interested in designing a building that fits in harmoniously with its surroundings, and in designing such a building, the architect may employ a model that captures the essentials of his or her concerns (namely, appearance) without

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getting into the complexities of plumbing, electrical circuits, and the design of interior office space. Similarly, an economic model will often focus on a particular kind of behavior and ignore complexities that are either not germane to that behavior or only of indirect importance.

Models used to generate insights about responses to a given economic stimulus are often not intended to forecast actual outcomes. For example, if we are interested in bow behavior is affected by stimulus B, with factors C, D, and E held constant, our model may not correctly forecast the observed behavior if stimuli C through E also change.

6. A law in one town of a Canadian province limits large supermarkets to just four employees on Sundays. Analyze this law using the concepts of normative economics.

Answer: Laws restricting employment essentially block mutually beneficial transactions. There are employees who want to work on Sundays, and there were employers who wanted to employ them on Sundays. The restrictions upon their employment prevented these transactions from occurring and therefore made both workers and their potential employers worse off. Thus from a positive point of view, this is not optimal. However, some may feel that fewer people should work on Sunday, and thus from a normative point of view, some may find it acceptable.

8. In discussing ways to reduce lung diseases caused by workplace hazards, one commentator said: “Gas masks are very uncomfortable to wear, but economists would argue that they are the socially preferred method for reducing the inhalation of toxic substances whenever they can be produced for less than it takes to alter a ventilation system.”

Comment on this quotation from the perspective of normative economics.

Answer: This commentator considers only the costs of production, and not any additional benefits from the ease of working without gas masks, so in fact it may be that this is not optimal from either a positive or normative view. From a normative point of view, some may feel that workers should not be compelled to wear uncomfortable gas masks, and thus it may be desirable to require ventilation systems rather than allowing the option of masks.

Answers to Even-Numbered Problems 2. (Appendix) Suppose that a least squares regression yields the following estimate: Wi = -1 + .3Ai, where W is the hourly wage rate (in dollars) and A is the age in years. A second regression from another group of workers yields this estimate: Wi = 3 + .3Ai - .01(Ai)2. a. How much is a 20-year-old predicted to earn based on the first estimate? b. How much is a 20-year-old predicted to earn based on the second estimate?

Answer: a. W = -1 + .3x20 = 5 dollars per hour. c. W = 3 + .3x20 - .01x20x20 = 3 + 6 - 4 = 5 dollars per hour.

4. (Appendix) Suppose you have information on which of the 13 randomly selected teenage workers in the fast-food industry worked part time and which worked full time. Variable Fi is 9

equal to 1 if the worker is employed full time, and it is equal to zero otherwise. With this information, you estimate the following relationship between wages, age, and full-time employment: Wi = –0.5 + 0.25Ai + 0.75Fi (.10) (.20) (the standard errors are in parentheses). a. How much is a 20-year-old who works full time predicted to earn based on this estimate? b. How much is a 20-year-old who works part time predicted to earn based on this estimate?

Answer: a. W = –0.5 + 0.25(20) + 0.75(1) = $5.25 b. W = –0.5 + 0.25(20) + 0.75(0) = $4.50 6. (Appendix) Compare the first regression estimate in Problem 2 with the regression estimate in Problem 4. a. Is there an omitted variable bias when the full-time variable is not included? Explain. b. What can be said about the correlation between age and full-time employment? Explain.

Answer: a. Omitting the full time/part time dummy variable creates omitted variable bias. The estimate for the full-time worker is too low, and the estimate for the part-time worker is too high. b. The assumption of the regression model is that the independent variables are uncorrelated. However, it is possible that older workers are more likely to work full time, which would create a multicollinearity problem.

Suggested Essay Questions 1. Child labor is an issue that has been discussed a lot recently. From the perspective of normative economics, explain the problem with child labor.

Answer: Pareto efficiency requires that transactions have mutual benefits, and this can be assured only if the transactions are voluntary and take place with complete information. Children may be compelled by their parents to work, and they have limited capacities to make informed decisions even in the absence of compulsion.

2. Recent television news shows have equated low wages and poor working conditions of many immigrant workers in the United States with “slave labor.” Using the concepts of normative economics, comment on the idea that the “market” outcomes of low wages and poor working conditions constitute slave labor.

Answer: The job of the labor market is to promote mutually beneficial transactions, and to work well the market must be characterized by the absence of barriers to the accomplishment of these transactions. Enslavement implies the lack of ability to transact freely, so slavery is inconsistent with the goal of accomplishing mutually beneficial transactions. While low wages and poor working conditions do characterize slavery, they may be accepted voluntarily by workers whose alternatives (for example, those in their country of origin) are even worse. Thus, low wages and poor working conditions do not necessarily imply the existence of slavery.

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3.

Consider the following statement: “The government should not let the income of those who lose their jobs fall below what they were previously earning.” Does this statement fall into the category of normative economics? Explain.

Answer: Economic theory, used normatively, is concerned with mutually beneficial transactions and the condition of Pareto efficiency. While the above statement is normative, in that it indicates what the government should do, it is “redistributive” in nature and does not address the concept of mutually beneficial transactions. To be categorized as within the scope of “normative economics,” a statement must in some way address the standards economists apply toward the achievement of Pareto efficiency: Can all parties gain by a transaction? Can some gain without anyone else losing? If some gain and some lose, can the gainers compensate the losers?

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CHAPTER 2 - OVERVIEW OF THE LABOR MARKET Our goal in this text is to move students along very carefully from what they do know to the mastery of new concepts. It is our belief that students learn most efficiently if they can associate these new ideas with an overall framework, and it is the purpose of Chapter 2 to provide that framework. This chapter has both a descriptive and an analytical purpose. One aim is to introduce students to the essential concepts, definitions, magnitudes, and trends of widely used labor market descriptors. To this purpose, the chapter discusses and presents data on such topics as the labor force, unemployment, the distribution of employment, and the level of (and trends in) labor earnings. The second aim is to provide students with an overview of labor market analysis. To this end, we discuss basic concepts of demand and supply so that students will be able to see their interaction at the very outset.

We start the overview with a discussion of demand schedules and their corresponding demand curves. Particular attention is given to the distinction between movement along a curve and shifts of a curve. Distinctions between individual and more aggregated demand curves are discussed, as is the distinction between short-run and long-run demand curves. A similar discussion and set of distinctions are made for the supply side of the market.

After both the demand and supply sides of the market have been discussed and generally modeled, we turn to the question of wage determination and wage equilibrium. Forces that can alter market equilibria are comprehensively discussed, and the chapter's major concepts are reinforced by discussions of the effects of unions, the existence of disequilibrium, and the concept of being "overpaid" or "underpaid" (including a discussion of economic rents). The chapter ends with a discussion of unemployment across various countries.

List of Major Concepts 1. The labor market and its various subclassifications (national, regional, local; external, internal; primary, secondary) are defined.

2. The "labor force" consists of those who are employed or who are seeking work, and major trends in labor force participation rates are discussed.

3. The "unemployed" are those who are not employed but are seeking work (or awaiting recall); trends in the unemployment rate are noted.

4. Changes in the industrial and occupational distribution of employment are facilitated by the labor market, which also facilitates adjustments to the "birth" and "death" of job opportunities.

5. The distinction between nominal and real wage rates is made, and the calculation of real wages is illustrated.

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6. Distinctions among wage rates, earnings, total compensation, and income are depicted graphically.

7. The labor market is one of three major markets with which an employer must deal; in turn, labor market outcomes (terms of employment and employment levels) are affected by both product and capital markets.

8. The concepts underlying a labor demand schedule are associated with product demand, the choice of technology, and the supply schedule of competing factors of production; scale and substitution effects are ultimately related to these forces.

9. Underlying a supply schedule for labor are the alternatives workers have and their preferences regarding the job's characteristics.

10. Distinctions between individual and market demand and supply curves are discussed.

11. Movements along, rather than shifts of, demand and supply curves occur when wages of the job in question change; when a variable not shown on the graph changes, the curves tend to shift.

12. The interaction of market demand and supply determines the equilibrium wage.

13. Changes in the equilibrium wage rate are caused by shifts in either the demand or supply curves. Disequilibium will persist if the wage is not allowed to adjust to shifts in demand or supply.

14. The concepts of "overpaid" and "underpaid" compare the actual wage to the equilibrium (market) wage rate.

15. Individuals paid more than their reservation wage are said to obtain an "economic rent."

16. The concepts of shortage and surplus are directly related to the relationship between actual and equilibrium wage rates.

17. Unemployment rates, and especially long-term unemployment rates, have risen in Europe relative to the United States and Canada over the recent decade; this rise may reflect the existence of relatively stronger nonmarket forces in Europe.

Answers to Even-Numbered Review Questions 2. Analyze the impact of the following changes on wages and employment in a given occupation:

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a.) A fall in the danger of the occupation. b.) An increase in product demand. c.) Increased wages in alternative occupations.

Answer: (a) A fall in the danger of the occupation, other things being equal, should increase the attractiveness of that occupation, shifting the supply curve to the right and causing employment to rise and wages to fall. (b) An increase in product demand will shift the demand for labor curve to the right causing both wages and employment to increase. (c) Increased wages in other occupations will render them relatively more attractive than they were before and cause the supply curve to the occupation in question to shift to the left. This will cause employment in this market to fall and wages to rise.

4. Suppose a particular labor market was in market-clearing equilibrium. What could happen to cause the equilibrium wage to fall? Suppose price levels were rising each year, but money wages were “sticky downward” and never fell; how would this market adjust?

Answer: Starting from the position of equilibrium, a labor market could experience a fall in the equilibrium wage if either the demand curve shifts to the left or the supply curve shifts to the right. If wages are sticky downward, the wage cannot fall when demand falls. Thus, at the old wage, there will be a surplus of labor (unemployment).

6. Ecuador is the world’s leading exporter of bananas, which are grown and harvested by a large labor force that includes many children. Assume Ecuador now outlaws the use of child labor on banana plantations. Using economic theory in its positive mode, analyze what would happen to employment and wages in the banana farming industry in Ecuador. Use demand and supply curves in your analysis.

Answer. Outlawing child labor on banana plantations reduces the supply of labor to these plantations, shifting the supply curve to the left. With a fixed demand curve, this shift in the supply curve drives up wages and drives down employment.

8.

Assume that the war in Iraq increased the desired size of the U.S. military, and assume that potential recruits were reduced by the prospect of facing dangerous, unpleasant wartime conditions. First, analyze how the war affected the supply curve and the demand curve for military personnel. Second, use your analysis to predict how the war affected the wages and the employment level of military personnel.

Answer: The demand for military personnel increases while the supply of military personnel decreases. This will increase the wages of military personnel, but the effect on employment depends on the relative size of the shifts.

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10. Suppose we observe that employment levels in a certain region suddenly decline as a result of (a) a fall in the region's demand for labor, and (b) wages that are fixed in the short-run. If the new demand for labor curve remains unchanged for a long period and the region's labor supply curve does not shift, is it likely that employment in the region will recover? Explain.

Answer: The initial response to a leftward shift in the labor demand curve in the context of fixed wages is for there to be a relatively large decline in employment. This decline in employment is larger than the ultimate decline in employment. The initial disequilibrium between demand and supply in the labor market should force wages down in the long-run, and as wages decline firms will move downward along their labor demand curves and will begin to employ more labor.

However, employment in the region would recover to its prior level (assuming no subsequent shifts in demand or supply curves) only if the supply curve was vertical; if supply curves are upward-sloping, the declining wage will cause some withdrawal of labor from the market and employment will not recover to its prior level.

Answers to Even-Numbered Problems 2. Suppose that the supply curve for school teachers is Ls = 20,000 + 350W and the demand curve for school teachers is Ld = 100,000 – 150W, where L = the number of teachers and W = the daily wage. a. Plot the demand and supply curves. b. What are the equilibrium wage and employment level in this market? c. Now suppose that at any given wage 20,000 more workers are willing to work as school teachers. Plot the new supply curve and find the new wage and employment level. Why doesn't employment grow by 20,000?

Answer: a. See the figure. Plot the Ld and Ls curves by solving for desired employment at given wage rates. If W = 500, for example, employers desire 25,000 workers (Ld = 100,000 – 150x500); if W = 400, they would desire 40,000. Since the equation above is for a straight line, drawing a line using these two points gives us the demand curve. Use the same procedure for the labor supply curve.

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b. To find the equilibrium, solve for the wage at which the quantity of labor supplied equals the quantity of labor demanded: Ls = 20,000 + 350W = 100,000 – 150W = Ld. Solve for W by adding 150W to both sides and subtracting 20,000 from both sides to yield 500W = 80,000.

Dividing both sides by 500 reveals that W = $160 per day. Plugging W = $160 into both the labor demand and supply equations shows that L = 76,000 schoolteachers. c. The new labor supply curve is Ls' = 40,000 + 350W. Setting this equal to Ld and solving shows that W = $120 per day; L = 82,000 school teachers. Employment doesn't grow by 20,000 because the shift in the supply curve causes the wage to fall, which induces some teachers to drop out of the market.

4. Suppose the adult population of a city is 9,823,000 and there are 3,340,000 people who are not in the labor force and 6,094,000 who are employed. a. Calculate the number of adults who are in the labor force and the number of adults who are unemployed. b. Calculate the labor force participation rate and the unemployment rate.

Answer: a. Number in the labor force = 9,823,000 – 3,340,000 = 6,483,000 people.

Number unemployed = 6,483,000 – 6,094,000 = 389,000. b. Participation = 6,483,000/9,823,000 = .659 or 66%.

Unemployment rate = 389,000/6,483,000 = .06 or 6%.

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6. The following table gives the demand and supply for cashiers in retail stores.

Wage Rate ($)

Number of Cashiers Demanded

Number of Cashiers Supplied

3.00

200

70

4.00

180

100

5.00

170

120

6.00

150

150

7.00

130

160

8.00

110

175

9.00

80

190

a. Plot the supply and demand curves. b. What are the equilibrium wage and employment levels in this market? c. Suppose the number of cashiers demanded increases by 30 at every wage rate. Plot the new demand curve. What are the equilibrium wage and employment level now?

Answer: a. Can be easily plotted from the table. b. The equilibrium wage is $6.00, and the employment level is 150 cashiers. c. Demand shifts rightward. The equilibrium wage is $7.00, and the employment level is 160 cashiers.

Suggested Essay Questions 1. American students have organized opposition to the sale by their campus stores of university apparel made for American retailers by workers in foreign countries who work in “sweatshop” conditions (long hours at low pay in bad working conditions). Assume this movement takes the form of boycotting items made under sweatshop conditions. (a) Analyze the immediate labor market outcomes for sweatshop workers in these countries, using demand and supply curves to illustrate the mechanisms driving this outcome.

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(b) Assuming that actions by American students are the only force driving the improvement of wages and working conditions in foreign countries, what must these actions include to ensure that the workers they are unambiguously better off?

Answer. (a) The demand curve for low-wage workers in foreign countries shifts to the left when the product demand for the apparel they made falls. This drives down wages and employment (assuming a fixed supply curve). (b) To avoid the effects in (a), students in the U.S. must be willing to buy the same quantity and quality of apparel at higher prices – that is, they must be willing to pay a premium for apparel made by better-paid workers.

2. Comment on the following quotation: “One way that a minimum wage could result in expanded employment is if the government sets the minimum below the market equilibrium wage.”

Answer: Absent conscription, firms cannot pay below the market wage, because at that wage, demand exceeds supply (supply becomes the constraint on employment). With wages below equilibrium, the competition for employees among employers will drive the wage up toward the market-clearing level. Thus, a below-market minimum wage will not be binding (that is, firms will voluntarily pay more than the minimum wage to their workers).

3. Part-time workers are generally paid less than full-time workers on an hourly basis. Think about why this is the case by considering a situation in which the demand curves for fulltime and part-time workers are different, but supply to the two kinds of jobs comes from the same pool of workers. Could a wage gap between part-time and full-time jobs be sustained in this situation? Explain your answer.

Answer: Workers from the same pool will apply for the same jobs, and a wage gap between full- and part-time jobs would lead to more applications in the higher-wage sector and fewer in the lower-wage one. Thus, the responsiveness of applications to wage differences will eventually eliminate such differences. Note that it is the difference in wages that drives applications, not the difference in demand curves between the two sectors.

4. How will a fall in the civilian unemployment rate affect the supply of recruits for the volunteer army? What will be the effect on military wages?

Answer: Supply curves to a given occupation are drawn holding alternative opportunities constant. If those opportunities become more attractive, the supply curve to the given occupation will shift left and tend to drive up wages. Thus, a fall in the unemployment rate will shift the army's supply curve to the left (there will be fewer recruits at each army wage rate), and the army's wages will be driven up.

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CHAPTER 3 - THE DEMAND FOR LABOR This chapter studies the downward sloping nature of the labor demand curve. It begins with a section that discusses profit maximization, and it moves deductively from the assumption of profit maximization to the marginal conditions with respect to labor. These conditions are expressed in simple mathematical terms, and they are also discussed verbally. Additional insights into the marginal productivity theory of demand are provided in a section discussing common objections to this theory of demand.

The analysis of demand begins with the assumption that both labor and product markets are competitive; in this context, we first consider the short-run before moving on to the long-run and the case with more than two inputs. Next we consider the demand for labor when the product market is not competitive, and then move to an analysis of demand when the labor market is monopsonized. In the latter context, we contrast the wage and employment effects of "market" and "mandated" shifts in the labor supply curve.

The chapter concludes with a policy analysis of payroll taxes that demonstrates the insights that can be derived from an understanding of the demand for labor. The principal conceptual tool employed involves distinguishing between the wage rate employers pay and the wages employees receive. When these two wages differ, one must be stated in terms of the other for the demand and supply curves to be shown together. When a payroll tax is introduced, one of the two curves must therefore shift, and there will be related changes in both wages and employment.

The appendix to Chapter 3 is designed for students who feel comfortable using microeconomic theory at the intermediate level. We derive the demand for labor graphically using a two-factor model in both the long-run and short-run. Both substitution and scale effects are graphically illustrated, and the assumptions underlying the demand curve are more rigorously presented.

Any instructors wishing to skip over the appendix can do so without loss of concepts needed to understand the basics of the demand for labor.

List of Major Concepts 1. The assumption of profit maximization by firms underlies the theory of labor demand. The process of profit maximization requires considering small changes in inputs (or outputs), and comparing the marginal revenue generated by an additional input with its marginal expense.

2. The marginal product of labor is the added output generated by adding a unit of labor, holding capital constant.

3. If markets are competitive, firms perceive prices as given.

4. The difference between the short-run and long-run depends on the fixity of capital.

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5. The concept of diminishing marginal productivity is discussed.

6. The relationship between the demand for labor curve and the downward sloping portion of a firm's marginal product of labor curve is analyzed.

7. The demand for labor can be stated in terms of either the real or the nominal wage.

8. The relationship between the demand curve of individual firms and the market demand curve is briefly discussed.

9. Two principal objections to the marginal productivity theory of labor demand are presented and discussed.

10. The conditions for profit maximization with respect to capital are relevant in the long-run, and adjustments of capital to changes in relative prices generate substitution effects on employment.

11. Generalizing to more than two inputs, the demand for one grade of labor is influenced by the wages of other grades of labor.

12. The concepts of substitutes in production, gross substitutes, complements in production, and gross complements are defined and related.

13. Product market monopoly affects the profit maximization conditions, and thus, the demand for labor.

14. The imposition of payroll taxes on the employer will shift the demand for labor curve (when drawn as a function of employee wages) to the left, causing worker wages and/or employment levels to fall.

15. (Appendix) The graphical depiction of a production function is presented.

16. (Appendix) The demand for labor in the short-run is graphically derived.

17. (Appendix) The demand for labor in the long-run, showing both substitution and scale effects of a wage change, is graphically illustrated.

Answers to Even-Numbered Review Questions 2. Assume that wages for keyboarders (data entry clerks) are lower in India than in the United States. Does this mean that keyboarding jobs in the United States will be lost to India? Explain.

Answer: It depends on productivity in the two countries. If workers in the U.S. and India have equal productivity, all other things equal, then this is a possibility. However, the demand for 20

labor (and thus wages paid) is a function of productivity, so where productivity varies, wages will be different without inducing job losses. Indian data entry clerks will be substituted for American ones only if the ratio of their wage to their marginal productivity is lower.

4. Suppose that prisons historically have required inmates to perform, without pay, various cleaning and food preparation jobs within the prison. Now, suppose that prisoners are offered paid work in factory jobs within the prison walls and that the cleaning and food preparation tasks are now performed by non-prisoners hired to do them. Would you expect to see any differences in the technologies used to perform these tasks? Explain.

Answer: Since cleaning and food preparation tasks now require employing outside workers, the cost of labor has risen. This will induce the prison to substitute capital for labor (because the relative price of labor has increased), and thus more capital-intensive technologies are likely to be used.

6. Suppose the government were to subsidize the wages of all women in the population by paying their employers 50 cents for every hour they worked. What would be the effect on the wage rate women received? What would be the effect on the net wage employers paid?

(The net wage would be the wage women received less 50 cents.)

Answer: Consider a simple competitive labor market in which the demand and supply of women are both expressed in terms of the wage received by women (which, in the absence of any subsidy, is assumed to be equal to the wage paid by employers). Given the demand curve, D0, and the supply curve, S0, market clearing wage and employment levels will be W0 and E0, respectively.

Suppose the government now subsidizes employers by paying them 50 cents for every hour women work. Viewed in terms of the wage received by women, the employers' demand curve will shift up by exactly 50 cents (reflecting the fact that this amount will be paid by the government). At the old market clearing wage received by women, W0, the number of women employers want to hire, E2, exceeds the number who are willing to work, E0. This puts upward pressure on the wage received by women, and this wage rises until the excess demand for labor is eliminated. This equilibrium occurs at the wage rate W1, and the employment level E1.

It is clear from the figure that the wage received by women increases by less than 50 cents as 21

long as the supply of labor curve is not vertical (i.e., as long as labor supply is responsive to wages). Indeed, the more responsive labor supply is to the wage rate, the less the women's wage will rise. Since the wage paid by employers now equals the wage women receive less the 50-cent subsidy, it is also clear that the wage paid by employers declines (by 50 cents minus the increase in the wage women receive).

It is important to stress to students that one would reach identical conclusions if one analyzed the subsidy in terms of the wage employers pay. If supply and demand curves are drawn in terms of this variable, a 50-cent-an-hour subsidy for women would shift the female labor supply curve down by 50 cents. At the old wage paid by employers, the supply of female labor would now exceed the demand. Downward pressure would be placed on the wage paid by employers and it would fall by less than 50 cents (as long as labor supply was responsive to the wage). As a result, the wage received by women would rise by 50 cents less the fall in the wage paid by employers.

8. If anti-sweatshop movements are successful in raising pay and improving working conditions for apparel workers in foreign countries, how will these changes abroad affect labor market outcomes for workers in the apparel and retailing industries in the United States? Explain.

Answer: If increased labor costs abroad are not accompanied by increases in marginal productivity, then there will be incentives to substitute for these foreign workers (with capital or workers elsewhere, including the United States). However, increased costs of manufacturing university apparel also would be expected to reduce sales and the scale of output, which will put downward pressure on employment in the American apparel and retailing industries. The presence of both substitution and scale effects – working in opposite directions – implies that the ultimate effect on American workers in these industries cannot be predicted by theory alone.

10. Suppose that all employers in the internet industry currently allow their programmers and web designers to work from home, which appeals to those with childcare or other responsibilities that can be accomplished at less cost than if they had to leave home and commute to work. Now suppose that these employers become convinced that they can increase the productivity of their programmers and designers by requiring them to work together in company offices. Use concepts covered in chapters 2 and 3 to analyze the likely labor-market effects of this new policy on the internet industry.

Answer: The supply of workers who are interested in such jobs will decrease, because these jobs are less appealing to those with certain responsibilities. At the same time, if productivity does increase by having workers in the same office, the demand for these workers will increase. Thus wages can be expected to rise, but the effect on employment is unclear.

Answers to Even-Numbered Problems 22

2. The marginal revenue product of labor in the local saw mill is MRPL = 20 - .5L, where L = the number of workers. If the wage of saw mill workers is $10 per hour, then how many workers will the mill hire?

Answer: The mill will hire workers until MRPL = W.

20 - .5L = 10 when L = 20 workers.

4. The output of workers at a factory depends on the number of supervisors hired (see below).

The factory sells its output for $.50 each, it hires 50 production workers at a wage of $100 per day, and needs to decide how many supervisors to hire. The daily wage of supervisors is $500 but output rises as more supervisors are hired, as shown below. How many supervisors should it hire?

Supervisors 0 1 2 3 4 5

Output (units per day) 1,000 4,800 8,000 9,500 10,200 10,600

Answer: The firm needs to compare the marginal cost to the marginal revenue of hiring an additional supervisor. The marginal cost is always $500 for each extra supervisor. The marginal revenue is the number of additional units produced times the price of output.

Number of Supervisors 1 2 3 4 5

MC $500 $500 $500 $500 $500

MR $.50 x 3,800 = $1900 $.50 x 3,200 = $1600 $.50 x 1,500 = $750 $.50 x 700 = $350 $.50 x 400 = $200

The firm will hire three supervisors since the marginal revenue generated from hiring the third supervisor exceeds $500 but the marginal revenue generated from hiring the fourth supervisor is less than $500.

6. The following table shows the number of cakes that could be baked daily at a local bakery, depending on the number of bakers.

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a. b. c. d. e.

Number of Bakers Number of Cakes 0 0 1 10 2 18 3 23 4 27 Calculate the MPL. Do you observe the law of diminishing marginal returns? Explain.

Suppose each cake sells for $10. Calculate the MRPL. Draw the MRPL curve, which is the demand curve for bakers.

If each baker is paid $80 per day, how many bakers will the bakery owner hire, given that the goal is to maximize profits? How many cakes will be baked and sold each day?

Answer: a. The MPL is 10, 8, 5, 4. b. There are diminishing returns, because the marginal productivity of each worker is less than the previous worker. c. The MRPL curve’s points (on the vertical axis) are 100, 80, 50, 40. d. The firm will hire two bakers and produce 18 cakes.

8. The demand curve for gardeners is GD = 19 – W, where G = the number of gardeners, and W = the hourly wage. The supply curve is GS = 4 + 2W. a. Graph the demand curve and the supply curve. What is the equilibrium wage and equilibrium number of gardeners hired? b. Suppose the town government imposes a $2 per hour tax on all gardeners. Indicate the effect of the tax on the market for gardeners. What is the effect on the equilibrium wage and the equilibrium number of gardeners hired? How much does the gardener receive? How much does the customer pay? How much does the government receive as tax revenue?

Answer: a. The wage is $5.00, and there will be 14 gardeners hired. b. First, add the tax to the supply curve. W = -2 + ½G, so adding the tax, W’ = ½ G. Equating supply and demand gives W = $6.33 and G = 12.67. After paying the tax, gardeners now receive $6.33 – 2 = $4.33. The government receives $2*(12.67) = $25.34.

Suggested Essay Questions 1. “Despite free trade and the need to compete with American and Canadian manufacturers, most Mexican factories continue to use outdated equipment and inefficient (labor-using) work systems.” If true, does this indicate that, in the face of very low wages in Mexico, plant owners there are making mistakes?

Answer. The choice of technology is affected by the marginal costs of producing using labor (W/MPL) compared to the marginal costs of producing using capital (C/MPK). When wages are low and capital is costly, other things equal, economic theory leads us to expect that firms would use labor-intensive methods to produce.

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2. The new German government is concerned about Germany's slow growth of employment.

The government is therefore considering a program that would reduce employer payroll taxes (which are quite high in Germany). Please analyze how this reduction of employer payroll taxes would be likely to affect German employment levels. Explain your reasoning.

Answer: The proposal cuts employer labor costs associated with each level of employee wage; therefore, employers want more labor at each employee wage (a shift up of the labor demand curve). This shift could drive employment up if the labor supply curve is upward sloping.

However, if the supply curve is vertical, the employee wage is increased by the amount of tax reduction, and employment would remain unchanged. Based on the empirical evidence to date, the latter situation is likely to hold in the long run.

3. Suppose that in your firm, American workers, who are paid an hourly wage of $15, can produce 20 units of output per hour (each unit sells for $1). Workers in country X, who are paid $6 per hour, can produce 9 units per hour (again, each sells for $1). If production is such that capital and transportation costs can be ignored, and if the firm is trying to maximize profits, in which country should your firm produce these items? Why? Answer:. To maximize profits requires that the desired level of output be produced at minimum cost. The cost of producing an extra unit of output using an hour of American labor is 75 cents ($15/20 units), while the cost of using workers in country X is 67 cents ($6/9units); therefore, using labor in country X is cost-minimizing. [Note: it is incorrect to conclude that American labor is preferred because the difference between its marginal revenue product and wages ($20 $15 = $5) is greater than in country X ($9 - $6 = $3). To see this, suppose the firm wants to add 180 units (worth $180) to its total hourly output level. It can do this by hiring 9 Americans at a cost of $135, and make $45 in profits – or it can add 20 X-ians at a cost of $120 and make profits of $60.]

4. Assume that there are two grades of professional football players. There are a limited number of "stars," whom the fans most want to watch, and an unlimited number of "nonstars."

There are too few stars to staff each team fully, but there are enough for a few to be on each team if an owner decides to hire them. a. Assume that football teams keep all the "gate" and TV revenues they generate and that players are free to choose their teams at the end of any season. Do stars earn more than nonstars? How are the wages of each group determined? b. Continue to assume that players are free to choose their teams, but assume now that teams agree to share all their gate and TV revenues equally (they put them into a "pool" and divide it equally among the team owners). What happens now to salaries of stars and nonstars?

Answer: (a) It is important to realize that the wage an employee receives is determined by his or her alternative offers (W'). An employer must offer a wage that keeps desired employees from taking the alternative offer, but the employer will not pay above marginal revenue product 25

(MRP). Because stars attract more fans and TV viewers than non-stars, their salaries will exceed those of non-stars (teams bid more for their services). Non-stars will get at least W', however, for if they did not, they would cease playing football. (b) When all teams "pool" all revenues, individual teams no longer have the incentive to bid for a star player. The star's MRP to an individual team is diluted by a factor of I/N (where N = number of teams) because any increased revenue generated by the star must be shared with all other teams. In fact, a star's MRP to an individual team could be zero--the extra fans attracted to watch his new team could be offset by the loss of fans caused by his departure from his old team. The net effect would be no change in the size of the total pool, so no increase (or decrease) in revenues of the new (old) team.

Under these circumstances, stars and non-stars would get the same wage -- something close to W'. Their wage would be the minimum required to get them to play football, but there would be little or no competition among the teams for their services (and thus no mechanism to bid wages above W').

5. Suppose the government is considering imposing a payroll tax of $1.00 per person hour worked to finance a massive training program for the unemployed. Will the new equilibrium wage and employment level depend upon whether it is employers or employees who are legally liable for the tax? Explain.

Answer: If labor markets work reasonably well in adjusting to incentives, it will make no longrun difference whether employers or employees are legally liable for the tax. If employers are liable for the tax and the supply curve is vertical, the tax is shifted to employees in the form of a wage cut equal to the tax. Hence, in the long run, the employees pay the tax anyway. If employers are liable and the supply curve is horizontal, employer labor costs rise but fewer employees are hired; the response would be the same if employees paid directly (the supply curve would shift up by the amount of the tax). Finally, if the labor supply curve is upwardsloping, the end result of both alternatives for placing the tax liability is for employer labor costs to rise, employee take-home wages to fall, and for employment to fall.

6. The city of Rochester, New York, was declared a "foreign trade zone" by the U.S. Department of Commerce. A foreign trade zone is designated as "international ground," and companies in that zone are exempt from paying customs duties on component parts they import to manufacture their products. Analyze the effects of this foreign trade zone designation on the demand for labor in the Rochester area.

Answer: For firms located in the city of Rochester, there are two effects: a substitution and a scale effect. The ability to import cheaper component parts will reduce the costs of producing in Rochester and should increase the product demand of the firms located in that city. Increases in the scale of operations will tend to increase the demand for labor (shifting the demand curve to the right). However, there may also be a substitution effect, in that the ability to import less 26

expensive foreign components may induce firms to manufacture a greater percentage of their final products overseas. In effect, this would substitute foreign workers for Rochester workers, and this substitution effect would have the tendency of shifting the demand for labor curve to the left. Whether the scale or substitution effect would dominate, of course, is not something that theory can predict. The declaration of Rochester as a foreign trade zone, however, might also attract employers from other areas in the United States to the Rochester area so that they could benefit from the ability to import cheaper foreign components. This reaction would serve to increase employment in Rochester, although it might reduce employment in other areas.

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CHAPTER 4 - LABOR DEMAND ELASTICITIES While Chapter 3 dealt with the downward sloping nature of labor demand curves, Chapter 4 deals with the magnitude of the employment response to a change in the wage rate. We begin the chapter by defining and discussing the own-wage elasticity of demand. In this regard the HicksMarshall laws of derived demand are explained, with each of the four laws being related to the substitution and scale effects (concepts that were introduced in Chapters 2 and 3).

After discussing the laws of derived demand in the context of own-wage effects, we move to a discussion of the cross-wage elasticity of demand. Here we stress the concepts of gross substitutability and gross complementarity (as distinguished from substitutes or complements in production). Another section is devoted to a discussion of the empirical evidence on both the own-wage elasticity of demand and cross-wage elasticities.

The chapter concludes with sections that apply the concepts of demand elasticity to analyzing the effects of minimum-wage legislation and technological change. The appendix to Chapter 4 analyzes the labor-market effects of international trade.

List of Major Concepts 1. The own-wage elasticity of demand is the percentage change in employment of a class of labor induced by a one-percent change in the wages of that class.

2. Cross-wage elasticities of demand are the percentage change in employment of a class of labor induced by wage changes in another class; they may be positive or negative.

3. The four Hicks-Marshall laws of derived demand are introduced and related to the substitution and scale effects of a wage change.

4. The concepts of gross substitutability and gross complementarity are defined and distinguished from substitutability or complementarity in production.

5. Empirical evidence concerning the own-wage and cross-wage elasticities of demand, based on both statistical studies and inferential analyses, is presented.

6. Standard labor demand theory predicts that an increase in the minimum wage will result in the loss of employment.

7. Actually measuring the employment effects of minimum-wage increases requires that we distinguish between nominal and real changes in the rate, that other things influencing employment levels be controlled for, and that the presence of uncovered sectors and intersectoral shifts in product demand be built into the design of the study.

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8. The results of studies estimating the effects of minimum-wage increases are sensitive to the specification employed, with some studies finding the "conventional" negative effects and some finding none. Even those studies with negative employment effects generally find labor demand elasticities that are much smaller than those summarized earlier in the chapter.

9. Technological change in product markets can change the slope and placement of product demand curves, thereby shifting and/or changing the elasticity of labor demand curves.

10. The labor-demand effects of technological improvements in capital depend on cross elasticities; in attempting to analyze the likely dominance of the substitution or scale effect in this case, the Hicks-Marshall laws applicable to own-wage changes cannot be slavishly applied.

11. Technological change causes total employment to be reallocated, not permanently reduced.

Answers to Even-Numbered Review Questions 2. California employers of more than 50 workers are now required to offer paid family leave for workers with newborn children. Under this law, businesses with more than 50 workers are required to hold a job for a worker who goes on paid leave for up to six weeks. When on leave, workers receive 55 percent of their normal pay. What are the likely responses on the demand (employer) side of the labor market? Include in your analysis a consideration of factors that would affect the size of these responses.

Answer: This policy clearly increases the expected cost of employing women of childbearing age by imposing on employers a quasi-fixed cost (equal to 4 months of normal earnings). This increased cost, other things equal, will reduce the employment of younger women; the quasifixed nature of the cost implies that their employment will fall more than their average hours of work (see Chapter 5). Since the law also applies to male parents, the same thing is true, although it is more difficult to determine when a male worker might be likely to be the parent of a newborn. For older women, for whom the costs of employment are unaffected, there will be both scale and substitution effects. The former will tend to reduce demand for their services, while the latter will tend to increase it.

4. The public utilities commission in a state lifts price controls on the sale of natural gas to manufacturing plants and allows utilities to charge market prices (which are 30 percent higher).

What conditions would minimize the extent of manufacturing job loss associated with this price increase?

Answer: This question involves the cross-elasticity of demand. A higher price of natural gas will have a substitution effect that could favor increased employment, and a scale effect that tends to reduce employment. Factors that minimize the extent of job loss are those that make for a robust substitution effect and a small scale effect. A large substitution effect will tend to occur if labor is easily substituted for natural gas in the production process, and if the supply of 29

labor is relatively elastic. A small scale effect would be created if natural gas is a small part of the overall cost of production, and if the demand for the products made using natural gas is relatively inelastic.

6. In 1942 the government promulgated regulations that prohibited the manufacture of many types of garments by workers who did the sewing, stitching, and knitting in their homes. If these prohibitions are repealed, so that clothing items may now be made either by workers in factories or by independent contractors doing work in their homes, what effect will repealing the prohibitions have on the labor demand curve for factory workers in the garment industry?

Answer: Repealing the prohibitions enables garment manufacturers to substitute home workers for factory workers. Assuming that the 1942 regulations were constraining, one can assume that there will be at least some substitution of home workers for factory workers; this substitution will tend to shift the labor demand curve for factory workers to the left. However, there may be a favorable scale effect for certain factory workers performing tasks (such as packaging and shipping) complementary with home production.

Besides the shift to the left of the labor demand curve, the new substitution possibilities opened up by repealing the 1942 regulations should serve to make the labor demand curve for factory workers more elastic. Just as the greater ability to substitute capital for labor will tend to make the labor demand curve more elastic, so too will the ability to substitute home labor for factory workers.

8. In 2012, a group in Germany proposed a “wealth tax”—on buildings, machinery and equipment— that would be levied on all employers having at least $1.4 million invested in such assets. Use theory learned in this chapter to analyze the labor-market effects on employees in large German firms, and explain under what conditions German workers would be worse off.

Answer: German workers will be worse off if the tax reduces the scale of production and substitution effects are limited or zero. In other words, if firms produce less and cannot substitute relatively less expensive labor for capital, employment will decrease (and wages will fall).

Answers to Even-Numbered Problems 2. Professor Pessimist argues before Congress that reducing the size of the military will have grave consequences for the typical American worker. He argues that if one million individuals were released from the military and flooded into the civilian labor market, average wages in the civilian labor market would fall dramatically. Assume that the demand curve for civilian labor does not shift when workers are released from the military. First, draw a simple diagram depicting the effect of this influx of workers from the military. Next, using your knowledge of a) the definition of the own-wage elasticity of labor demand, b) the magnitude of this elasticity for the economy as a whole, and c) the size of the American labor force in comparison to this flood from the military, graph these events and estimate the magnitude of the reduction in 30

wages for civilian workers as a whole. Do you concur with Professor Pessimist?

Answer: You will probably not concur with Professor Pessimist. Own-wage elasticity of demand for labor = %(quantity demanded)/%(wage) = Ld/Ld)/(W/W). In this case Ld = 1 million, Ld = about 130 million employed workers, and the own-wage elasticity of demand for labor is approximately -1. Thus, -1 = (1 million/130 million)/W/W, so W/W will be very small -about -1/130 (or -0.0077). This implies that wages will fall by 0.77 percent.

4. The following table gives the demand for labor at Homer’s Hideaway, a motel in a small town.

Wage ($) 10 8 6 4 2

Number of Hours 2 3 4 5 6

a. Draw the demand for labor curve. b. Calculate the wage elasticity of demand at points along the demand curve. Indicate whether the elasticity is elastic, inelastic, or unitary elastic. c. As you slide down along the demand curve, does the demand curve become more or less elastic?

Answer: a. Demand is easily graphed from the chart. b. Calculated as point elasticity: Wage ($) Number of Hours Elasticity 10 2 -2.5 8 3 -1.33 6 4 -0.75 4 5 -0.4 2 6 -0.16 c. The demand curve becomes more inelastic.

6. Calculate the own-wage elasticity of demand for occupations a, b, and c below. ED and W are the original employment and wage. E′D and W′ are the new employment and wage. State whether the demand is elastic, inelastic, or unitary elastic. a. %∆ED = 5, %∆W = –10 b. ED = 50, W = 7 E′D = 40, W′ = 8 c. ED = 80, W = 8 E′D = 100, W′ = 6 31

Answer: a. -0.5 (inelastic) b. -1.67 (elastic) c. -0.78 (inelastic)

Suggested Essay Questions 1. One anti-terrorism expert proposes the development of two capabilities that would protect shipments of hazardous materials by truck. One is to maintain continuous satellite monitoring of all such shipments, and the other is to install devices that automatically shut down any truck that has been hijacked or deviates from its approved route. Discuss how implementing this proposal is likely to affect the demand for truck drivers, noting especially the conditions under which this effect is likely to be largest.

Answer. This proposal is an attempt to monitor truck drivers, and it really raises the cost of labor (trucks now require both a driver and monitoring equipment). Thus, the four factors underlying the elasticity of labor demand are relevant. Where it is easier to substitute capital for labor, then trucks will tend to get bigger and the number of drivers needed will go down more.

The substitution effect will also be larger if the supply of capital (in the form of larger trucks) is elastic. If product demand is more elastic, the scale effect will be larger and product demand will go down more. Finally, where the monitoring equipment represents a larger share of overall cost, the scale effect will be larger.

2. The new German government is concerned about Germany's slow growth of employment. It is also heavily influenced by the "Greens," a political group committed to improving the environment. The government is therefore considering an ecology tax, which would tax German employers proportionally to the amount of electrical and other energy their plants use in running their production machinery. Please answer the following questions: a. Explain how the proposed ecology tax is likely to affect German employment levels. b. Explain under what conditions the ecology tax would have the most favorable effects on German employment (that is, would either increase it the most or decrease it the least).

Answer: (a) The tax increases the cost of capital, causing an incentive to increase employment by substituting labor for capital. However, it also raises production costs, causing a scale effect that tends to reduce employment. The overall effect on employment is uncertain, since either effect could dominate. (b) Employment is most favorably affected when the substitution effect is large and the scale effect is small. The substitution effect is larger when labor and capital are easily substituted, and when supply of labor is elastic (so the wage doesn’t rise much with labor substitution). The scale effect is smaller when the share of capital in total costs is small (although there is an 32

exception to this rule) and when product demand is inelastic.

3. If the unskilled wage were to rise, would the demand for skilled workers be more favorably affected in the long-run than the short-run? Explain your answer, including a discussion of under what conditions the demand for skilled workers would be most favorably affected.

Answer: Whether the demand for skilled workers rises or falls when the unskilled wage rises depends on the relative strength of the substitution and scale effects. The scale effect tends to work in the direction of reducing the demand for skilled workers, while the substitution effect tends to increase such demand. Because the substitution can only take place in the long-run as new technology is installed, the forces tending to increase the demand for skilled workers are greater in the long-run than in the short-run. The conditions under which the demand for skilled workers would be most favorably affected are those making for a small scale effect (when product demand is inelastic and, although there is an exception, when unskilled labor constitutes a small part of overall cost) and a large substitution effect (when skilled workers are easily or cheaply substituted for unskilled workers, and when the supply of skilled workers is elastic).

4. A national study concludes that hourly pay received by part-time workers is always less than hourly pay received by full-time workers in comparable jobs. It also concludes that part-time workers are disproportionately women, teenagers, the elderly, and the hard-toemploy. Thus, the study suggests that Congress pass a law compelling employers offering part-time jobs to pay the full-time wage rate prevailing in their area for the relevant jobs.

Analyze as completely as you can the effects on both part-time and full-time workers.

Answer: The answer can be separated into the effects on the part-time and the full-time labor markets. An increase in the part-time (P-T) wage rate will increase the cost of hiring P-T labor, inducing a reduction in the use of P-T labor for two reasons. First, there will be a scale effect as the cost of production is increased and output (and hence employment of P-T labor) is reduced.

Second, there will be substitution of other factors of production (full-time labor, capital) for P-T labor.

There will be two potential effects on the demand curve for full-time (F-T) workers. First, as PT wages rise, F-T labor will be substituted for P-T labor in some cases. Its price has not increased and P-T labor's price has, so clearly there is greater incentive to use F-T labor now than there once was. Second, however, as the scale of output is reduced, this reduction in scale also affects F-T labor. Thus, there will be forces tending toward less F-T employment. If the scale effect dominates the substitution effect, the demand curve for F-T labor shifts to the left ("gross complementarity"). Assuming the supply curve remains stable, wages and employment in the F-T market fall. If the substitution effect dominates, the demand curve for F-T employees shifts to the right ("gross substitutability") and employment and wages rise. There are also supply curve shifts to consider. If supply to tendency pushes toward increased employment and a reduced wage. Given all these possibilities, it is not clear what the effects will be in the FT labor market.

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4. Union A faces a demand curve in which a wage of $4 per hour leads to demand for 20,000 person hours and a wage of $5 per hour leads to demand for 10,000 person hours. Union B faces a demand curve in which a wage of $6 per hour leads to demand for 30,000 person hours, while a wage of $5 per hour leads to demand for 33,000 person hours. a.

Which union faces the more elastic demand curve? b.

Which union will be more successful in increasing the total income (wages times person hours) of its membership?

Answer: (a) As noted in the text, the elasticity of demand for labor is not necessarily a constant along a given demand curve. Indeed, when we speak of changes in wage rates that are not infinitesimal, the actual value of the elasticity depends on the wage rate from which one is starting. Given the data on union A and the formula for the elasticity of demand, %E/%W, union A's elasticity when one increases its wage rate from $4.00 to $5.00 is given by (20,00010,000)/20,000 divided by ($4.00-5.00)/4.00, or (1/2)/(-1/4), which equals -2. In contrast, when one decreases union A's wage from $5.00 to $4.00, its elasticity is given by (10,00020,000)/10,000 divided by (5.00-4.00)/5.00 or (-1)/(1/5) or -5. Its elasticity over the interval $4.00 to $5.00 depends on which wage we use as a base.

To prevent this type of result, economists often define the average elasticity over the wage interval W1, to W2 as [(E2-E1,)/.5(E1,+E2)]/[(W2-W1,)/.5(W1,+W2)].

Note that this elasticity estimate does not vary with the end of the wage interval (high or low) at which one starts. In the present question the average elasticities for union A and union B are given by Elas. (A): [(20,000-10,000)/15,000]/[(4.00-5.00)/4.50] = (2/3)/(-2/9) = -3 Elas. (B): [(33,000-30,000)/31,500]/[(5.00-6.00)/5.50] = -.524 Given the above data, union A faces the more elastic demand curve. (b) One cannot say which union will be more successful in increasing its members' total earnings.

This depends upon a number of factors, including the bargaining power of the two unions and the firms with which they deal. It is true, however, that the union with the more elastic demand curve will suffer a larger percentage employment loss for any given percentage increase in wages, and this is likely to reduce its incentive to push for large wage gains. Thus, one's inclination is to say that the union facing the less elastic demand curve is likely to be more successful in raising its members' wages.

(This answer assumes that wage/employment contracts under collective bargaining lie on the demand-for-labor curve. As shown in the appendix to Chapter 12, this need not always be the case.)

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5. Clerical workers represent a substantial share of the U.S. work force -- over 15 percent in recent years. Concern has been expressed that computerization and office automation will lead to a substantial decline in white-collar employment and increased unemployment of clerical workers. Is this concern well founded?

Answer: Offices have become more computerized in recent years because the cost of using computers has fallen relative to labor's price (the wage rate). This causes a substitution effect, tending to shift the labor demand curve to the left for categories of labor that are substitutes in production with capital. However, there is also a scale effect tending to increase employment for the above categories, so we cannot tell in advance which effect will dominate. (For labor categories that are complementary with capital in the production process, the labor demand curve clearly shifts to the right.) Therefore, it is not necessarily true that white-collar employment will fall; the scale effect may prevail for many of these jobs (a dominant scale effect is more likely if product demand is elastic, if it is difficult to substitute capital for labor, and if the share of capital in total cost is large).

Even if labor demand shifts left for a particular occupational category, unemployment will not be the long-term result unless wages are rigid. Adversely affected workers would have to shift to other occupations and may experience some transitional joblessness, but only if wages are rigid and employees refuse to shift to lower paying jobs will their unemployment be permanent.

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CHAPTER 5 – FRICTIONS IN THE LABOR MARKET This chapter considers how the demand for labor is affected when it is costly to make changes to behavior when demand or supply changes. It begins with a discussion of the law of one price and explains how deviations from the law of one price in labor markets results in monopsony conditions. When the firm faces an upward-sloping supply of labor, the marginal expense of labor exceeds the wage rate, and thus firms will hire fewer workers at lower wages, as compared to a competitive labor market.

The second section begins with a descriptive section on the magnitude and growth of nonwage labor costs, because the quasi-fixed costs of labor are generally nonwage in nature. In this section we discuss employee benefits (not all of which are quasi-fixed in nature), and we also introduce the concept of hiring and training costs.

One implication of the existence of both variable and quasi-fixed labor costs is that there arises a trade-off between increasing employment through hiring added workers and increasing employment through hiring workers for longer hours. This trade-off is discussed in the second section of the chapter, and the importance of distinguishing between employment and hours is highlighted in our policy analysis of the overtime pay premium and mandated benefits for parttime workers.

In the third major section we move from a general discussion of quasi-fixed labor costs to an indepth analysis of one particular kind of quasi-fixed cost: firms' labor investments. An investment is a type of expenditure that occurs primarily in some initial period and then does not recur. While the firm hopes to recoup the investment over a period it expects the worker to be with the firm, the cost of investment becomes a "sunk cost." This section analyzes the implications of these labor investment characteristics for the demand for labor (after first introducing the concept of present value and modeling the labor investment decision by the firm).

The fourth and fifth sections offer detailed analyses of the two principal types of labor investments: training investments and hiring investments. In the section on training investments the student is introduced to the notion of general and specific training, as well as to the implications of training investments for the demand for labor. While Chapter 9 also covers aspects of education and training, it is our belief that this introduction to human capital theory in Chapter 5 is useful. In this chapter, as throughout the text, we introduce particular concepts or tools as they are called for by the larger context of analysis, because by maintaining a clear view of the overall context of analysis, the student is better able to learn the insights that economics has to offer. In this particular case, we deliberately chose to spread the concepts of human capital theory across different chapters--using these concepts as necessary and maintaining the overall substantive organization of the text (built around demand and supply).

For similar reasons, the section on hiring investments includes a discussion of credentials and signaling, as well as an introduction to the concept of internal labor markets. These topics are 36

also discussed elsewhere in the text (notably in Chapters 11 and 12), but we felt that a complete discussion of the effects of quasi-fixed costs on the demand for labor was impossible without a discussion of these concepts. Again, we wanted to maintain the organizational overview in the minds of the students. (We also firmly believe that discussing concepts or phenomena in several contexts and at different points in the book reinforces the learning process.)

List of Major Concepts 1. The costs of quitting and searching for a new job may produce an upward sloping supply curve to individual firms, leading to monopsonistic behavior.

2. Monopsony in the labor market affects wages, employment, and the labor conditions for profit maximization. The reason for this derives from the upper-sloping labor supply curve facing the individual firm, and the resultant increase in the marginal expense of labor above the wage rate.

3. In the context of monopsony, wage increases accompanying market shifts (to the left) in the labor supply curve produce the conventional expectations of decreased employment.

Mandated wage increases, however, flatten the labor supply curve and reduce the marginal expense of labor, leading to ambiguous expectations regarding employment changes, at least in the short-run.

4. The distinction between variable and quasi-fixed labor costs is made.

5. The relative growth of wage and non-wage costs is presented.

6. The essential characteristic of an investment is that resources are expended in the current period and returns are received later; the principal types of labor investments that firms undertake relate to training and hiring.

7. There are both explicit and implicit costs of job training.

8. Employee benefits are categorized and the types typically received are listed.

9. The presence of quasi-fixed costs causes an employment/hours trade-off, and the firm must determine its optimum mix of employment and hours per worker.

10. Increased overtime pay premiums that might be required under the Fair Labor Standards Act would tend to reduce the use of overtime, but whether they increase the number of workers employed depends on the size of the reduction in total labor hours demanded.

11. The concept of present value and the need for discounting when economic decisions are made in the context of several time periods are discussed.

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12. The multi-period demand for labor, the way this demand is affected by investment costs in the initial period of hire, and the way investment costs alter profit-maximizing conditions with respect to labor are all generalizations of the single-period analysis in Chapter 3.

13. The distinction between general and specific training is defined, and the effects of specific training on the relationship between wages and marginal productivity is analyzed.

14. Training investments are recouped through the creation of a "surplus" (a gap between marginal product and wage) that also cushions the worker from layoffs over the business cycle.

15. The presence of hiring costs induces firms to use credentials and internal labor markets in the recruiting, selection and promotion processes.

16. Like training costs, hiring investments increase the productivity of selected job applicants (by distinguishing among them on the basis of productivity), and they are recouped by paying wages less than productivity.

Answers to Even-Numbered Review Questions 2. Why do upward-sloping labor supply curves to firms cause the marginal expense of labor to exceed the wage rate?

Answer: Since the firm faces an upward-sloping supply of labor, in order to hire more workers, the firm must increase wages for all workers. Thus the marginal expense of labor is not simply the wages of the additional worker but those wages plus the increased cost of wages for all other workers.

4. “Minimum wage laws help low-wage workers because they simultaneously increase wages and reduce the marginal expense of labor.” Analyze this statement.

Answer: This statement is true only if (1) labor markets are monopsonistic, and (2) the minimum wage is set above the monopsony wage and less than or equal to the competitive wage. If labor markets are competitive, this statement is untrue because the marginal expense of labor is not decreasing, and if markets are monopsonistic but the minimum wage is set to high, employment could be reduced (and thus some workers will be worse off).

6. Workers in a certain job are trained by the company, and the company calculates that to recoup its investment costs, the workers’ wages must be $5 per hour below their marginal productivity.

Suppose that after training, wages are set at $5 below marginal productivity but that developments in the product market quickly (and permanently) reduce marginal productivity by $2 per hour. If the company does not believe it can lower wages or employee benefits, how will its employment level be affected in the short run? How will its employment level be affected in the long run? Explain, being sure to define what you mean by the short run and the 38

long run!

Answer: In the short-run (that is, when training investments have already been concluded, so all that is variable is the employment levels of trained workers), marginal revenue product still exceeds wages by $3 per hour, so it is advantageous for the company to continue employing workers it has already trained. The company is not making back enough to make the training be a good investment, but making back $3 per hour is better than laying off the workers and making back nothing! Thus, workers will not be laid off.

In the long-run (that is, when the company is deciding about investing in new workers), the $3 payback per hour is not sufficient to justify the training investment if wages remain as they are.

Thus, the firm will not hire and train new workers under the current circumstances.

Employment will fall as the firm fails to replace those who leave, and the decline in employment will eventually serve to raise the marginal productivity of labor. The decline in employment will stop when the marginal revenue product of labor is once again $5 greater than the wage rate.

8. The manager of a major league baseball team argues: “Even if I thought Player X was washed up, I couldn’t get rid of him. He’s in the third year of a four-year, $24-million deal. Our team is in no position financially to eat the rest of his contract.” Analyze the manager’s reasoning using economic theory.

Answer: A baseball team that has committed itself to a four-year contract has made an investment, in the hopes, of course, of receiving a return. The cost has been “sunk,” so it is of no relevance to any decision about how to use the player during the contract period. The only thing of relevance is the player’s marginal revenue productivity as compared to the marginal revenue productivity (less marginal cost to the team) of an alternative player.

10. The State of North Carolina created a program for state-subsidized training of disadvantaged workers at its community colleges. Employers adding at least 12 jobs can arrange for a community college to provide a program tailored to the individual firm. The college places ads for new hires and screens the applicants, the firms choose whom they want trained from the list supplied by the college, and the college provides the training (using equipment supplied by the firm). Finally, the firm selects employees from among those who successfully complete the training. Trainees are not paid during the training period. Analyze the likely effects on wages, employment, and hours of work associated with adopting this program.

Answer: This program reduces training costs for employers, and workers who are ultimately hired will receive higher wages (because they do not require training, so their productivity is higher). The effect on employment and hours depends on a number of factors, but it would be reasonable to think that employment might increase. However, since the firm now has minimal investment in worker training, workers are more likely to be laid off when demand is low, and it is also possible that there might be difficulties in attracting candidate to the college program since now workers bear most of the cost of their training.

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Answers to Even-Numbered Problems 2. Assume that the labor supply curve to a firm is the one given in Problem 1. If the firm’s marginal revenue product (MRPL) = 240 – 2E, what is the profit-maximizing level of employment (E*), and what is the wage level (W*) the firm would have to pay to obtain E* workers?

Answer: The supply curve is E = 5W. Rearranging, W = 1/5 E, so ME = 2/5 E. E = 600; W = $120.

4. As with the own-wage elasticity of demand for labor, the elasticity of supply of labor can be similarly classified. The elasticity of supply of labor is elastic if elasticity is greater than 1. It is inelastic if the elasticity is less than 1, and it is unitary elastic if the elasticity of supply equals 1. For each of the following occupations, calculate the elasticity of supply, and state whether the supply of labor is elastic, inelastic, or unitary elastic. ES and W are the original supply of workers and wage. E'S and W' are the new supply of workers and wage. a. %ΔES = 7, %ΔW = 3 b. ES = 120, W = $8 E'S = 90, W' = $6 c. ES = 100, W = $5 E'S = 120, W' = $7 Answer: a. 7/3 = 2.33 (elastic). b. 1 (unitary) c. 0.54 (inelastic) 6.

Teddy’s Treats, the dog biscuit company in Problem 5, has the following MRPL: Number of Hours

MRPL

18

29

19

27

20

25

21

23

22

21

a. Add the marginal revenue product curve to the drawing in Problem 5. b. If Teddy’s Treats is maximizing profits, how many hours of labor will be hired? What wage will be offered?

Answer: a. Graph should show a monopsony figure, as in the text. b. The ME is calculated in the previous problem. ME = MRP at 20 hours of work; the wage will be $6.00.

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8. Suppose the marginal expense of hiring another worker is $150, and the marginal expense of hiring current workers for an extra hour is $10. The added output associated with an added worker, holding both capital and average hours per worker constant, is 120. The added output generated by increasing average hours per worker, holding capital and the number of employees constant, is 7. If the firm is interested in maximizing profits, what should it do?

Answer: Assuming that the firm wishes to expand output, it is better off hiring a new worker.

150/120 = 1.25; 10/7 = 1.42. The expense per unit of output is $1.25 for the new worker and $1.42 for increasing existing worker hours.

Suggested Essay Questions 1. One recent magazine article on economic recovery from a recession argued, “Labor productivity growth usually accelerates in the first year of an expansion, because firms are slow to hire new labor.” Comment.

Answer. One reason firms are slow to hire in expansions is that they are slow to lay off workers during a recession. Workers in whom the firm has made an investment are paid less then the value of their marginal product, so that the firm can recoup investment costs, and this difference offers employment protection when productivity falls in a recession (because investment costs are sunk and the firm will continue to employ a worker in the short run as long as productivity exceeds the wage). As productivity rises during expansion, firms will not hire workers (which involves an investment) until the gap between productivity and wages is again large enough so that the firm can recoup investment costs.

2. An author recently asserted, “Low wage jobs provide fewer hours of work than high-wage jobs.” Using economic theory, is this statement likely to be correct? Why? Answer. Low wage jobs involve less training than high wage jobs, and if the training in high wage jobs is firm-specific, employers will want to substitute longer hours of work for hiring more workers. Thus, it is consistent with economic theory for employers to require longer hours of work for workers with more skills.

3. In recent years, many plants have closed, forcing thousands of workers out of their jobs and into new ones. Studies of wage loss suffered by these displaced workers find that, among groups of workers with exactly the same skills and types of training, workers who had been with the firm for many years and were in the 55-64 age range, had greater wage losses than those in the 25-34 age range. Is it possible that the presence of employer-provided specific training (among the new employers of these displaced workers) could cause this outcome?

Answer: If the new employers of these displaced workers needed to provide specific training to anyone they hired, then they would find that the shorter expected tenures of older workers would make training them less attractive, other things equal. The decreased attractiveness of older workers (as objects of human capital investments) would drive down their wage offers relative to those of otherwise comparable younger workers.

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4. Wages in the U.S. Postal Service have been attacked for being higher than wages elsewhere for people of the same age and education. The Postal Service answers that it must pay higher wages than workers could get elsewhere in order to keep the quit rate below average. Are there circumstances under which this argument has any merit?

Answer: This question can be answered in two ways. The first would note that a firm should seek to minimize its total cost of labor, not just its wage costs. The former includes the costs of hiring and training individuals to replace workers who have quit. If the costs of hiring and training replacements are high and a firm's quit rate is sensitive to the wage rate it pays, it may make sense for the firm to pay above-average wages in the hope of discouraging quits. This would make sense as long as the marginal costs the firm incurs in paying higher wages are less than the marginal benefits associated with reduced hiring and training costs. (The student would then have to discuss whether hiring and training costs are likely to be high for the Postal Service and whether the quit rate of Postal Service workers is likely to be sensitive to their wage rate.)

A second, more formal, type of answer would stress the distinction between specific and general training. Only if training is specific will firms bear any of the cost of training, and only in this situation will they pay above-market wages to discourage quits. As a result, if specific training is required in the Postal Service, Postal Service workers would get paid more than people of the same age and education bear only a share of the costs and thus reap only a share of the benefits.

5. Major league baseball teams scout and hire younger players whom they then train in the minor leagues for a period of three to five years. Very few of their trainees (perhaps 5 percent) actually make it to the major leagues, but if they do they are bound to the team that owns their contract for a period of five years. After five years, the player can become a "free agent" and choose any major league team on which to play. Keeping in mind that the major league teams pay the costs of, but derive no revenues from, their minor league teams, what would be the most important predictable effects of allowing players to become free agents immediately upon entry into the major leagues?

Answer: During the training period, teams are paying the salaries of their minor league players and expending other resources on their training without receiving any revenues in return. These costs represent investments in general training. A firm has no incentives to offer general training at its own expense unless it can somehow tie the trainee to the firm for a period long enough to recoup its investment expenditures. The rule under which players are tied to the major league team owning their contract is intended to offer teams a period over which to recoup these general training expenses.

If players were able to become free agents immediately upon making it to the major leagues, teams that did not train these players would bid their wages up to a level equal to their marginal productivity. Teams offering the training would therefore have no way of recouping their investment expenditures, which can only be done by paying a wage less than marginal 42

productivity. Thus, with immediate free agency, teams would no longer have incentives to scout and train their own players, and they would tend to adopt a strategy of "raiding" players already trained by other teams. The major effect of immediate free agency would therefore be to destroy the current minor league arrangements for training players. The major league teams might give up their minor league teams and rely solely on colleges for training professional baseball players. Immediate free agency might also cause independent baseball training schools to arise, with tuition charged directly to the trainees. A final alternative might be for the major league baseball teams to collectively operate a minor league system that is financed by assessing each team an equal share of the total costs of running the training operation.

6. Suppose that a firm is considering hiring a worker and providing the worker with general training. The worker's MPL is $100 during the training period, but rises to $200 in the post-training period. The worker's wage is $100 during the training period, the cost of training is $50 and the discount rate is 10%. What is the most that a profit-maximizing firm can afford to pay the worker in the second period?

Answer: The firm will undertake the training if the discounted net benefits from the posttraining period exceed the net expense from the training period, i.e., if W0 + Z - MP0 < (MP1 W1)/(1 + r). Plug in the values to solve for W1 at the breakeven point. $100 + $50 - $100 = ($200 - W1)/1.1, or $50x1.1 = $200 - W1, so W1 = $145. If the post-training wage is less than $145, the firm will make a profit.

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CHAPTER 6 - SUPPLY OF LABOR TO THE ECONOMY: THE DECISION TO WORK Beyond introducing some descriptive material on labor force trends in this century, the primary purpose of Chapter 6 is to present an analysis of an individual's decision concerning whether and for how long to work. The context of this decision is the traditional labor/leisure choice framework and the chapter is carefully constructed to build the concepts necessary for this analysis. The analysis begins with a section that discusses the choice process verbally, building upon what students know concerning product demand. It then moves to a specific analysis of the demand for leisure time (which in this context is the obverse of the supply of labor), and introduces the concepts of income and substitution effects (they are more rigorously dealt with later in the context of a graphic analysis).

Our graphic analysis is intended to accomplish two ends. One is to fix and define more precisely the concepts of income and substitution effects. The second is to equip students with a tool necessary to analyze many policy issues affecting work incentives. A sampling of such policies and their analyses is given in the final section of the chapter (following a section that discusses empirical findings concerning labor supply to the economy).

List of Major Concepts 1. Measures of aggregate labor supply generally focus on labor force participation rates and weekly hours of work; trends in these measures are presented and discussed.

2. The relationship between the demand for leisure, the demand for other goods, and the supply of labor is the focal point for beginning our analysis of labor supply theory.

3. The substitution effect is defined as the change in hours supplied attendant on a change in the wage (price of leisure), holding income constant.

4. The income effect is the change in hours supplied for a given change in income, holding the wage constant.

5. The major forces affecting labor supply are preferences, wages, and income; these forces can be graphically depicted.

6. The five assumptions underlying indifference curves (a graphic depiction of preferences) are discussed.

7. The incorporation of information on wages and income into the drawing of budget constraints is illustrated.

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8. Graphical analyses of the income and substitution effects are presented.

9. The concept of "reservation wage" is defined and illustrated graphically.

10. Empirical findings with respect to the labor/leisure choice, from both nonexperimental crosssection data and experimental studies, are presented.

11. Analyses of the budget constraints created by several government income support programs are presented. Analyzed are those with “spikes”, those with zero net wage rates (including those with work requirements), and those with positive effective wage rates (as illustrated by an analysis of the Earned Income Tax Credit program).

Answers to Even-Numbered Review Questions 2. Evaluate the following quote: “Higher take-home wages for any group should increase the labor force participation rate for that group.”

Answer: This quotation is correct because for labor force participation decisions, the substitution effect dominates the income effect. The strength of the income effect is relatively weaker when the initial hours of work are smaller. When initial hours of work are zero – as is the case when a person is out of the labor force – then the income effect is zero if leisure is a normal good (increased resources cannot induce one to increase the consumption of leisure, since leisure hours are already at their maximum).

4. The way the workers' compensation system works now, employees permanently injured on the job receive a payment of $X each year whether they work or not. Suppose the government were to implement a new program in which those who did not work at all got $0.5X but those who did work got $0.5X plus workers' compensation of 50 cents for every hour worked (of course, this subsidy would be in addition to the wages paid by their employers). What would be the change in work incentives associated with this change in the way workers' compensation payments are calculated?

Answer: This change in workers' compensation has two effects. First, it reduces the subsidy for people who do not work from $X to $0.5X. This reduction in income by itself would produce an income effect that tends to induce the injured worker to work more (he or she is poorer if not working than under the previous workers' compensation system). On the other hand, for those who work, the wage rate is increased by 50 cents an hour. (We assume here that the change in workers' compensation payments is not so large as to influence market wages.) The increased wage by itself would tend to induce injured workers to work more because the cost of leisure has risen by 50 cents an hour; however, the eventual outcome is theoretically unclear.

The effects of these changes can be seen in the figure below. Along segment DE there is a clearcut strengthening of work incentives. Segment DE has a steeper slope than the previous budget constraint BQ and it also lies to the southwest of BC. Thus, along segment DE there is a 45

substitution effect inducing more work and an income effect that also induces more work. To the left of point E, however, along segment EF, there are income and substitution effects that work in opposite directions. Along segment EF the 50-cents-an-hour increase in the wage rate is sufficient to increase the injured worker's income under workers' compensation, thereby creating an income effect that reduces work incentives, other things equal. However, the substitution effect of the increased wage continues to exert an increase in work incentives and the outcome of the two effects is not predictable in advance.

Thus, if the tangency point between the worker's indifference curve and the full budget constraint used to be along BC but to the right of point E, the worker faces a clear-cut strengthening of work incentives under the new program. If, however, the worker's tangency point along BC was to the left of point E, the new program would have an unpredictable effect on work incentives.

8. The Tax Reform Act of 1986 was designed to reduce the marginal tax rate (the tax rate on the last dollars earned) while eliminating enough deductions and loopholes so that total revenues collected by the government could remain constant. Analyze the work incentive effects of tax reforms that lower marginal tax rates while keeping total tax revenues constant.

Answer: Reducing the marginal tax rate has the effect of increasing the wage rate because workers are allowed to keep more from any extra hours worked. Keeping tax revenues constant suggests that workers' after-tax incomes also remain constant. Thus, the Tax Reform Act tended to increase the wage while keeping workers' incomes constant, creating a pure substitution effect that tended to increase hours of work.

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10. Assume that the current Disability Insurance (DI) benefit for those who are unable to work is $X per day and that DI benefits go to zero if a worker accepts a job for even 1 hour per week.

Suppose that the benefit rules are changed so those disabled workers who take jobs that pay less than $X per day receive a benefit that brings their total daily income (earnings plus the DI benefit) up to $X. As soon as their labor market earnings rise above $X per day, their disability benefits end. Draw the old and new budget constraints (label each clearly) associated with the DI program, and analyze the work-incentive effects of the change in benefits.

Answers to Even-Numbered Problems 2. Nina is able to select her weekly work hours. When a new bridge opened up, it cut one hour off Nina's commute to work, but Nina did not change her weekly hours. Does Nina's labor supply curve slope upward, bend backward, or is it vertical?

Answer: When the new bridge opened, Nina didn't change her work hours despite a parallel outward shift in her budget constraint. She did not respond to this "income" increase by increasing her leisure, so income is not a normal good for her (neither is it an inferior good).

Because Nina's income effect is zero, an increase in her wage rate should lead her to work more (because her substitution effect is acting alone). Therefore, her labor supply curve slopes upward--i.e. her desired hours of work rise with the wage rate.

4. The federal minimum wage was increased on July 24, 2007, to $5.85 from $5.15. If 16 hours per day are available for work and leisure, draw the daily budget constraint for a worker who was earning the minimum wage rate of $5.15 and the new budget constraint after the increase.

Answer: This is a simple increase in the wage. The slope of the budget line changes from -5.15 to -5.85, and the vertical intercept increases.

6. Stella can work up to 16 hours per day at her job. Her wage rate is $8.00 per hour for the first 8 hours. If she works more than 8 hours, her employer pays “time and a half.” Draw Stella’s daily budget constraint.

Answer: Stella’s budget constraint changes slope from -8 to -12 at the point where she has 8 hours of leisure (and 8 hours of work). Thus the vertical intercept should be $160.

Suggested Essay Questions 1. In 2002, a French law went into effect that cut the standard workweek from 39 to 35 hours (workers got paid for 39 hours even though working 35), while at the same time prohibiting overtime hours from being worked. (Overtime in France is paid at 25% above the normal wage rate.) (a) Draw the old budget constraint, showing the overtime premium after 39 hours of work. (b) Draw the new budget constraint. (c) Analyze which workers in France are better off under the 2002 law. Are any worse off? Explain.

Answer. In the drawing below, the old (pre-2002) constraint is ABC, where slope of BC is 25% 47

greater (in absolute value) than the slope of AB. The constraint created by the new law is ADE, where earnings at D are equal to those at B, and the slope of DE is horizontal (workers cannot get paid for more than 35 hours of work). Workers who formerly worked short hours would have had a tangency point between their highest indifference curve and the budget constraint along AB; these workers will experience increased utility. Workers with tangencies along BC, but very close to B (that is, they worked close to 39 hours before), will also be better off if their original utility-maximizing indifference curve passed below point D. However, for those whose original utility-maximizing indifference curves passed above point D (almost surely the case for most of those with original tangencies along BC), utility will fall under the new law.

Income C

D E

B

A 39

35

0 Hours of Work

2. Country X cuts the income tax rates applicable to those with the highest incomes, and it newly adopts a wealth tax – a tax that is based on the value of family assets (personal assets, real estate and financial assets) above a certain threshold. Discuss the likely work incentive effects of these tax changes on high-income workers.

Answer: Clearly, the income tax rate reduction increases the slope of the budget constraint (increases the net wage rate). If the wealth tax reduces a person’s overall command over resources, then work incentives are clearly increased – wages are increased while wealth falls. If the effect of the two tax changes serve to increase both the wage rate and the command over resources, then the tax changes have an ambiguous effect on work incentives, because the substitution and income effects have opposite effects on work incentives.

3 (a) Last year, a welfare-eligible mother with one child living in County X could 48

receive a daily living allowance from the welfare department of $40, which was reduced dollar-for-dollar by any earnings she might have had. In algebraic terms, where E = daily earnings, the welfare subsidy was calculated as follows Daily subsidy = 40 - E Assuming she could earn $5 per hour, draw her daily budget constraint assuming she had 16 hours per day of available time. (b) Are there any circumstances in which a welfare-eligible mother in County X would have chosen to work? Explain. (c) Suppose that County Y has the same $40 subsidy for welfare-eligible mothers who do not work, but that it reduces the subsidy for those who have earnings by 80 cents for every dollar earned. That is, its daily subsidy is as follows: Daily subsidy = 40 - .8E Draw the budget constraint facing welfare-eligible mothers in Country Y, again assuming a mother who can earn $5 per hour. At what level of earnings does the subsidy become zero? (d) Do you expect the labor force participation rate among low-income mothers in County Y to be above that in County X? Why? (e) Now focus on a group of low-income mothers in County X who choose to work 10 hours a day (at $5 per hour). Would they work more, less, or the same number of hours if they faced a constraint like that in County Y? Answer: (a) See constraint ABCD in the following graph.

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Figure A (b) To work and still receive welfare payments requires that one’s utility is maximized along segment BC of the constraint – an impossibility if one has downward sloping indifference curves. (c) See constraint ABED in the drawing above. The subsidy becomes zero when earnings reach $50 per day. (d) Yes, the labor force participation rate in County Y is expected to be higher because the effective wage rate for low-income mothers is not zero (unlike in County X, some who are on welfare will work in County Y). (e) Looking at the drawing above, one can see that a person who works 10 hours and earns $50 without a subsidy could enhance her utility if faced with a constraint like that in County Y. If her original curve is labeled curve #1, and a curve indicating enhanced utility is labeled curve #2, you will note that curve #2 is tangent to the “welfare” constraint along BE, and fewer hours will be worked (both income and substitution effects associated with the “welfare” constraint push in the direction of fewer work hours). . 4 . Suppose the Social Security disability insurance (DI) program was structured so that otherwise eligible recipients lost their entire disability benefit if they had any labor market earnings at all. Suppose, too, that Congress was concerned about the work disincentives inherent in this program, and that the relevant committee was studying two alternatives for increasing work incentives among those disabled enough to qualify for it. One alternative was to reduce the benefits paid to all DI recipients but make no other changes in the program.

The other was to maintain the old benefit levels (for those who receive them) but allow 50

workers to earn $300 a month and still keep their benefits. Those who earn over $300 per month would lose all DI benefits.

Analyze the work incentive effects of both alternatives. (The use of graphic analyses will be of great help to you.)

Answer: The proposal to reduce the average DI benefit may cause recipients to seek work or it may not, depending on their preferences and the extent of the cut. Compare, for example, cases a, b, and c below.

The proposal to allow DI recipients to keep their benefits until a certain earnings level is reached will induce some of those now not working to work at least a little (case d). Others may have preferences that preclude work (case e). However, some of those who medically qualify for DI but would now work may decide to cut their hours of work (case f). Thus, it is not clear from theory which proposal would have the stronger work incentives.

5. When the late Francois Mitterrand was the president of France, he instituted a number of programs designed to appeal to his "blue-collar" constituency. He raised the income tax rate applicable to the rich and expanded the free, government-provided social service programs to 51

all (medical services and education being prominent among these). Analyze the work incentive effects of Mitterrand's programs.

Answer: The income tax increase applicable to the rich is essentially a reduction in their takehome wage rate and as such will have both income and substitution effects that work in opposite directions vis-à-vis work incentives. On the one hand, the tax rate increase will make the rich less wealthy (the income effect) and tend to induce them to work more. On the other hand, the reduced wage will reduce the price of leisure (the substitution effect) and tend to induce the rich to work less and consume more leisure. Which effect dominates is unclear in advance of empirical evidence.

The expansion of social welfare programs will increase the command of less wealthy citizens over goods and services, thus increasing the wealth and real income of the poor. If it is assumed that the taxes the poor must pay are not raised to cover the cost of these programs, the provision of these programs to the poor will have a pure income effect on their work incentives.

That is, the expansion of social services to the poor without a corresponding increase in their taxes will tend to induce them to work less.

If the rich also consume "free" government services, then provision of these services will help mitigate the income effect on them (that is, the incentives to increase work effort among the rich will be smaller than otherwise).

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CHAPTER 7 - LABOR SUPPLY: HOUSEHOLD PRODUCTION, THE FAMILY, AND THE LIFE CYCLE Chapter 7 analyzes the labor supply decision (the decision to work for pay) in the context of household production theory. In this chapter, the primary alternative to working for pay is not assumed to be leisure, but household production. This framework quite naturally leads the discussion of labor supply into the context of families, thereby raising the issue of family labor supply decisions. Further, since one's household productivity varies considerably across the life cycle (as, of course, do wages), the concepts of household production also lead to a discussion of labor supply over the life cycle.

Instructors facing severe time constraints may wish to skip this chapter. The insights provided by the analysis in Chapter 7 are refinements of the basic concepts introduced in Chapter 6, and they do not contradict the insights or predictions of Chapter 6. However, Chapter 7 summarizes some recent directions in which labor supply theory has been going, and to sacrifice Chapter 7 would mean forgoing concepts and empirical work close to the frontiers of economic analysis.

The chapter begins with an introduction to the concept that households combine time and goods to produce commodities that are consumed at home. The graphic analysis of household production and the choice of household production technology is shown to be completely analogous to the graphic analysis and fundamental implications of the labor/leisure choice discussed in Chapter 6. The household production context of the labor supply decision, however, yields insights about that decision that go beyond those of Chapter 6. These insights are discussed after our brief introduction to household production theory in the first section.

In particular, we point out the tripartite choice between market work, household work, and leisure in analyzing why the substitution effects for women might be expected to be larger than those for men. We discuss such family labor supply decisions as who stays home to care for children (if anyone does), whether both spouses will work for pay, and the interdependency of the spouses' labor supply decisions. The "additional worker" and "discouraged worker" hypotheses are also discussed in this context.

Our discussion of the life-cycle aspects of labor supply begins with the observation that household productivity does indeed vary over the life cycle. The traditional interrupted careers of married women cannot be explained without reference to the shifts in household productivity that take place when children are born and as they grow older. Labor supply over the life cycle is also affected by the way wages typically vary with age, causing intertemporal substitution effects; in this context, we discuss the important issue of choice of retirement age (including data on the way lifetime Social Security benefits vary with age of retirement).

The chapter concludes with a policy analysis of "child support assurance" programs.

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List of Major Concepts 1. The basic concepts of household production theory include the combining of goods and time to produce commodities that yield the family utility.

2. Household commodities may be produced by time-intensive methods or by goods-intensive methods; the method chosen is in part a function of the price placed on time.

3. The principal predictions associated with the income and substitution effects in the labor/leisure model are unchanged in the context of the household production model. The latter model, however, adds a third dimension of choice about time usage (market work, household work, leisure).

4. As wages change, there will be changes in the time intensity of commodities consumed as well as in the time intensity of household production technologies.

5. Joint household production decisions (which spouse, if either, should remain home instead of working for pay) have yet to be completely modeled, but they must clearly take account of the partners' marginal productivities at home and the wages they can command in the "market."

6. The "discouraged worker hypothesis" and the "additional worker hypothesis" are discussed in the context of household production theory.

7. Labor supply decisions over the life cycle are affected by household productivity changes and predictable changes in wages over the life cycle that create intertemporal substitution effects without corresponding income effects.

8. Graphic analysis of the choice of optimum retirement age is presented, emphasizing how delaying retirement by a year can affect the present value of one's total income over the remaining years of expected life.

9. Child support assurance programs ensure transfer payments to custodial parents based on the age and number of children, not on income. In contrast with welfare programs, which tend to create budget constraints with zero net wage rates, child support assurance programs preserve incentives to engage in market work. However, for those who worked for pay in the absence of such programs, the pure income effect created by support assurance programs should tend to induce fewer hours of paid work.

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Answers to Even-Numbered Review Questions 2. A study of the labor force participation rates of women in the post–World War II period noted: Over the long run, women have joined the paid labor force because of a series of changes affecting the nature of work. Primary among these was the rise of the clerical and professional sectors, the increased education of women, laborsaving advances in households, declining fertility rates, and increased urbanization.

Relate each of these factors to the household production model of labor supply outlined in this chapter.

4. Is the following statement true, false, or uncertain? Why? “If a married woman’s husband gets a raise, she tends to work less, but if she gets a raise, she tends to work more.”

Answer: Empirically speaking, this statement is generally true. If a married woman's husband gets a raise, that raise (to her) has an income effect. This increased income without a corresponding increase in her wage rate tends to induce her to work fewer hours. However, if her wage rate rises, she will experience both an income and a substitution effect. While theory cannot predict which one is dominant, most empirical studies suggest the dominance of the substitution effect for married women.

However, it was pointed out in the text that the spouses may make their labor supply decisions jointly. For example, if the husband's wage increase caused him to work more, the wife may also decide to work more if they are complements in household production (or consumption). Thus, the answer to this question really depends upon whether one assumes the two spouses have household productivities that are interdependent; if so, they must make their labor supply decisions jointly.

6. Assume that a state government currently provides no child-care subsidies to working single parents, but it now wants to adopt a plan that will encourage labor force participation among single parents. Suppose that child-care costs are hourly, and suppose the government adopts a child-care subsidy that pays $3 per hour for each hour the parent works, up to 8 hours per day.

Draw a current budget constraint (net of child-care costs) for an assumed single mother and then draw in the new constraint. Discuss the likely effects on labor force participation and hours of work.

Answer. If the old budget constraint is AB below, the new one will have a steeper slope (reflecting a net wage that is $3 per hour higher) for the first 8 hours of work (see AC); after that, the budget constraint is segment DB. Among those single parents not working before the subsidy is adopted, the higher wage rate will tend to increase labor force participation (the substitution effect dominates for participation decisions). For those already working (tangencies along AC), the income effect and substitution effects of this wage increase will have opposite tendencies on the hours of work, so the net effect is not predictable. However, some people working over 8 hours a day before may reduce their supply of hours and move to point C on the constraint.

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Income

B

D

C

8

A

Hours of Work

8. A state government wants to provide incentives for single parents to enter the labor market and become employed. It is considering a policy of paying single parents of children under age 18 $20 per day if the parent works at least 6 hours a day, 5 days a week. Draw an assumed current daily budget constraint for a single parent and then draw in the constraint that would be created by the $20 subsidy. Discuss the likely effects on (a) labor force participation and (b) hours of work.

Answer. In the drawing below, the pre-subsidy constraint is AB. The subsidy of $20 per day (CD) begins at 6 hours of work and continues for all levels of work hours beyond 6 (segment DE, which is parallel to AB). Thus, the new constraint is ACDE. Those single parents who were out of the labor force before (maximized utility at A) and who have very steep indifference curves will tend to remain at point A; however, those with flatter indifference curves will find that their utility is maximized at point D. Thus, some workers who were out of the labor force before will now join, and those who do will desire jobs offering exactly 6 hours of work per day.

For those along AC before (working less than 6 hours per day), the tendency also will be to move to 6 hours of work (although it is possible that some will have such a steep indifference curve to the left of their tangency along segment AC that they will not be better off by working 6 hours). For those working more than 6 hours per week before, the income effect of this subsidy will create a tendency for them to desire fewer hours of work (as long as the hours do not fall below 6).

Income 56

E B

D C 6 A

Hours of Work

10. Assume that a state government currently provides no child-care subsidies to working single parents, but it now wants to adopt a plan that will encourage labor force participation among single parents. Suppose child-care costs are hourly and that the government adopts a child-care subsidy of $4 per hour if the single parent works 4 or more hours per day. Draw the current daily budget constraint (assume a wage that is net of the hourly child-care costs) for a single mother and then draw in the new constraint. Discuss the likely effects on labor force participation and hours of work.

Answer: Similar to the previous questions, in this case, the budget constraint is the same for the first four hours. At four hours of work, the budget constraint has a small spike (because the worker now receives the subsidy for the first four hours, and then increases in slope by $4.

Among those single parents not working before the subsidy is adopted, the higher wage rate plus the spike in the budget constraint will tend to increase labor force participation (the substitution effect dominates for participation decisions). For those already working, the income effect and substitution effects of this wage increase will have opposite tendencies on the hours of work, so the net effect is not predictable. Those working fewer than 4 hours are likely to increase hours to at least 4; for those over 4 hours, hours of work could decrease.

Answers to Even-Numbered Problems 2. Suppose a single parent can work up to 16 hours per day at a wage rate of $10 per hour.

Various income maintenance programs have been developed to assure a minimum level of income for low-income families. Aid to Families with Dependent Children (AFDC) was established with the Social Security Act of 1935. The family was given an income subsidy depending on family size. Under this program, the family’s benefit was reduced by $1 for every dollar earned. Suppose the maximum daily subsidy for the single parent described in this problem is $40. a. Draw the daily budget constraint without program participation for the single parent 57

described in this problem. b. On the same graph, draw the daily budget constraint under AFDC for the single parent described in this problem. c. What effect does this program have on the incentive to work? Explain.

Answer: a, b. See graph.

Income 160

40

12

c.

16

Leisure

Up to four hours of work, income is $40, no matter how many hours are worked. For workers who would have chosen to work fewer than four hours, this program has only work disincentives, and that is likely to also be true for workers who would have chosen close to four hours of work. After that point, the program has no effect.

4. Suppose a single parent can work up to 16 hours per day at a wage rate of $10 per hour. Various income maintenance programs have been developed to assure a minimum level of income for low-income families, such as AFDC (see Problem 2). One of the problems with AFDC is that benefits were reduced by $1 for every dollar earned. An alternative income maintenance program is Temporary Assistance for Needy Families (TANF), which also offers a no-work benefit but has a smaller reduction in wages for every dollar earned. A simplified version of this type of program is one that would give this single parent a $40 (no-work) grant accompanied by a benefit reduction of 75 cents for every dollar earned. a. Draw the daily budget constraint without any program participation for the single parent described in this problem. b. On the same graph, draw the daily budget constraint under TANF for the single parent described in this problem. At what level of income does the subsidy end? How many hours of work would this be? Discuss the effect of program participation on work incentives. c. On the same graph, draw the daily budget constraint under AFDC for the single parent described in Problem 2. d. Compare the effect of the TANF program on work incentives compared to the AFDC program.

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Income 160

40

12

16

Leisure

Answer: a, b, c: See graph. The red line segment represents the TANF program. This program does not phase out until the worker earns 40/.75 = $53.33, which occurs at 5.3 hours of work (10.7 hours of leisure). d. The TANF program, while still having an income effect that reduces work incentives, has fewer disincentives than the AFDC program, since families can achieve higher incomes by working. After 5.3 hours of work, there are no further effects.

Suggested Essay Questions 1. Assume that the government now has a program for helping working parents with childcare costs. Assume that this program (Program A) gives every working parent $1 per hour for every hour worked, up to a maximum of $8 per day (for 8 or more hours of work, the daily childcare allowance remains at $8). (a) Draw a “market” budget constraint for a parent who can earn a maximum of $80 per day ($5 per hour for 16 hours of work). Then draw in the constraint produced by Program A (you need not draw the constraint exactly to scale, but should try to get the dimensions roughly correct).

Now suppose that legislators are concerned about the children of parents who work very long hours and are therefore considering changing the program in a way they believe will induce parents to avoid working long hours. Their proposal, Program B, would also give every working parent $1 per hour worked, up to a maximum of 8 hours per day, but it would differ from Plan A in that after 8 hours of work the childcare subsidy would be reduced to zero. (b) Draw a “market” budget constraint for a parent who can earn a maximum of $80 per day ($5 per hour for 16 hours of work). Then draw in the constraint produced by Program B (again, you need not draw the constraint exactly to scale, but should try to get the dimensions roughly correct).

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(c) Now you are asked to compare the effects on labor supply of the two programs (hint: in answering this question, you may want to draw a diagram that combines the two constraints in one drawing to compare the programs more easily). In particular, analyze whether Program B is superior to Program A in terms of inducing parents who are now working more than 8 hours a day to reduce their hours of work.

Answer: (a) and (b) The constraints for the market, Program A and Program B are as follows:

Figure B Market constraint = AB; Program A constraint = ACD (CD parallel to AB); Program B constraint = ACEB a. This question asked the student to focus on the labor supply effects of moving from Program A to Program B on parents now working more than 8 hours per day. Thus, the answer should focus on comparing the work incentive effects of Programs A and B on parents with indifference curves indicating 8 or more hours of work under Program A (the program that the question indicates is now in effect).

There are two possibilities. One alternative is that the parent is initially on an indifference curve that is tangent to CD, and when segment CD is removed (by moving to Program B), the parent then maximizes utility at point C. The economic meaning of this is that some parents will reduce work effort (from more than 8 hours to exactly 8 per day) in order to still obtain the subsidy.

The other possibility is that parents with indifference curves initially tangent along CD will now 60

maximize utility along EB, which increases work incentives. For these parents, indifference curves are so flat (the desire for income so strong) that the curve tangent to the market constraint passes above point C. This means that when Program A is changed to Program B, such workers experience a pure income effect (a loss of income) and thus decide to work more.

2. A company whose workers now retire at age 65 wants to induce its employees to retire earlier -- and it would prefer them to retire at age 60. It is considering two alternative plans to achieve this goal. Plan A would give workers a $25,000 lump sum payment if they retire at age 60, but would not give them any bonus if they retire later (if they retire later, they would get their normal pension benefits).

Plan B would give them, in addition to their normal pension, a bonus of $25,000 if they retire at age 65, a bonus of $20,000 of they retire at age 61, a bonus of $15,000 if they retire at age 62, a bonus of $10,000 if they retire at age 63, and a bonus of $5,000 if they retire at age 64.

Discuss the strengths and weaknesses of the two plans in light of the company’s goals.

Answer: Plan A creates a “spike” in the constraint facing a 60-year-old worker, and if that worker’s indifference curves are relatively flat (the person is work/income-oriented), then earlier retirement may not be induced. With plan A, a worker will either retire at age 60 or at age 65 (that is, if they retire early it will be only at age 60). With plan B, which shifts a 60-year-old worker’s budget constraint to the northeast and also reduces its slope, there is a more continuous incentive to retire early (the income and substitution effects both work in the direction of earlier retirement at ages between 60 and 65). Workers attracted to early retirement under plan A will also retire early (but not necessarily at age 60) under plan B, but plan B will also induce early retirement among some of those not attracted to earlier retirement under plan A. 3. Several studies have indicated that for prime-age males, the income effect of a wage increase tends to dominate the substitution effect. Other recent studies point out that hourly wages tend to rise over the early stages of the life cycle (the young receive lower wages than the middle-aged) and that young males tend to work fewer hours than middle-aged males, ceteris paribus. Employing a theory of life-cycle allocation of time, explain the apparent discrepancy.

Answer: Studies showing that for prime-aged males the income effect of a wage increase tends to dominate the substitution effect look either at wage increases that have occurred as society has become wealthier and more productive or at wage rates across individuals in a population. In both cases there are both substitution effects and income effects of wage changes. However, the studies of the life-cycle effects of lower wages in the early stages of one's working career with higher wages later on are examining these wage change effects over an individual's lifetime, holding constant the individual's expected lifetime wealth. With these studies there is a substitution effect--leading to more work as wages rise--but no corresponding income or wealth 61

effects. The latter studies are in the pure life-cycle mode of analysis, where at a given point in time an individual has an expected lifetime wealth and also faces predictable changes in the wage rate over his or her career.

4. A recent study of the labor force participation rates of women in the post-World War II period notes: Over the long-run women have joined the paid labor force because of a series of changes affecting the nature of work. Primary among these was the rise of the clerical and professional sectors, the increased education of women, labor saving advances in households, declining fertility rates, and increased urbanization.

Relate each of these factors to the household production model of labor supply that was outlined in Chapter 7.

Answer: One of the central aspects of the household production model of labor supply is the importance of the relative productivity in paid employment as compared to household production. Increased opportunities in the clerical and professional sectors, as well as increased educational levels, serve to increase productivity in paid employment (that is, to increase the wage rate that women can command). Declining fertility rates tend to reduce the productivity of hours spent at home, while the invention of labor saving devices in household production make it easier to substitute goods purchased with cash for time at home; both of these factors flatten the household utility isoquants (an hour of household productivity forgone can be replaced more readily by goods purchased with money). Increased urbanization also tended to make it easier to substitute goods for household production. All these factors tended to raise market productivity relative to household productivity, and some of them served to increase the strength of the substitution effect relative to the income effect.

5. Suppose that, under state law, the financial settlement in a divorce case that does not involve dependent children depends upon the economic contribution each marriage partner made up to the date of divorce. Thus, if the wife contributed half of the couple's initial assets and earned an income equal to her husband's throughout the years, she would be determined to qualify for half of the assets at the date of divorce. Based on what you have learned in Chapter 7, how could an equitable settlement be determined in the case of a woman who stayed home, raised the family's children, and never worked for pay?

Answer: A wife who did not work for pay nevertheless contributed to the family's income by performing household production services that would otherwise have had to be purchased in the market at some cost. Put differently, a woman who performs household services saves the family money that it would otherwise have had to spend. For a discussion of how these services can be valued, see Example 7.2.

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CHAPTER 8 - COMPENSATING WAGE DIFFERENTIALS AND LABOR MARKETS Chapter 8 introduces students to the concept of compensating wage differentials. Following the practice in earlier chapters, it seeks to move students from concepts they are familiar with to new concepts and tools. Again, the analysis begins with a verbal exposition of occupational choice and the wage outcomes that flow from this choice when jobs differ along nonpecuniary dimensions. Once the essential assumptions and predictions of economic theory in this context are explained, we introduce students to a graphic analysis that is intended to yield additional insights. The graphic analysis of the issue of occupational choice is also intended to provide students with a tool for analyzing the effects of government policies on the labor market.

We first apply the concepts of hedonic theory to a "bad" job injuries. Policy implications are related to occupational safety and health legislation. We then apply the theory to an analysis of how elements in the employment "package" on which employees place a positive value affect the wage rate. The application in this section of the chapter relates to the regulation of employee benefits, particularly pensions.

For those who wish to enrich the coverage in Chapter 8, we have added an appendix that analyzes worker choice of jobs that have different probabilities of layoff. This appendix offers another application of the theory of compensating wage differentials to an interesting policy problem, and in so doing elucidates certain issues not commonly understood. The analysis also introduces the student to the notions of "risk aversion" and the willingness to pay for insurance ("certainty").

List of Major Concepts 1. In the context of full information and choice, worker behavior will generate compensating wage differentials for job characteristics that are unpleasant or costly.

2. Compensating differentials play a dual role in allocating labor to unpleasant jobs and in compensating those who accept unpleasant work.

3. The prediction that there will exist compensating wage differentials for unpleasant work rests on assumptions of utility maximization, worker information, and worker mobility.

4. Employee preferences are graphically expressed in the concavity and slope of indifference curves.

5. Employers with different costs of eliminating unpleasant job characteristics can be graphically represented.

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6. A market equilibrium curve (or offer curve) is derived from the zero-profit isoprofit curves of the employers in the market.

7. If the market is working properly, employees who are least averse to an unpleasant job characteristic become employed with firms that find it most expensive to eliminate that characteristic.

8. The theory of compensating differentials can only be tested using techniques that control for other influences on job characteristics.

9. Government attempts to regulate the outcome of labor market decisions that are made in a perfectly functioning market could lead to a reduction of utility for the workers the government is intending to help.

10. Government intervention into the labor market can increase worker utility if the market is not functioning perfectly (that is, if not all costs or benefits of the decision are borne by those making them).

11. The mix of wages and benefits in the compensation package depends on both employee preferences and the trade-offs employers are willing to make.

12. (Appendix) Some job characteristics normally considered bad may be considered good by some workers (layoffs may be preferred if they are known in advance).

13. (Appendix) There are two issues relating to the undesirable characteristics of layoffs: the degree to which yearly layoffs (known in advance) constrain a worker's hours of work to lie below those otherwise desired, and the degree to which layoffs cause the worker's income each year to fluctuate.

14. (Appendix) The concept of risk aversion is related to the hypothesis that the expected utility of a level of income ($X) received with certainty is greater than the expected utility of a stream of income that may fluctuate over time but yield an expected yearly value of $X. Answers to Even-Numbered Review Questions 2

Statement 1: "Business executives are greedy profit maximizers, caring only for themselves."

Statement 2: "It has been established that workers doing filthy, dangerous work receive higher wages, other things equal." Can both of these statements be generally true? Why?

Answer: Both statements can be simultaneously true. If workers are informed about job hazards and have a choice about the jobs they take, their behavior will force even the most greedy executives to pay higher wages for filthy, dangerous work. Even the greediest profit maximizer must obtain a work force, and to do so must pay a wage that workers will accept. If workers 64

have alternative job offers that pay the same wage but offer better working conditions, they will accept those offers and turn down work at the more dangerous or filthy workplaces. Their behavior then will force owners either to pay the compensating wage differentials or to clean up the workplace.

4. Suppose that someone claims that low-wage jobs lack the healthcare and pension benefits enjoyed by higher-wage employees. Assuming this claim to be true, does this fact contradict the theory of compensating wage differentials? Explain.

Answer. The theory of compensating differentials predicts that, other things equal, jobs with low non-wage benefits would have to pay higher wages. This statement is implicitly comparing those in low-skilled jobs with those in high-skilled jobs, where clearly “other things” are not comparable. Thus, the facts in this statement do not contradict the theory of compensating wage differentials.

6. Suppose Congress were to mandate that all employers had to offer their employees a life insurance policy worth at least $50,000 in the event of death. Use economic theory, both positively and normatively, to analyze the effects of this mandate on employee well-being.

Answer: From the perspective of positive economics, mandating that employers offer at least $50,000 in life insurance to their employees will obviously have no effect on those who are already offering that much or more, but it will add to the costs of those who were previously offering less. To be competitive in the labor market, those previously offering less must have been compensating their workers in some other way (to make their jobs – and job offers – as attractive as those of their competitors). It is thus highly likely that low-insurance employers were paying higher wages than those offering more insurance. To compete with their competitors in the product market, the affected employers must reduce their wages (to keep overall costs in the competitive range). Thus, the (positive) compensating wage differential associated with offering less insurance will decline as firms affected by the mandate strive to remain competitive in the product market. Of course, if wages do not, or cannot, decline by enough to fully offset the added costs of more insurance, then employment among these employers will fall.

From the perspective of normative economics, we would like to know if this mandate will improve the welfare of the workers affected. If the labor market is perfectly functioning, it facilitates mutually beneficial transactions, and workers are able to obtain the combination of wages and life insurance that maximizes their utility. If the mandate forces them to take some other mix, then their utility will decline (in economic terms, the reduction in their wages reduces their utility more than the increased insurance adds back). If the market is not allowing workers to “buy” (in the form of lower wages) the life insurance they want, then mandating increased

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insurance could improve the welfare of affected workers (as long as the mandate does not require workers to buy more than for which they are willing to pay).

8. "The concept of compensating wage premiums for dangerous work does not apply to industries like the coal industry, where the union has forced all wages and other compensation items to be the same. Since all mines must pay the same wage, owners of dangerous mines will have to pay the same wage as owners of safe mines. Therefore, compensating differentials cannot exist." Is this statement correct? (Assume wages and other forms of pay must be equal for dangerous and non-dangerous work and consider the implications for individual labor supply behavior.)

Answer: This statement is not correct. Compensating wage differentials can exist in this context, although they are somewhat more difficult to observe. To understand how the market would adjust, let us assume that we have a set of relatively safe coal mines and a set of relatively dangerous coal mines. Both sets of mines must pay the same wage rate and offer the same fringe benefits.

Suppose now that both sets of mines are trying to assemble work forces. They both advertise for help and, assuming workers quickly find out which mines are safe and which are dangerous, the safe mines receive many more applications than the dangerous mines. The safe mines can thus be highly selective about the applicants they choose, and will tend to hire the most dependable, hardest working, most motivated employees. On the other hand, the dangerous mines, with very few applicants, will have to take whom they can get--those workers who were not chosen to work in the safe mines. Therefore, while the wages of workers in the two sets of mines will be equal, the quality of workers will not be equal. Safe mines will have high quality, highly productive workers getting wage $X, while the dangerous mines will have lower quality workers obtaining the same wage. Thus, workers of unequal skill or productivity would receive the same wage--and this is tantamount to the receipt of a compensating wage differential.

Put differently, the theory of compensating wage differentials says that people of equal skill will receive different wages when working conditions differ. But a natural corollary of this is that, when working conditions differ, people of different skills might receive the same wage. In both cases workers in less desirable circumstances receive higher wages than they would otherwise receive.

10. In 2005, a federal court authorized United Airlines (UAL) to terminate its pension plan. The government will take over pension payments to retired UAL employees, but this action means that pension benefits will be less than promised by UAL to both its current retirees and current workers. What future labor market effects would you expect to occur from this sudden and unexpected reduction of pension benefits?

Answer: The reduction of pension benefits makes UAL employment less desirable. Thus it is likely that in order to attract workers, UAL will have to offer higher wages or other benefits to new (and possibly existing workers).

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Answers to Even-Numbered Problems 2. Consider the conditions of work in perfume factories. In New York perfume factories, workers dislike the smell of perfume, while in California workers appreciate the sme of perfume, provided that the level does not climb above S*. (If it rises above S*, they start to dislike it.)

Suppose that there is no cost for firms to reduce or eliminate the sme of perfume in perfume factories and assume that the workers have an alternative wage, W*.

Draw a diagram using isocost and indifference curves that depicts the situation. (The New York and California isocost curves are the same, but their indifference curves differ.) What level of perfume smell is there in the New York factories? In the California factories? Is there a wage differential between the California and New York workers?

Answer: See the figure below. The California workers are paid exactly the same as the New York workers. This wage equals W*. The level of smell in California is S*; in New York it is 0.

4. The following two figures represent the labor market for two industries that require workers with the same skills and experience; however, Industry B is characterized by much noisier working conditions than Industry A. What is the compensating wage differential between the two industries?

Answer: Missing due to missing graph.

6. The demand for labor in Occupation A is LD = 20 – W, where LD = number of workers demanded for that occupation, in thousands. The supply of labor for Occupation A is LA = –1.25 + .5W. For Occupation B, the demand for labor is similar, but the supply of labor is LB = –.5 + .6W, which is indicative of a more pleasant environment associated with that occupation in 67

comparison with Occupation A. What is the compensating wage differential between the two occupations?

The zero-profit isoprofit curve for Company ABC is W = 4 + .5R, where W = the wage rate that the firm will offer at particular risk levels, R, keeping profits at zero. The zero-profit isoprofit curve for Company XY is W = 3 + .75R. a. Draw the zero-profit isoprofit curves for each firm. What assumption about marginal returns to safety expenditures underlies a linear isoprofit curve? b. At what risk level will the firms offer the same wage? c. At low-risk levels, which firm will be preferred by workers? At high-risk levels, which firm will be preferred by workers? Explain.

Answer: a. Linear isoprofit curves imply that there is a constant tradeoff between wages and safety expenditures for these firms. b. The firms will offer the same wage at risk level 4. c. Workers will prefer firm ABC for risk levels up to 4, since wages are higher for the same level of risk. After risk level 4, Company XYZ will be preferred.

Wage

XYZ ABC 4 3 Risk 4

Suggested Essay Questions 1. A country passes a law, applying only to large firms, that cuts the standard workweek from 39 to 35 hours (workers are paid for 39 hours even though working 35), while at the same time prohibiting overtime hours from being worked. This law does not apply to smaller firms in the country. (Overtime had been widespread in both sectors, and is paid at 50% above the normal wage rate.) Using economic theory, how do you think this law might affect wages and employment in the two sectors?

Answer. The immediate effect on workers in large firms is to give them a wage increase of around 10% (work 35, are paid for 39), but the law also prevents them from working overtime.

How wages and employment respond depends on the value workers put on overtime work. If

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they value the ability to work overtime, some in the large-firm sector may seek jobs in the smallfirm sector (where it is still possible to earn a 50% premium for hours in excess of 39) – which would drive down wages in the small-firm sector and drive them higher in the large-firm sector.

The higher wages in the latter sector would reflect a compensating differential for the restricted access to a valuable workplace characteristic. However, if workers now see jobs in the large-firm sector as more desirable than before (given the immediate wage increase and the inability of employers to demand overtime work of their employees), then more would seek work in that sector. In this latter case, employment shrinks and wages rise in the small-firm sector, while employment grows and wages fall in the large-firm sector.

2. Yearly working hours in the United States have been rising over the past two decades, on average, and they are roughly twenty percent higher than in many European countries (where paid vacation days are much more frequent). Currently, some American employers offer as little as one week of paid vacation, while others offer four or more.

Suppose that the U.S. government believes that workers should have more leisure time to spend with family and friends – and that it therefore mandates that all employers offer at least four weeks of paid vacation to their employees. Use economic theory, both positively and normatively, to assess the effects of requiring four weeks of paid vacation on the wellbeing of employees.

Answer: From the perspective of positive economics, mandating that employers offer at least 4 weeks of paid vacation to their employees will obviously have no effect on those who are already offering that much (or more) paid vacation, but it will add to the costs of those who are now offering less. To be competitive in the labor market, those now offering less must have been compensating their workers in some other way (to make their jobs – and job offers – as attractive as those of their competitors). It is thus likely that these latter employers are paying higher wages than those offering more vacation. Having to offer four weeks of vacation will require (to compete in the product market) and allow the affected employers to reduce their wages. Thus, the (positive) compensating wage differential associated with having fewer paid vacation days will decline as firms strive to remain competitive in the product market. Keep in mind that the labor market – the other market in which firms must successfully compete – will accept some decline in wages, because workers are being given something of value (paid vacation days). Of course, if wages do not, or cannot, decline by enough to fully offset the added costs of the employers affected by the mandate, then employment among these employers will fall.

From the perspective of normative economics, we would like to know if this mandate will improve the overall welfare of the workers affected. If the labor market is perfectly functioning, it facilitates mutually beneficial transactions, and workers are able to obtain the combination of wages and vacation days that maximizes their utility. If the mandate forces them to take some other mix, then their utility will decline. In economic terms, the reduction in their wages might reduce their utility more than the increased number of vacation days adds back. If the market is not allowing workers to “buy” (in the form of lower wages) the vacation days they want, then mandating increased vacation days could improve the welfare of affected workers. However, if 69

the government mandated too many vacation days, then the worker could be made worse off by the government mandate.

3. Some employers offer jobs for which overtime is mandatory. Others offer jobs for which overtime hours are usually available to workers if they wish to work them, and still others offer jobs for which overtime hours are not commonly worked. Suppose a careful study of wages found that jobs for which overtime hours are commonly available pay lower wages than jobs for which overtime is not usually worked (after controlling for all other factors affecting the wage rate). Moreover, jobs for which overtime is required are found to pay wages comparable to those found in jobs for which overtime is unusual, again controlling for all other factors affecting wages. What would the results of these studies tell us about worker attitudes regarding overtime? Why? Answer: What these hypothetical studies show is that there is no compensating wage differential for the requirement of mandatory overtime and that there is a negative compensating differential associated with the right to work overtime at the worker's discretion. Put differently, it appears that higher wages are not necessary to attract workers into jobs for which there is mandatory overtime. Moreover, it would appear that firms offering overtime hours on a steady basis to employees can pay lower straight-time wages than employers who do not regularly offer overtime hours. This negative compensating wage differential comes about because employers offering overtime on a regular basis have an abundance of applicants, allowing them to reduce wage offers below what other employers are paying. Thus, the results would seem to indicate that employees (at least those at the margin) are enthusiastic about working overtime, especially when it can be worked at their discretion. They are more reluctant to take jobs for which overtime is mandatory or not offered at all.

4. Suppose we observe a city in which highway workers are required to give the Supervisor of Highways an under-the-table payment of X dollars per year. Suppose we were to compare the wages paid by this city with the market-clearing wage paid to comparable workers in the area. Would we expect wages paid to highway workers by this city to be higher or lower than the market wage? Would we expect the salary paid by the city to its Supervisor of Highways to be above or below market? Explain.

Answer: We would expect wages for highway workers in the city to be high relative to the market wage. In order for workers to be attracted to highway jobs in the city they must take home wages that are at least as great as they could obtain elsewhere. This means that the wages they receive, less any bribes they must pay, must be at least equal to the prevailing wage. If the supervisor is able to extract under-the-table payments from these workers, it is an indication that the wages paid by the city are relatively high. Alternatively, one can look upon the bribe as an undesirable element of employment for which the workers would have to receive a compensating wage differential.

The supervisor's wage, by analogy, can be low relative to the market. Under-the-table payments provide a supplement to the supervisor's regular salary, so that even if the supervisor's salary is low the job may attract a satisfactory flow of applicants.

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CHAPTER 9 - INVESTMENTS IN HUMAN CAPITAL: EDUCATION AND TRAINING Chapter 9 introduces students to the concept of human capital and treats in detail education and training investments. The chapter begins with a section on the demand for education by workers, in which a theory of human capital investment is formulated and a formal model of choice is presented. Implications of this model for both individual and aggregate (market) behavior are then derived.

The second section of the chapter analyzes the relationship between education and earnings. We introduce age/earnings profiles and discuss the reasons for their convexity. Included in this section is an analysis of the differential convexity among such profiles for men and women.

Next, we consider the question of whether education is a good investment. We analyze this question from both an individual and a social perspective. The major findings of the literature with respect to the individual rates of return to education are summarized, and we discuss possible biases (including selection biases) inherent in these findings. When discussing education as a social investment, we introduce both the traditional answers of the "human capitalists" and the more agnostic views of those who see education as purely a signaling device. In this context of evaluating education and training as investments, we devote a section to evaluations of government job training programs.

Appendix 9A presents and explains a "cobweb" model of labor market adjustment, in which the need for educational investments slows down the supply response to changes in market demand. Appendix 9B presents a hedonic model of education and wages that uses the graphic tools of Chapter 8. This hedonic model is useful in explaining several empirical facts about the relationship between education and wages, and the discussion also serves to integrate the concepts in Chapters 8 and 9.

List of Major Concepts 1. Investments in human beings are part of the general category of investments.

2. Investments entail costs in the current term with returns flowing in over later periods.

3. Costs of human capital investments include out-of-pocket expenses, forgone earnings, and psychic losses.

4. Because investment returns flow in over several years, an analytical tool to convert future sums to present value is required (the concept of present value and discounting future sums is explained in some detail).

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5. Human capital investments are more likely to be made by people who are not present oriented, by people who are young, in situations in which the costs of human capital investments are lower, and in situations in which the returns to these investments are larger.

6. Variations in the returns to human capital investments call forth supply responses by individuals, affecting college enrollments in predictable ways.

7. Because education is costly, jobs that require more education or training must pay a higher wage to attract workers (that is, to compensate them for the cost of investment).

8. Age/earnings profiles are flatter for less educated workers, reflecting smaller human capital investment costs in their early years and lower growth of productivity.

9. Post-schooling investments in on-the-job training can help account for both the convexity and the fanning out of age/earnings profiles.

10. Post-schooling investments reduce actual earnings below potential earnings, and as such investments decline over age, one's actual earnings approach potential.

11. Some differences between men and women in the acquisition of education and training (including university majors) can be explained by lower rates of return to some human capital investments among "traditional" women, who expect interrupted labor market careers.

12. Evaluations of whether education is a good individual investment typically present rate of return estimates that involve three sets of biases: upward biases associated with the correlation between education and ability, downward biases associated with the failure of monetary earnings to reflect all the benefits of a college education, and selectivity biases arising from the fact that people who choose one career may be more productive in that career than a comparably trained person who does not choose that career.

13. Evaluations of whether education is a good social investment must consider the hypothesis that education acts as a screening device, rather than an activity that enhances productivity.

14. If the full cost of education is inversely related to ability, and if ability is positively related to on-the-job productivity, then firms can use educational attainment as a screening device (workers will sort themselves out according to ability in choosing their level of educational attainment).

15. Public sector job training programs have created demonstrable earnings gains only for adult women, and the present value of these gains typically exceed program costs.

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16. (Appendix 9A) Delays in supply responses associated with the long gestation periods of some human capital investments can create periods of oversupply followed by periods of shortage (the "cobweb model" as it applies to the labor market).

17. (Appendix 9B) The hedonic model implies that those who obtain the most education are least averse to learning and probably most able to learn quickly.

Answers to Even-Numbered Review Questions 2. "The vigorous pursuit by a society of tax policies that tend to equalize wages across skill groups will frustrate the goal of optimum resource allocation." Comment.

Answer: As indicated in Chapter 1 and elsewhere, the optimum allocation of resources requires that all mutually beneficial transactions be accomplished. If wages are forced toward equality by government fiat, potentially beneficial human capital transactions may be discouraged. That is, because the acquisition of training and education is costly, human capital investments will not be undertaken unless there is a future return to them. These returns normally are in the form of higher wages paid to those with the higher skill levels, and if these higher wages cannot be paid, human capital investments that might have been made will be discouraged. Thus, the pursuit of wage equalization across skill levels will discourage human capital investment and may result in too few workers entering skilled occupations.

4. When Plant X closed, Employer Y (which offers no training to its workers) hired many of X’s employees after they had completed a lengthy retraining program offered by a local agency.

The city’s Equal Opportunity Commission noticed that Employer Y hired only the younger workers from X and launched an investigation. During this investigation employer Y claimed that it hired all of the applicants from X who had successfully completed the retraining program, without regard to age. From what you know of human capital theory, does Y’s claim sound credible? Explain.

Answer: Y’s claim is consistent with human capital theory in two respects. First, its own hiring and training costs appear to be negligible (we are told that it offers no training on its own, and that its hiring standards consist of taking successful graduates of another program). Because it makes no major investments in its workers, it therefore has no reason to prefer younger workers. Second, because the retraining program to which X’s former employees had access was “lengthy,” it may well be that only the younger workers from X decided to invest in this retraining. All workers have to decide whether a human capital investment opportunity will have expected benefits (properly discounted to the present) that are at least equal to the costs, and a shorter period over which benefits are received reduces these benefits. Thus, older workers are less likely to have decided to invest in retraining – with the result that only the younger workers became qualified to apply to Employer Y. 6. A study shows that, for American high school dropouts, obtaining a General Equivalency Degree (GED) by part-time study after high school has very little payoff. It also shows, 73

however, that for immigrants who did not complete high school in their native countries, obtaining a GED has a relatively large payoff. Can signaling theory be used to explain these results?

Answer. Graduating from high school is more or less the expectation for American students, and those who drop out may be viewed as having a low aptitude (or low tolerance) for learning, even if they later obtain a GED. Immigrants may come from countries in which high schools are either more demanding or less available, so dropping out may not send the same signal of low aptitude or tolerance. If, though a GED, these immigrants are certified as knowing the equivalent of American high school graduates, employers may prefer them to American GED recipients, other things equal.

8. Many crimes against property (burglary, for example) can be thought of as acts that have immediate gains but run the risk of long-run costs. If imprisoned, the criminal loses income from both criminal and noncriminal activities. Using the framework for occupational choice in the long run, analyze what kinds of people are most likely to engage in criminal activities. What can society do to reduce crime?

Answer: People who have low expectations of both current and future income from all activities are more likely to engage in crime, because the forgone benefits of other activities due to imprisonment are lower. Thus to reduce crime, society needs to increase labor market opportunities for these individuals.

10. The following statement was overheard at a party: “It is just not right that Joe, who never went to college, makes more than Ken, who has a master’s degree. People with higher degrees deserve to earn more!” Use human capital theory to comment on this quotation.

Answer: Human capital theory suggests that those making decisions about investing in schooling weigh the present value of expected future benefits against the near-term cost. One element of cost is forgone earnings. Joe, who did not go to college, may earn more in the near term, but Ken is likely to earn more in the long run (or he made a poor investment in education).

Answers to Even-Numbered Problems 2. (Appendix) Suppose the supply curve for optometrists is given by Ls = -6 + .6W, while the demand curve is given by Ld = 50 - W, where W = annual earnings in thousands of dollars per year and L = thousands of optometrists. a. Find the equilibrium wage and employment levels. b. Now suppose that the demand for optometrists increases and the new demand curve is L'd = 66 - W. Assume that this market is subject to cobwebs because it takes about three years to produce people who specialize in optometry. While this adjustment is taking place, the short-run supply of optometrists is fixed. Calculate the wage and

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employment levels in each of the first three rounds and find the new long-run equilibrium. Draw a graph to show these events.

Answer: a. Initial equilibrium W = $35, W = 15. (Find this by setting Ls = -6 + .6W = Ld = 50 W and solving for W.) b. First round: L is still 15, so W = $51. This is point A in the figure. (Find W by plugging L = 15 into the new Ld equation.)

Second round: Labor supply reacts to first round wage, L = 24.6, but this pushes W down to $41.4 (at point C). Find this by plugging W = $51 into the Ls equation to find L = 24.6, and then plugging L = 24.6 into the new Ld equation.

Third round: Labor supply reacts to second round W, L = 18.84, but this pushes W up to $47.16 (see point E). Find this by plugging W = $41.4 into the Ls equation to find L = 18.84 and then plugging L = 18.84 into the new Ld equation.

Long-run equilibrium, W = $45, L = 21. (Find this by setting Ls = -6 + .6W = Ld = 66 - W and solving for W.) 4. Prepaid college tuition plans, also known as Prepaid Education Arrangements (PEAs), allow you to prepay college tuition at present-day prices. The value of the investment is guaranteed 75

by the state to cover public college tuition, regardless of its future cost. You are considering the purchase of an education certificate for $25,000, which will cover the future tuition costs of your 8-year-old daughter. You expect the tuition costs of your daughter’s bachelor’s degree to total $50,000 in 10 years. What would your personal discount rate need to be in order for it to be worthwhile for you to make the investment and purchase the certificate?

Answer: Set the future value (50,000) equal to the present value (25,000) times (1 + i)10. The discount rate is 7%.

Suggested Essay Questions 1. Assume that a developing country with a labor force that includes many children, ages 1014, wants to reduce the use of child labor. Suppose that it decides to open more schools, so that children who do not now have a school near their home can attend a school without a long commute. Analyze how opening new schools will affect child labor, explaining these effects fully.

Answer. Human capital theory suggests that those making decisions about investing in schooling weigh the present value of expected future benefits against the near-term cost. One element of cost is forgone earnings, which will be nonzero for children who could work. A second element, however, is the cost of commuting (time and expense, perhaps involving living away from home) to school. Making schools more geographically accessible, then, lowers the cost of investing in human capital – and theory predicts that more young students would attend school rather than work.

2. Suppose financial aid to college students was financed by income taxes on the general population and the president cut this aid significantly (correspondingly cutting taxes).

Analyzing the likely labor market effects of these cuts, identify the groups that would gain and lose from these cuts over their lifetimes. Discuss your reasoning concerning each in turn.

Then analyze the likely effects on the retirement ages of these groups.

Answer: If the costs to individuals of attending college are raised, fewer high school graduates will decide to attend. The market for high school graduates will experience an increase in supply at any given wage -- a shift in the supply curve that tends to decrease wages. The smaller number of college students reduces supply to college-educated jobs, tending to increase the wage. The growth in the earnings differential between high school and college graduates serves as an inducement for people to go to college, and this gap will grow to the point where the higher costs of going to college are offset by the greater returns. The marginal student, therefore, is just compensated for his or her more costly investment.

The gainers are (1) those who have already gone to college (at lower cost) and now find themselves the beneficiaries of wages that are higher than expected, (2) those who go to college and would never have been supported by the subsidy anyway (they get higher wages as fewer subsidized students attend), and (3) firms that hire high school graduates and can now pay lower wages. All three groups also are the beneficiaries of the tax cuts. The probable losers are 76

(1) current college students who assumed they would be subsidized and whose subsidies are lost after they enter college, (2) students and former students who stop at high school (whose wages are now lower), and (3) firms that hire college graduates. Group I may continue on and receive a lower rate of return than anticipated or may quit and get the lower wages high school graduates now must take. All three groups gain from the tax cut to some extent, so an overall assessment of their gains and losses is difficult.

Students who are at the margin of deciding whether to go to college or not are neither big gainers nor big losers. Those who decide to go despite the increased costs will receive higher wages as college graduates decrease in numbers; thus, their rate of return is more or less the same as it would have been before. Those who would have gone to college but do not go after the subsidy is cut are the very ones -- the ones at the margin -- who received the smallest return from going.

While they lose, their losses are not large, and may be fully offset by the tax cut.

For those already out of college, the tax cut and higher wages induce both a substitution effect (retire later) and an income effect (retire earlier). One cannot tell which effect will dominate. For those who now go to college, the higher wages just offset the greater costs of investment in human capital. Their lifetime wealth is thus held constant, but their wages rise. This induces a pure substitution effect and later retirement. For high school graduates, lower wages are to some extent offset by lower taxes, mitigating both substitution and income effects; effects on their retirement decisions are thus unclear.

4. The United States is currently facing an education crisis in its high schools, which are graduating people with insufficient skills in mathematics and communications to perform tasks now required in the workplace. One suggested solution is to increase the level of competency required for high school graduation. The other suggestion stems from the observation that employers seem to care much more about job applicants' possession of a high school degree than their high school grades; this suggestion is that employers tie wage offers for entry-level jobs to applicants' high school grades (higher grades would mean higher wages). Compare the labor market effects of these two strategies for improving competency levels among high school graduates.

Answer: The first proposal, which basically increases the difficulty of graduating from high school, will tend to reduce the supply of high school graduates and increase their wages relative to the wages of those who do not graduate. Thus, the returns to graduating from high school should rise, and along with it will rise the incentives for obtaining the threshold of competency required to graduate.

The second proposal also increases incentives for students to study harder because better grades result in higher wages. This proposal would also serve to increase rates of return to studying in high school, but the incentives to acquire competencies above the graduation threshold are stronger than under the first proposal (because pay is tied to grades, not just graduation).

The first proposal would slightly reduce employers' costs of hiring workers because they could be guaranteed that all applicants with diplomas met required levels of competency. However, if 77

they needed workers with competency levels above the threshold for graduation, they would then have to engage in some kind of testing on their own (as they would have to do now). The second proposal might slightly increase hiring costs because it would require employers to look at grades (which they could be doing now but presumably have chosen not to).

5. Currently, anyone can advertise as an auto mechanic. Some of those who offer their services as mechanics are highly competent, but others are not as well-trained or otherwise not as good. Suppose that the government, in an effort to upgrade the quality of mechanics, promulgates legislation requiring all new mechanics to take three years of post-high school training and to pass a competency test. Those who are currently mechanics will not be subjected to these requirements. What are the likely labor market effects of this legislation?

Which labor and consumer groups would gain and which would lose?

Answer: The overall effect of this requirement to license mechanics will be to reduce the supply of mechanics and to increase their wages (average quality will rise as well.) The labor market groups that gain are current mechanics, whose wages will be increased but who are not subject to the licensing procedure themselves, and future mechanics of high quality (who will not have to compete with low quality, lower cost mechanics in the future). The labor market groups that lose include those who would have become low cost, low quality mechanics; these potential mechanics will either be barred from the market or will have to make training investments that they would not otherwise have made. Put differently, the returns to training for those who would have obtained it anyway will rise, but mandating such training will prevent some from entering the profession and force others to undertake such training even though it might be very costly for them in economic or psychic terms.

Among consumers, the gainers will be those who want high quality repairs and previously had to spend time and effort to distinguish the high quality from low quality mechanics. Losers will be poorer consumers, who may have preferred low cost, low quality repairs to doing the work themselves, to paying the higher cost for high quality repairs, or to having no repairs at all.

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CHAPTER 10 - WORKER MOBILITY: MIGRATION, IMMIGRATION, AND TURNOVER This chapter employs the human capital framework to analyze the phenomena of geographic mobility and worker turnover. It demonstrates how the insights of human capital theory can explain the observed patterns of mobility and turnover, including the personal characteristics of those most likely to exhibit either kind of mobility.

The chapter also describes and analyzes immigration policy in the United States. It considers the problem of illegal immigration and uses economic theory to identify the gainers and losers from a more restrictive immigration policy. Finally, the section on immigration concludes with an analysis of the overall effects of immigration (including illegal immigration) on the "native" population.

The lengthy section on U.S. immigration policy is, of course, motivated by our human capital analysis of individual migration. However, the section does not directly employ human capital analytics. Thus, instructors who want their students exposed to human capital analysis as it applies to geographical mobility and turnover, and who are willing to forgo an analysis of the very topical issue of illegal immigration and what to do about it, could save some time in the course by eliminating the section of the chapter on immigration policy.

List of Major Concepts 1. Worker mobility can be viewed as a human capital investment, in which the benefit is added utility in the future and the costs are the direct and psychic costs of quitting one employer and seeking work elsewhere.

2. People will move from jobs or areas where pay is relatively low to jobs or areas where pay is relatively high unless such mobility is inhibited by a short time horizon (or high discount rate), costs of finding out about alternatives elsewhere, or high costs of the move itself.

3. There is an element of self-selection in immigration because those who are most likely to migrate are those for whom the net benefits of migration are largest (although the benefits are often initially depressed by unfamiliarity with the language or customs of the area to which they have moved).

4. Countries in which the earnings distributions is more compressed than in the United States will tend to send relatively skilled workers to the United States, while those with distributions that exhibit greater variance will tend to send less-skilled workers to the United States. U.S. immigration has tended to become less-skilled in recent years.

5. Like other investments, migration investments can fail to work out as expected, resulting in "return migration."

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6. A large influx of immigrants will tend to lower wages in the relevant labor markets and create more employment, but only in special circumstances would an influx of X immigrants take X jobs away from "natives."

7. The argument that immigrants fill jobs no "native" would take overlooks the fact that inducements to work in a particular occupation are not independent of the wage being offered.

8. Immigration may increase product demand and the demand for other skill grades of labor.

9. If immigrants receive wages equal to their marginal product, the native population as a whole will not experience a loss of income unless the immigrants receive government services whose value exceeds the taxes they pay.

10. "Matches" between employer and employee are improved through the process of voluntary quits and involuntary layoffs. The human capital model can be used to model quit behavior.

11. Human capital theory can shed light on the cyclical pattern of quit rates, the pattern of quit rates across age groups, and international differences in quit rates.

12. The costs of quitting and searching for a new job may produce an upward sloping supply curve to individual firms, leading to monopsonistic behavior.

Answers to Even-Numbered Review Questions 2. One way for the government to facilitate economic growth is for it to pay workers in depressed areas to move to regions where jobs are more plentiful. What would be the labor market effects of such a policy?

Answer: Clearly, interregional migration would be increased as a response to this migration subsidy, and employment would grow in areas of high economic opportunity. The effects on employment in areas of reduced economic opportunity and the effects on wages in both areas depend on assumptions made about the labor market.

If it is assumed that the labor markets in both areas are in equilibrium and that wages in the area of reduced economic opportunities are lower than they are elsewhere, then there would be incentives for workers to leave the low wage area and migrate to the higher wage area. If there are high costs of migration, some workers would not respond to a moderately large wage differential because the gains from migration (that is, the increase in wages) would not be sufficient to cover the cost of migration. However, when the costs of migration are reduced by the subsidy, more people will respond to a given wage differential and move from the depressed area to the area of better opportunity. This move will shift the supply curve for the depressed area to the left, shift the supply curve for the area of better opportunities to the right, and thus reduce the wage differential between the two areas. Thus, if equilibrium is assumed, the migration subsidy 80

reduces employment in the sending area at the same time it raises wages there; it increases employment in the receiving area at the same time it reduces wages there. A new equilibrium wage differential across the regions will be created (and of course it will be smaller).

If the problem in the sending area is one of unemployment due to wage inflexibility in that area (that is, the wage rate lies above the equilibrium wage), then an increase in out-migration will reduce unemployment in the sending area, although it may not affect the wage rate. If wages were correspondingly inflexible in the receiving areas, the greater influx of migration to that area could increase unemployment there. However, if the demand for labor in the receiving areas is shifting to the right for some reason, the added influx of workers may indeed be accommodated without a rise in unemployment. (In Chapter 12 we discuss the issue of "wait unemployment.")

4. Suppose the United States increases the penalties for illegal immigration to include long jail sentences for illegal workers. Analyze the effects of this increased penalty on the wages and employment levels of all affected groups of workers.

Answer: Jail sentences for illegal immigrants would reduce the net gains from immigration, even if the probability of being apprehended is small. The reduced net benefits from migration should reduce the number of illegal immigrants coming into the country and, assuming these immigrants are unskilled workers, this reduction should raise wages in the unskilled labor market. Thus, unskilled native workers benefit by the imposition of jail sentences on illegal immigrants who are apprehended. Employment in the unskilled market goes down, although unskilled employment among natives increases.

Skilled workers may be adversely affected by this new policy because reduced immigration may mean reduced product demand (and therefore have a scale effect on the demand for their services). Moreover, if skilled and unskilled workers are gross complements, the reduction of unskilled employment and the increase in the unskilled wage may cause the demand for skilled workers to decline. If there is a leftward shift in the demand for skilled workers, there will be a reduction in wages and employment in the skilled markets. (Of course, if skilled and unskilled workers are gross substitutes, the decline in demand brought about by the reduction in product demand would be mitigated or even offset by the increased substitution of skilled workers for the now-more-expensive unskilled labor.)

Workers from outside the United States who would otherwise have become illegal immigrants (but who are now deterred from immigration) will be worse off. However, those who decide to immigrate and are not apprehended will be better off because they will receive higher wages in the unskilled market. Finally, those workers in the sending country who would not immigrate in either situation may be worse off under the new policy if there is a labor surplus in their country.

6. As pointed out in Chapter 9, the last two decades in the United States have been characterized by a very wide gap between the wages of those with more education and those with less. Suppose that workers eventually adjust to this gap by investing more in education, 81

with the result that the wages of less-skilled workers rise faster than those of the more-skilled (so that the wage gap between the two falls). How would a decline in the wage gap between the skilled and the unskilled affect immigration to the United States?

Answer: Immigrants at least implicitly compare the wages they can expect in the United States with those they can expect in their place of origin. Thus, if the American unskilled wage rises relative to the skilled wage, the United States should experience a rise in unskilled relative to skilled immigration. Further, because this declining gap between the educated and the lesseducated serves to make the American distribution of earnings more equal, changes in the countries of origin can be expected.

Skilled workers tend to come from countries with more equal earnings distributions than found in the United States (many European countries, for example), while unskilled workers tend to come from countries (often developing countries) with less equal earnings distributions. When the American earnings distribution becomes more equal, there will be reduced incentives for immigration from countries that previously had more equality, and more incentives for immigration from countries with less-equal distributions. One interesting possibility is that the American earnings equality could surpass the equality in some other countries, and in this case the immigration from these countries could go from being “positively selected” to being “negatively selected.”

8. Two oil-rich middle-east countries compete with each other for the services of immigrants from India and Pakistan, who perform menial jobs that local workers are unwilling to perform.

Country A does not allow women to work, drive or go out of the house without a chaperone.

Country B has no such restrictions. Would you expect the wages these two countries pay for otherwise-comparable male immigrants to be roughly equal? Why or why not? Explain.

Answer. The supply of immigrants to A will be restricted, partly because female immigrants who want to work will not go there and partly because married men will avoid A because of the restrictions on their wives. The wages in A will have to be higher in order to attract immigrants.

10. A recent study by a noted economist has found evidence that a 10 percent increase in immigration within a given skill group reduces the wages of “natives” in that skill group by 3.5 percent. One social commentator has said, “These findings suggest only one conclusion: immigration is bad for American workers and therefore bad for American society.” Using economic theory, comment on this quote.

Answer: The social commentator’s answer is too simple. First, consumers gain through lower prices due to lower labor costs. Employers gain from less-expensive labor, at least in the short run. Since rough labor and skilled labor are generally gross complements, wages may increase for skilled workers as the demand for these complementary workers increases. Immigrants also add to society as both consumers and producers of goods and services, and thus in general give positive returns to the economy as a whole. There are other factors that may need to be considered, such as the initial costs of public subsidies that may be needed, but in general, the argument for immigration cannot simply be summarized by looking at the effect on wages of native workers in the same skill group.

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Answers to Even-Numbered Problems 2. Suppose that the demand for "rough laborers" is Ld = 100 – 10W, where W = wage in dollars per hour and L = number of workers. If immigration increases the number of rough laborers hired from 50 to 60, by how much will the short run profits of employers in this market change?

Answer: The short-run profits of the employer equal the area below the MPRL curve and above the wage rate. See the figure. This will increase from area W1AB in the figure to area W2AC. Find the wage rates by plugging the employment levels into the Ld equation. 50 = 100 – 10W initially, so W = $5 per hour. 60 = 100 – 10W after the immigration, so W = $4 per hour. The area of the triangle is .5(base x height), so the area of W1AB is 50x$5x.5 = $125 per hour, and the area of W2AC is 60x$6x.5 = $180 per hour. Thus, profits have risen by $55 per hour.

4. The following table summarizes the market for labor in an occupation. “Demand” is the number (in thousands) of employees firms would be interested in hiring at particular wages. “Domestic supply” is the number (in thousands) of native workers who are interested in working in the occupation at particular wages, and “immigrant supply” is the number (in thousands) of immigrants who are interested in working at particular wages. a. Graph the following curves for this labor market: demand for labor, domestic supply, and total supply of workers. b. What is the equilibrium wage rate before immigration? How many workers would be hired? c. What is the equilibrium wage rate after immigration? How many workers would be hired?

How many domestic workers would be hired? How many immigrant workers would be hired? d. Comparing your answers in parts b and c, has immigration caused a change in the number of domestic workers hired? What was the change, if any? Why did the change, if any, occur?

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Answer: a. Easily graphed from table. b. Prior to immigration, the wage was $7, and 26 workers were hired. c. After immigration, the wage is $5. 28 workers are hired; 24 are domestic and four are immigrants. d. After immigration, two fewer domestic workers are hired. The change occurred due to the drop in the wage; at the lower, post-immigration wage, these workers choose not to work in this market.

Wage ($) 3 4 5 6 7 8 9 10

Demand 30 29 28 27 26 25 24 23

Domestic Supply 22 23 24 25 26 27 28 29

Supply 4 4 4 4 4 4 4 4

Suggested Essay Questions 1. A particular manufacturing company employs low-skilled workers in a developing country in which turnover among such workers is generally high. The company’s president states that it is her goal to ensure that “workers have a serious emotional connection to our company.” The company is unusual in that it offers air conditioning, showers, tuition for English courses, and monthly parties. In what ways might these policies make it difficult to retain employees, and in what ways might they help?

Answer. The provision of these non-wage benefits is costly, and the theory of compensating differentials suggests that their presence will serve to reduce the wages that their workers could otherwise command elsewhere. Lower wages, by themselves, will tend to increase turnover at the firm, especially among workers who do not value the non-wage benefits very highly.

However, these benefits will also serve to attract those who value the amenities of parties, education in English, air conditioning, and so forth – and because these amenities are unusual, those who place a high value on them will tend to remain with the firm (the could not get them elsewhere).

2. A recent article in University X’s student paper claimed that full professors at University X are paid much lower than full professors in most other comparable universities, even after controlling for the cost of living. If you were advising X’s president on whether to worry about this issue, explain what additional information you would seek, and why.

Answer: Employers need to pay wages and salaries high enough to attract and retain employees of the quantity and quality they desire. Wages at X could be lower because it offers other nonwage attractions (more generous benefits, a more pleasant working or living environment) that are valued by its professors. The president should thus investigate whether X is experiencing high turnover or difficulties in attracting new hires before he or she considers raising salaries.

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3. For the last 100 years coal mine operators in South Africa have recruited migrant workers from other African countries to work in their mines for a specified period (for example, three years). These miners have been housed in male-only dormitories and have not been permitted to live with their families. Recently, the migrant workers and their unions have resisted this policy of separating workers from their families, and in a few instances workers have defied company policy and moved their wives and children into their rooms. If the migrant workers are successful in their efforts to live with their families, what are the likely labor market consequences?

Answer: Although it is hard to say what will happen to employment, there are two major reasons to predict that the wages of migrant coal miners will fall. First, from the supply point of view, the ability of their families to accompany them will make coal mining jobs in South Africa more attractive. At any given wage rate the supply of workers to the coal mines should be increased, and this will put downward pressure on wages. Second, companies will have to build more dormitories if families are to accompany their employees, and the added dormitory costs will be treated as an increased cost of hiring workers. For this reason, therefore, the number of workers demanded at any employee wage rate will fall, shifting the demand curve to left and again putting downward pressure on employee wages. Because dormitory costs are quasi-fixed in nature, however, employers will want to increase hours per worker as they cut back on the number employed.

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CHAPTER 11 - PAY AND PRODUCTIVITY This chapter explores in detail the relationship between compensation and productivity. It begins with a discussion of the employment contract, which is largely implicit and legally unenforceable. How this contract can be made self-enforcing within the context of asymmetric information is the principal focus of this section.

After discussion of some general issues relevant to worker motivation, we turn (in sequence) to an analysis of how motivation is affected by the basis of pay, the level of pay, and the sequencing of pay. Thus, we discuss in turn issues related to piece rates, commissions, profit sharing, and hourly pay (including merit pay); efficiency wages; and deferred payment schemes, promotion tournaments and the issue of "career concerns. " The chapter ends with a short section on two puzzles: why earnings increase with tenure and why they increase with firm size.

List of Major Concepts 1. Productivity varies across workers and over time for a given worker, and it involves taking the initiative in a myriad of hard-to-observe ways that advance the employer's interests.

2. Contracts can be both formal and implicit, with the latter being incompletely specified and hence legally unenforceable.

3. For an implicit contract to be self-enforcing, the parties can rely on signals that they are contracting with the "right kind" of person; alternatively, they can structure the contract so that the other party derives more from honest continuation of the employment relationship than from reneging on their promises.

4. Dividing a "surplus" between marginal revenue product and the alternative wage is critical to a self-enforcing employment contract; this surplus can be created by labor investments of one sort or other.

5. Workers can be motivated to be highly productive by close supervision or by having their earnings tied to their performance; the latter method requires that the measures of their performance be correlated with their effort and the employer's objectives.

6. Because of group considerations, motivation techniques must take account of the perceptions of fairness and issues of group loyalty.

7. Compensation schemes are jointly chosen by employer and employee.

8. Schemes that tie pay to individual productivity must take account of worker risk aversion, but they are useful in eliciting signals about worker characteristics.

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9. Output is not normally one-dimensional, and if pay is based on objectively-measured aspects of output ("quantity"), workers will put forth little effort to increase output along the other (subjective, or "quality") dimensions.

10. Group incentive schemes run the risk of creating "free rider" problems.

11. Time-based pay with merit increases can be based on either absolute or relative output; absolute measures do not correlate as closely with individual effort, but relative measures can induce counterproductive behaviors among employees.

12. Employees who feel generously treated by their employers may put forth greater effort; hence, by increasing their wages employers can increase the productivity of their workers (the efficiency wage).

13. Efficiency wages are most effective when the employer-employee tenure is expected to be long.

14. With long expected tenures, the sequencing of pay is also an option; this option promises handsome future rewards for current effort.

15. One scheme involves a period of underpayment followed by later overpayment, which has both signaling value in obtaining future-oriented, hard-working employees and offers incentives for current workers to put forth effort.

16. Promotion tournaments also have signaling and incentive value.

17. Employee "career concerns" (which can involve future payoffs with other employers) can both distort and enhance efforts with one's current employer.

18. Concepts in this chapter contribute to the cluster of hypotheses that seek to explain why wages rise with tenure and why large firms pay higher wages.

19. As firms increase in size it becomes increasingly costly to monitor worker effort, and one way to cope with this monitoring problem is to pay higher wages. The higher labor costs associated with greater firm size suggests that the labor supply curve to a firm may be upward sloping, and this may explain monopsonistic behavior among firms in the labor market.

Answers to Even-Numbered Review Questions 2. The earnings of piece-rate workers usually exceed those of hourly paid workers performing the same tasks. Theory suggests three reasons why. What are they?

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Answer: First, if stability of hourly pay is preferred to the potential fluctuations of piece rate pay, then part of the "earnings premiums" enjoyed by piece-rate workers is a compensating wage differential. Second, piece-rate pay will appeal most to workers of above-average productivity; therefore, such workers are most likely to accept jobs paid by the piece. Third, piece rates increase the incentives of given individuals to expend effort, which increases their pay.

4. Suppose two pizza parlors employ drivers whose job it is to deliver pizzas to those who order over the phone. One company pays its drivers an hourly wage, and the other pays them by the number of pizzas delivered each day (which can be affected by efforts of drivers to deliver and hurry back for the next order). Which company is more likely to experience higher rates of traffic accidents among its drivers? Why? Answer: Drivers paid by the piece are motivated to deliver more pizzas per day. Thus, they may drive faster and deliver more quickly than those paid by the hour, other things being equal -- all of which increase their risk of accidents.

6. Some real estate brokers split the commission revenues generated by each sale with the responsible agent, as described in question 5. Others, however, require their agents to pay them (the brokers) money up-front, and then allow the agents to keep the entire commission from each sale they make. Which agents would you predict to have the larger volume of sales, those who split all commissions with their employer or those who pay an up-front fee to their employer and then keep the entire commission? Explain.

Answer: There are two reasons to expect that agents paying an up-front fee will generate more sales. First, having paid the fee, agents can keep the entire commission from each additional sale.

Their incentives to make an additional sale are therefore stronger, and one would expect them to work longer hours and engage in more intensive efforts to increase their sales volume. Second, the requirement to pay the broker an "employment fee" in advance of sales will restrict interest in that kind of pay scheme to those agents whose experience and skills give them reasonable assurance they will have a high sales volume. Thus, the "up-front fee" scheme calls forth signals about the agents' own expectations concerning volume (in this regard, it has effects analogous to those of the "underpayment-then-overpayment" compensation scheme described in the text).

8. Suppose that, in commenting on Japan’s system of offering some workers lifetime jobs, an analyst claims that Japanese employers are paying their senior workers more than they are worth. Is this comment consistent with economic theory? Explain.

Answer. Yes, it is consistent. Employers offering lifetime jobs have the ability, and often the incentive, to offer a payment scheme that underpays workers in their early years (wage less than marginal product) and overpays them later on (wages greater than current marginal productivity). The later overpayment serves to compensate workers for their earlier underpayment, and it is necessary to attract workers to the firm. The purpose of this scheme is to provide incentives for employers to stay with the firm and work diligently (and honestly), lest 88

they be discovered shirking and lose the opportunity for overpayment.

Answers to Even-Numbered Problems 2. A firm is considering adopting a plan in which it would pay employees less than their MRPL early in their careers and more than their MRPL late in their careers. For a typical worker at the firm MRPL = 10 + .1T, where T = the number of years which the worker has been employed at the firm and MRPL is measured in dollars per hour. The worker's wage per hour is W = 8 + .2T. Assume that this wage is high enough to attract workers from alternative jobs, that the discount rate for the firm is 0, and that the expected tenure of a typical worker is 35 years. If workers retire after 35 years, will this plan be profitable for the firm?

Explain. For how many years will the firm "underpay" it workers?

Answer: The graph shows the wage and MRPL lines, which cross after 20 years. The firm will adopt the plan because it expects to profit from it -- the early underpayments exceed the later overpayments. (Because the discount rate is zero, we can find the present value of underpayments and overpayments by simply adding them up.) Triangle A (the initial underpayment) and triangle B (the later overpayment) are equal when T = 40 years. Triangle A exceeds triangle B if retirement comes before tenure equals 40 years.

closely related to a CEO’s performance, and toward bonuses that are more discretionary in nature. Use economic theory to analyze the dual claim that stock options are not closely related to CEO 89

performance and that moving away from them and toward discretionary bonuses will strengthen incentives for CEOs to perform well.

Use economic theory to analyze the dual claim that stock options are tenuously related to CEO performance and that moving away from them and toward bonuses will strengthen incentives for CEOs to perform well.

Problems

1. Suppose that the market wage is $5 per hour, but Charlie will work harder if his employer pays him a higher wage. The relationship between Charlie’s wage and MRPL is given in the following table. What is the efficient wage for Charlie?

Wage ($/hour)

MRPL ($/hour)

4

6.00

5

8.00

6

9.50

7

10.25

8

11.00

9

11.50

10

12.00

11

12.25

12

12.50

13

12.75

4. Suppose the wage rate that is paid at a particular firm is W = 5 + 0.5T, where T = the number of 90

years that the worker has been employed at the firm. The marginal revenue product, which is measured in dollars per hour, is MRPL = 6 + 3T. Assume that the wage is high enough to attract workers from alternative jobs. a. Ignoring the discounting of future values to the present, graph the wages and MRPL over a period of 12 years. b. Would this pay scheme be more attractive to (a) a worker who is looking for stable employment with the same firm for the next 12 years or (b) a worker who plans to move to another geographic area in six years, which would necessitate leaving his or her job?

Explain.

Answer: a. Easily graphed from the equations or table below. b. See table. Since wages increase with tenure, this mght be more attractive for someone who is seeking a stable job. If you leave after 6 years, you do not reap the full benefits of wages increasing with time. However, the MRP always exceeds the wage in this example, so it could be argued that neither worker would really want to keep this job over time, and that if you leave after 6 years, the extent to which you are underpaid over time is lessened.

Year 1 2 3 4 5 6 7 8 9 10 11 12

Wage 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50 11.00

MRP 9 12 15 18 21 24 27 30 33 36 39 42

Suggested Essay Questions 1. Firm X is working with Firm Y on creating innovative educational materials that will be used to create courses to be taught using the internet. Firm X is supplying the computer specialists, while Firm Y is supplying the course content materials. Both firms will share in the profits of the courses they jointly produce. Firm X wants Firm Y to adopt financial incentives for its employees working on this project to finish their work according to a deadline. Under what conditions will incentives be most effective? Are these conditions likely to hold in this case?

Answer. Production incentives are most effective when they perfectly align the interests of workers and owners, and when a worker’s output is only affected by his or her effort (and not affected by factors outside the control of the individual). In this case, we must question whether either condition is met. First, producing a high-quality course in a brand new environment requires creativity in dealing with issues that cannot be foreseen, so tailoring incentives to 91

deadlines might not align the interests of employer (who wants quality) and employee (who wants to meet a deadline). Second, X and Y are jointly producing these programs, so delays or mistakes made by one team will affect the ability of the other to meet the deadline; put differently, the output of Y is not completely under the control of its workers.

2. In recent years, many plants have closed, forcing thousands of workers out of their jobs and into new ones. Studies of wage loss suffered by these displaced workers find that, among groups of workers with exactly the same skills and types of training, workers who had been with the firm for many years and were in the 55-64 age range had greater wage losses than those in the 25-34 age range. How might a compensation scheme designed to enhance worker motivation lead to this result?

Answer: The compensation scheme that pays workers less than they are worth initially, and more than they are worth later on, could result in this outcome. Older workers end up getting pay that is high relative to their productivity, and when they have to find another employer their pay drops substantially. Younger workers, who are lower paid under this scheme to begin with, do not experience such a drop in wages.

3. Most workers earn a straight hourly wage, but some have their compensation based entirely on a piece rate. List the reasons why workers on a piece rate earn more, on average, than comparably-skilled workers earning straight hourly wages.

Answer: There are three reasons why piece rate workers receive higher wages. First, piece rate workers are motivated to work faster than hourly-paid workers with similar skills. Second, under piece rates low-productivity workers get paid less, so only the most productive workers choose piece rates. Third, since the risk of low-productivity periods falls on the employee, a compensating wage differential may have to arise to lure workers into piece-rate employment.

4. An amusement park open only in the summer hires teenagers to operate its rides and concession stands, paying them $3.00 per hour and putting aside $1.50 per hour into a fund that they will receive as a lump-sum payment if they work through Labor Day (typically, its biggest day of the year). (a) What problem is the amusement park apparently trying to solve with its compensation plan, and in what two ways does this plan help to solve the problem? (b) Suppose the government rules that the compensation plan violates minimum wage laws because workers who quit before Labor Day receive only $3.00 per hour. How can the park now address the problem mentioned in your answer to (a)?

Answer: (a) The park has apparently had trouble keeping its teenage workforce through Labor Day. This compensation plan will appeal most to job applicants who intend to work through Labor Day (that is, it has signaling value), and it also gives current workers incentives to stay on through then. (b) If the plan is struck down, the park has limited alternatives owing to the seasonality of its 92

labor demand (which probably rules out efficiency wages and other plans based on long-term attachments). It could invest more in screening applicants, substitute capital for labor, or devote more resources to supervising employees (with an eye toward persuading them to stay on the job or capitalizing on "career concerns" by providing detailed recommendations to future employers).

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CHAPTER 12 - GENDER, RACE, AND ETHNICITY IN THE LABOR MARKET This chapter represents a comprehensive inquiry into wage differentials across gender, racial and ethnic groups. It begins with a section on earnings differences by gender, in which the overall differential is broken into two parts: that associated with measurable productivity differences and that associated with unobserved (unexplained) differences. The latter differences are associated with (but not confined to) current market discrimination. Discrimination is defined and problems of its measurement are discussed in the context of analyzing gender differences in earnings.

Black-white earnings differentials are analyzed next in a subsection that includes a brief treatment of differences in the ratios of employment to population. Earnings by ethnicity are also discussed. In each case, the analysis includes a review of attempts to estimate the effects of discrimination, with special emphasis on the effects of such hard-to-observe factors as English language proficiency, cognitive achievement, and school quality.

The second major section of the chapter analyzes theories of market discrimination. Becker's theories of employer, customer, and employee discrimination are discussed, and the theory of statistical discrimination is explained, along with noncompetitive models of discrimination (occupational crowding, dual labor markets, search-based monopsony, and theories involving collusive action).

The chapter concludes with in-depth discussions of governmental efforts to reduce or eliminate market discrimination: the Equal Pay Act of 1963 and the Civil Rights Act of 1964. Included in our discussion of the last are the evolution of the disparate impact standard by the courts (as opposed to a disparate treatment standard), legal decisions involving seniority, and the emerging comparable worth remedy. The chapter closes with an analysis of the federal contract compliance program, including the standards against which affirmative action plans are judged and the results of studies that have tried to assess the effects of the program.

The appendix to Chapter 12 contains an introduction to the problems of estimating comparable worth "earnings gaps." The purpose of this appendix is twofold: to give students a brief illustration of the use of regression analysis and to show them how comparable worth comparisons are made.

List of Major Concepts 1. Income disparities between men and women may have their roots in different incentives to acquire productive characteristics.

2. Current labor market discrimination is said to exist when the market places values on personal characteristics of workers that are unrelated to productivity.

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3. Earnings differentials caused by differences in productive characteristics are termed "premarket."

4. Occupational segregation is one form of discrimination, and it can be measured by an index of occupational dissimilarity; however, it is difficult to distinguish between the effects of occupational choice and those of employer discrimination.

5. To measure the extent of wage discrimination, one must determine what the earnings ratio would be if the protected class and white males had the same productive characteristics.

However, the adjusted differential is in reality an unexplained differential, and it could reflect the effects of unmeasured worker characteristics as well as market discrimination.

6. Much of what appears to be labor market discrimination against women takes the form of occupational segregation, which, while still rather marked, seems to be declining somewhat recently.

7. When productive characteristics are controlled in an analysis of earnings differentials, they account for nearly all of the gender wage differential.

8. Differences in the black-white employment-to-population ratio are a function of both higher unemployment rates and lower labor force participation rates among blacks.

9. Studies using conventionally-measured variables for productive characteristics suggest that about 11 percentage points of the observed disparity between black and white males may be due to current labor market discrimination. Studies that control for cognitive achievement scores as well suggest that black men earn from 8 percent more to 8 percent less than white men with comparable productive characteristics.

10. Human capital and language-proficiency differences account for A but 3 to 7 percentage points of the Hispanic wage differential.

11. If employers discriminate against some group of workers, they will act as if they believe the marginal product of those workers is lower than it really is. Thus, they will hire fewer such workers than would be called for by profit maximization, and those who are the most discriminatory will make the least profits.

12. Under employer discrimination, the behavior of prejudiced employers will reduce demand for the minority group and cause a wage differential to exist. The size of the differential depends on the size of the minority population relative to the distribution of prejudiced employers in the market.

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13. The implication that prejudiced employers will be less profitable suggests that discrimination ought to be eliminated over time as nonprejudiced (profitable) employers buy out less profitable, prejudiced employers.

14. Like employer discrimination, customer discrimination implies a shift to the left of the demand curve for the services of a protected class. However, with customer discrimination, a reduction in productivity is, from the employer's perspective, genuine.

15. Employee discrimination generates supply-related behavior that might cause employers to segregate their plants by race or sex if possible. If not, wage differentials will arise as a result of the need of employers to retain workers in the prejudiced group.

16. Statistical discrimination arises from a screening problem in which job applicants are evaluated both on their individual characteristics and on average characteristics of the group to which they belong. Statistical discrimination should be reduced in situations in which the variance of individual characteristics around the group average widens.

17. Both the crowding hypothesis and theories emphasizing the dual labor market suggest the presence of noncompeting groups, but they do not satisfactorily explain the creation of these groups.

18. If search costs create upward-sloping labor supply curves to individual employers, and if discrimination raises the search costs of certain groups of workers, then monopsonistic behavior will create wage differentials among otherwise identical workers.

19. Some theorists use collusive action on the part of employers to explain the creation and persistence of noncompeting groups. Employers are seen as deliberately dividing the labor force to guard against cohesive collective action by workers, but the theory does not explain how an employer cartel is maintained in the face of clear-cut incentives to cheat.

20. Antidiscrimination programs by the government must set standards for both employment and wages. If employment standards are the only ones used, prejudiced employers may comply by paying protected-class workers less than white males. If a wage standard is the only one applicable, then prejudiced employers will respond to increased wages for protected classes by reducing employment.

21. A disparate treatment standard imposed under the Civil Rights Act judges that discrimination has occurred if different procedures are used for different groups of people and if it can be shown that there was an intent to discriminate. Proving intent is difficult, and policies that may appear to be neutral on the surface may nevertheless perpetuate the effects of past discrimination.

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22. Courts have moved towards a disparate impact standard, by which it is labor market results, not motivation, that counts. Under this standard, policies that lead to different effects by race and sex are prohibited unless a business "necessity" can justify their use.

23. Because of occupational segregation, men and women often occupy dissimilar jobs. The comparable worth remedy is based on comparing the skill content, responsibility, and working conditions in jobs for purposes of pay comparisons; however, mandating wage increases for women could reduce the incentives of employers to hire them.

24. The Federal Contract Compliance Program seeks to shift the demand curve for protected classes to the right. Federal contractors are required to file affirmative action plans that state their goals for hiring and promoting members of protected classes (taking account of "availability").

25. Realistic estimates of availability should account for the compensation policy of the firm, the willingness of workers to commute to the firm, the degree to which the firm has incentives to train new employees, and the extent to which job applicants can be induced to move to the firm's labor market area.

26, Studies to evaluate the effects of government antidiscrimination efforts have focused on time series analyses of earnings ratios and effects on federal contractors (emphasizing changes in employment levels, wages, and quit rates for protected-class workers).

27. (Appendix) Estimating comparable worth earnings gaps typically involves evaluating characteristics of jobs for men and women and estimating the relationship between these characteristics and compensation for white males. This relationship can then be used to estimate what women would receive if they were paid on a basis comparable to men.

28. (Appendix) A precise and informative way of estimating the relationship between point scores and compensation would be to use ordinary least squares regression techniques to fit the "best" line through the observed points on the graph. The estimated coefficient on the point score variable is an estimate of how much a unit change in that variable affects earnings.

Answers to Even-Numbered Review Questions 2. “In recent years, the wage gap between skilled and unskilled workers in the United States has grown. This growth means that measured labor market discrimination against unskilled Mexican immigrants is also growing.” Comment on whether the second part of this statement is implied by the first part.

Answer: Labor market discrimination is said to exist when workers who are productively equivalent are systematically paid different wages based on their race or ethnicity (or some other demographic characteristic unrelated to productivity). It is true that rising inequality causes a 97

greater gap between the average wages of native whites and unskilled Mexican immigrants because native whites are better educated and more skilled, on average. However, the existence (and size) of labor market discrimination depends on the wage gap between unskilled native whites and unskilled Mexican immigrants (that is, the existence of a gap between two productively equivalent groups) – and the facts quoted in the statement are not sufficient to determine if labor market discrimination is growing.

4. Will government-mandated requirements to hire qualified minorities (at non-discriminatory wages) in the same proportions they are found in the relevant labor force reduce the profits of firms that formerly faced customer discrimination? Fully explain your answer.

Answer. If customers are prejudiced, they will tend to avoid businesses hiring workers from groups they are prejudiced against; thus, profit-maximizing employers will prefer to hire workers from groups that customers do not have distaste for. If the law requires employers to hire from all groups proportionately, firms previously attracting prejudiced customers will lose business (either to firms that might not be covered by the law, or when consumers substitute other goods or services for the one in question); however, their costs could go down now that there is no reason for paying a premium to workers from “favored” groups. Firms previously attracting non-prejudicial customers will now be unable to capitalize on the lower demand (and lower wages) for minority workers, so their costs will rise.

6. You are involved in an investigation of charges that a large university in a small town is discriminating against female employees. You find that the salaries for professors in the nearly all-female School of Social Work are 20 percent below average salaries paid to those of comparable rank elsewhere in the university. Is this university exhibiting behavior associated with employer discrimination?

Answer: There are reasons why salaries for professors, of comparable rank differ across fields that have nothing to do with discrimination. Medical doctors and lawyers on university faculties typically receive higher pay than English and history professors because their alternative salaries outside of academia are higher. Put differently, there are different relative demands and supplies by academic field and these are reflected in differential salaries. Professors of social work, therefore, may receive lower wages than average because the supply of labor to that field is greater relative to demand than average. The larger relative supply could, of course, be the result of occupational crowding or the socialization process (emphasizing the traditional roles of women). Whatever the cause of the large relative supply of women to the social work field, it is not obvious that this particular university is engaged in the behavior we could attribute to employer prejudice.

Prejudice of a particular employer can be observed in two instances. One occurs when, with equal wages paid to men and women, the employer clearly prefers to hire men over women of comparable productive characteristics. The other situation occurs when, given a lower market wage for women compared to men of comparable characteristics in an occupation, the employer fails to hire an all-female (or at least nearly so) work force. Because the university has 98

apparently hired a nearly all-female work force in the School of Social Work, it does not seem to exhibit this latter behavior. (Even a prejudiced employer could find wage differentials so large that it would be willing to hire members of a group against which it had some prejudice. One thus cannot rule out the possibility that this employer is prejudiced, but one cannot prove this from the facts given in the question.)

8. In the 1920s South Africa passed laws that effectively prohibited black Africans from working in jobs that required high degrees of skill; skilled jobs were reserved for whites.

Analyze the consequences of this law for black and white African workers.

Answer: The effects of the law on black Africans were unambiguously adverse. Blacks were crowded into low paying unskilled occupations, for which the wage was driven down still further by the requirement that blacks could not do other work. Those who would have chosen to obtain training for skilled positions were not able to do so.

The effects of the laws on white workers were ambiguous. Skilled white workers were helped, in the sense that they received higher wages than they would have otherwise received (had blacks been allowed into the skilled trades). Unskilled whites, however, were probably made worse-off by this law because of the effects the law had on the unskilled wage. Some unskilled whites, however, reacting to the increased wage differential between skilled and unskilled jobs, would have elected to obtain the training necessary for entrance to a skilled trade.

Answers to Even-Numbered Problems 2. Suppose that MRPL = 20 - .5L for left-handed workers, where L = the number of left-handed workers and MRPL is measured in dollars per hour. The going wage for left-handed workers is $10 per hour, but employer A discriminates against these workers and has a discrimination coefficient, D, of $2 per hour. Graph the MRPL curve and show how many left-handed workers employer A hires. How much profit has employer A lost by discriminating?

Answer: See the figure. A nondiscriminating employer will hire left-handers until wage = MRPL. Because 10 = 20 - .5L when profits are maximized, then L = 20 workers for a profitmaximizing employer. Employer A, however, will hire left-handers until wage + D = MRPL. Since 10 + 2 = 20 - .5L, then L = 16 for employer A. Lost profits equal triangle ABC, whose area is 4 x $2 x .5 = $4 per hour.

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4. (Appendix) In the market for delivery truck drivers, Ls = -45 + 5W and Ld = 180 – 10W, where L = number of workers and W = wage in dollars per hour. In the market for librarians, Ls = -15 + 5W and Ld = 180 – 10W. Find the equilibrium wage and employment level in each occupation and explain what will happen if a comparable worth law mandates that the librarian wage be increased to equal the delivery truck driver wage. Use a graph.

Answer: To find the equilibrium wage for truck drivers, set Ld = Ls and solve for W: -45 + 5W = 180 – 10W, or 15W = 225, so W = $15 per hour Plugging this into the two equations shows that, for truck drivers, L = 30. The calculation for librarians is as follows: -15 + 5W = 180 – 10W, or 15W = 195, so W = $13 per hour For librarians, L = 60. If the librarians' wage were increased to $15 per hour, employers would move back along the Ld curve from point A to point B on the figure below and hire fewer librarians, reducing their employment from 60 to 40.

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6. Suppose the hourly marginal revenue product of all workers in a particular labor market is MRPL = 20 – L, where L = the number of workers. The hourly wage rate for women in this market is W = $5.75. What is the gap between MRPL and wage in this labor market if L = 12? Is this gap a reliable measure of discrimination against women in this market?

Answer: If L = 12, the MRP = 8, and the wage is 5.75, so the gap is 2.25. This is not a reliable measure of wage discrimination for a number of reasons. We do not know what men are paid in this market; we do not know productivity differences, if any, as well as many other factors that would go into an accurate measure of wage discrimination.

8. Suppose a researcher estimated the relationship between salary, gender, and age among a group consisting of male and female workers but ignored the fact that, on average, male workers have more work experience than females. The estimated regression of salary on gender and age is Si = 21354.83 + 239.45 Gi + 93.17 Ai (15252.9) (95.6) (29.58) where Si = salary of a worker, Gi = 1 if the worker is male and 0 if the worker is female, and Ai = the employee’s age. Standard errors of the coefficients are in parentheses.

When experience was included in the regression, the estimated regression is Si = 21177.75 + 226.27 Gi + 89.73 Ai + 443 41 Xi (16111.3) (186.8) (34.64) (47.7) where Xi = the years of work experience of the worker. Comparing the two estimated regressions, does there appear to be salary discrimination by gender? Discuss the implications of omitting the experience variable in the first regression.

Answer: In the first equation, the t-statistic for the gender variable is 2.5, probably statistically 101

significant, depending on sample size. In the second equation, it is 1.21, not statistically significant. The experience variable is highly significant, with a t-statistic of 9.2. The first equation suffers from omitted variable bias, and thus there appears to be salary discrimination by gender when in fact including the experience variable makes it clear that there is not a statistically significant effect of gender on salary.

Suggested Essay Questions 1. Will government-mandated requirements to hire qualified minorities (at non-discriminatory wages) in the same proportions they are found in the relevant labor force reduce the profits of firms that formerly engaged in employer discrimination? Fully explain your answer.

Answer. Firms that engage in employer discrimination forgo profits in order to indulge their prejudices. Thus, requiring them to hire and pay qualified minorities in proportion to their availability will not reduce profits. (It will, however, reduce the utility owners derive from their businesses.)

2. Assume there is a central city school district in which the student population is predominantly black. Surrounding the central city are predominantly white suburban school districts. Together, the central city and suburban school districts can be thought of as a local labor market for teachers. Other things being equal, black teachers in this labor market are equally willing to work in central city and suburban schools, but white teachers prefer suburban schools and are reluctant to accept jobs in the central city. There are too few black teachers to completely staff central city schools, and teachers generally have choices in the jobs they can accept.

If federal law requires equal salaries for teachers of all races within a given school district but allows salaries to vary across school districts, will black teachers earn more, less, or the same salary as they would if white teachers were not prejudiced against black students? (Note: The prejudice of white teachers extends only to students, not to black teachers as coworkers. Note also: The chain of reasoning required in this answer should be made explicit in your answer.)

Answer: Because there are too few black teachers to completely staff central city schools, these schools must attract white teachers who, by hypothesis, prefer to teach in suburban schools.

Thus, to attract enough white teachers to fill the job slots, the central city schools must raise wages (this wage increment would act as a compensating wage differential, compensating white teachers for taking jobs they might otherwise find "distasteful"). Because salaries for all teachers within a school district must be equal, the black teachers in the central city schools must receive the higher wages there, also.

Wages in the suburban schools will be lower than the wages in central city schools because these schools can attract the white teachers without offering a compensating wage differential.

Because black teachers, by hypothesis, are equally willing to work in central city or suburban 102

schools when wages are equal, suburban schools will not be able to attract black teachers (who will find the higher wage at the central city schools more attractive).

Thus, black teachers will earn more than they would if white teachers were not prejudiced against black students. The reason for this is that if white teachers were equally willing to work at the same wage in the central city and suburban schools, there would be no need for a compensating wage differential to arise. The central city school would find it just as easy to fill jobs as suburban schools and would not have to raise wages to attract white teachers.

3. Suppose the government has two methods of awarding contracts to firms. One is competitive, with the award going to the lowest bidder (who cannot then charge more than his or her bid). The other is noncompetitive, with the award going to a selected contractor who is reimbursed for actual costs incurred plus a certain percentage for profits. Suppose, too, that government contractors must hire a certain quota of minorities, many of whom require general training to be fully productive. Suppose also that federal legislation prevents the employer from shifting the costs of this general training to the minority employees. If you were an already-trained minority worker, which method of contract award would you prefer? Why? Answer: If firms are awarded government contracts on a competitive basis and government contractors must hire a certain minimum of minority workers, the wage rates of already trained minority workers will be bid up as these firms struggle to meet their quotas. Competitive firms will be unwilling to provide general training to minority workers because they cannot by law shift the training costs to these workers and could not pay them less than the market wage for trained workers in the post-training period. Thus, they have no way to recoup their training costs and could be underbid by firms proposing to hire already trained minority workers. In a competitive environment, a premium would be placed on obtaining already trained minority workers, and because there might be too few of them to satisfy the demand, their wage rates would rise.

If the government awarded contracts on a noncompetitive basis, by which contractors were reimbursed for their actual costs and then a certain percentage of their costs was allowed for profits, firms would be able to receive reimbursement for any losses they sustained in providing general training to untrained minority workers. In this case, the firm is really indifferent between hiring an untrained minority worker or hiring a trained minority worker since any cost it bears in training will be reimbursed by the government. Thus, if contractor awards were noncompetitive, trained minorities would not be given preference over untrained minority workers, and a wage premium associated with being a trained minority worker would not arise.

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CHAPTER 13 - UNIONS AND THE LABOR MARKET The major focus of this chapter is on the economic effects of unions, in both the private and public sectors. It begins with some necessary definitions and descriptions of unionism in the United States compared to elsewhere in the world, before turning to elementary coverage of major pieces of labor legislation in the United States.

In seeking their objectives, unions are constrained by the demand for their members' services.

Unions facing relatively inelastic demand curves are better able to raise wages without adversely affecting employment levels very much. The simplest model of unions' objectives is the "monopoly union" model, in which the union sets the wage and the employer adjusts by setting the employment level. A more complex model is the "efficient contracts" model, in which the union and firm jointly bargain over wage and employment levels.

In attempting to explain the major activities of unions, we have organized the analysis around the demand for unions by workers and the supply of union services by labor unions. We use this analysis to help understand the major trends in American unionization. No discussion of union behavior would be complete without an analysis of strike activity and (for the public sector) interest arbitration. The section on strikes include an exposition of the Hicks model of bargaining and the Ashenfelter-Johnson political model of strike behavior (including the effects of the Landrum-Griffin Act). The section on arbitration discusses the contract zone in the context of both conventional and final-offer arbitration.

Having analyzed some key characteristics of union behavior, we turn to an analysis of the effects of unions on wages and other workplace outcomes. The measurable effect of unions on wages is the relative wage advantage, found by comparing union wages to wages in the nonunion sector. The true (or absolute) effects of unions on wages are not measurable, and the possible biases inherent in measuring the absolute effects using relative-effect measures are discussed at length. We close the chapter by summarizing empirical evidence on the effects of unions on relative wages, total compensation, employment, productivity, and profit, and discuss both "traditional" and alternative views of union effects on the overall social welfare.

The appendix to Chapter 13 analyzes how the uncertainty of arbitrators' decisions affects bargaining outcomes. As in the appendix to Chapter 8, the discussion defines and illustrates the concept of risk aversion..

List of Major Concepts 1. Union membership as a fraction of the population in the United States is low relative to the other major industrial countries, and American union activities are relatively decentralized.

2. Unions are constrained in their objectives by the labor demand curve.

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3. The monopoly-union model assumes that the union sets the wage and the employer sets the employment level.

4. The "efficient-contracts" model emphasizes that if unions and employers bargain only over wages, the resulting employment/wage outcome will be inferior to another set of outcomes that would improve the welfare of both parties. Under this model, the two parties bargain over both wage and employment levels.

5. The decline in American union membership can be understood, in part, by reference to shifts in the demand and supply curves for union services (caused by the feminization of the work force, a change in industrial composition, regional shifts, competitive pressures, and employer resistance).

6. Unions often take actions designed to shift the demand curve for labor to the right and/or to reduce the elasticity of demand for union labor.

7. Strikes are intended to impose financial costs on employers if they do not agree to union offers, but because they also impose costs on employees, both sides become more willing to make concessions as strike duration increases. The Hicks bargaining model suggests when strikes will end, but it does not explain why strikes occur in the first place.

8. While strikes can occur because one party mistakes the other's true position, they can also occur because, in the context of asymmetric information, one party wants to elicit a signal from the other about its true preferences or constraints.

9. The Ashenfelter-Johnson model of strike activity, which is tripartite in nature, views union leaders and union members as sometimes having conflicting perspectives. Union leaders, who have better information than their members, may pursue the twin goals of maintaining their positions in the union and educating union members by recommending a strike.

10. Unions' propensities to strike vary over the business cycle and have trended down over time, but the increase in union democracy associated with the Landrum-Griffin Act caused a one-time increase in strike activity (as predicted by the Ashenfelter-Johnson model).

11. Interest arbitration is used in the public sector, where strikes are generally not permitted, and interest arbitration can be "conventional" or "final offer."

12. The "contract zone" into which pre-arbitration offers will fall can be widened by both the uncertainty about what an arbitrator might decide and the parties' aversion to the risk of an adverse outcome. However, it is not clear whether a wider contract zone increases or reduces the chances a dispute will go to arbitration.

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13. One would like to measure the effects of unions on wages in the absolute (comparing wages in a world with unions to wages in a world without); however, measuring this absolute wage advantage is impossible. We can only measure union wages relative to nonunion wages, but this is not a good measure of the absolute effect because the presence of unions alters the nonunion wage also.

14. If the nonunion labor market is in equilibrium, the presence of unions should lower the nonunion wage below what it would have been otherwise and cause the relative wage effect to overstate the absolute effect of unions.

15. If employers raise wages in the nonunion sector to keep unions out (thus creating unemployment in that sector), the relative wage effect is smaller than the absolute union wage effect.

16. The presence of wait unemployment in the union sector will inhibit the growth in labor supply in the nonunion sector and could even cause the supply curve there to shift left.

Whether wait unemployment causes the relative wage effect to be greater or smaller than the absolute wage effect depends on whether the supply curve of labor to the nonunion sector shifts to the right or left.

17. In an overall sense, unions appear to raise the wages of their members above the nonunion wage by something like 10 to 20 percent. These wage effects are larger in the private than the public sector, larger in the United States than elsewhere, and largest among unskilled (and minority) workers.

18. Union effects on employee benefits as a percentage of total compensation tend to be positive; thus, the total compensation effects of unions may be greater than the relative wage effects.

19. The compensation advantages enjoyed by union members; however, may be in part a compensating wage differential for the more structured, more hazardous and less flexible work settings in unionized firms.

20. Empirical evidence tends to suggest that, in the United States, unionization reduces employment or employment growth, has an ambiguous effect on productivity, and a negative effect on profits.

21. The traditional view of union effects stresses the social loss caused by inequality in wages (and marginal productivities) among workers of comparable skill. The traditional view also stresses the losses associated with union staffing requirements, restrictive work practices, and strikes.

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22. The alternative view of unions is that they provide a method of collective "voice" that tends to reduce turnover and encourage firms to provide specific training to employees. Improved communications between labor and management may also increase productivity and worker motivation directly, but employer resistance to unions and the degree to which stock market prices are depressed when union organization drives are initiated suggest a widespread belief that unions reduce profitability.

23. (Appendix) When collective bargaining impasses can be decided by arbitration, the range of possible nonarbitrated settlements is widened by greater uncertainty about how the arbitrator will decide (if an agreement is not reached) and by greater risk aversion on the part of the parties.

Answers to Even-Numbered Review Questions 2. Some collective bargaining agreements contain "union standards" clauses that prohibit the employer from subcontracting with firms that pay wages below those specified in the agreement. That is, the employer is prohibited from "farming out" work normally done in the plant to other firms (the subcontractors) if the subcontractors pay less than the union wage. a. What is the union's rationale for seeking a union standards clause? b. Under what conditions will a union standards clause most likely be sought by a labor union?

Answer: (a) The union's goal for seeking the union standards clause is to remove incentives for the employer to substitute cheaper nonunion labor for more expensive union labor. In other words, the goal is to minimize the substitution away from union workers towards cheaper factors of production. (b) The ultimate goal of the union, of course, is to raise wages while preserving employment (or at least not having to undergo large employment declines). A union standards clause will be most attractive to a union when the firm can easily substitute outside factors of production for those it employs and when these substitution effects are large. Analogously, the union standards clause will be most successful in preserving employment of union members if the firm finds it difficult or expensive to substitute capital for labor within the firm. Likewise, if the supply of capital to the firm is relatively inelastic, any tendency to substitute capital for labor will be met with a rising price of capital, which will mitigate the amount of capital/labor substitution that might otherwise accompany a union standards clause. Moreover, a union standards clause will be most successful in preserving employment, and therefore most sought-after, if the product demand curve is relatively inelastic (so that scale effects are small).

4. It has been observed that unions in the capital-intensive steel industry were able to negotiate higher-than-average wage increases during the very period in which steel output in the United States was declining. Using economic theory, how can this pattern be explained?

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Answer: When output is contracting, one would think that the shrinking demand for workers (owing to the scale effect) would reduce a union’s ability to negotiate wage increases without harming job opportunities for its members. However, when output is contracting, employers are not adding to their capital stock or opening new plants, so technological improvements that substitute capital for labor are not easily made. The reduced ability to substitute capital for labor serves to strengthen the union’s hand because even if wages rise the substitution of capital for labor may not take place.

6. American unions often try to win public support for boycotting goods made in less developed countries by workers who work very long hours at low pay in unhealthy working conditions. (a) If successful, will these efforts unambiguously help the targeted foreign workers?

Explain fully. (b) Will they unambiguously help the union’s American workers? Explain fully.

Answer. (a) If manufacturers in these less developed countries are induced to raise wages and improve working conditions, output price will tend to rise and only those consumers willing to pay the higher prices will remain in the market. Boycotting goods made by workers in “sweatshop” conditions, then, tends to reduce demand (because of both scale and substitution effects) for the services of low-wage labor, and these workers may end up losing their manufacturing jobs and having to go back to farming or some other job they previously felt was inferior, given their preferences and opportunities. (b) If manufactured items from abroad become more expensive, we would expect that consumers would tend to substitute American goods (now relatively cheaper) for foreign-made goods. Thus, foreign and American workers may be considered substitutes in production, and if this substitution effect is dominant, the will be gross substitutes. If so, when the costs of foreign labor rise, the demand for American labor may rise. However, we must also consider the scale effects associated with higher costs overseas. Some American workers may have jobs (in packaging, selling, distributing) that depend on the scale of output produced both in the U.S. and abroad. Clearly, the scale of output will fall owing to the boycott, and the costs of producing the items in question will rise; some workers, therefore, may be gross complements with foreign workers, and these workers will be worse off if the boycott lasts and is successful.

8. A certain country has very centralized collective bargaining, under which wage bargains are applied nationally. This country is thinking about adopting a bargaining structure that is more decentralized so that wage bargains will be made at the individual plant or firm level. How would you expect decentralization to affect wages and employment? Explain your answer.

Answer: In general, there are many possible results, depending on such factors as the extent of union coverage and the bargaining power of unions both before and after the change, and thus, as with different arrangements in different countries, the result may not be easily predictable.

However, a number of factors might be considered. First, unions might be more or less effective, depending on the extent of unionization in different sectors, but in general, bargaining power might decrease. Second, to the extent that there may be differences in bargaining power between sectors, this might create wage differentials (and productivity differentials) between firms that are more or less unionized. This would also presumably increase the costs of contracting, which would reduce market efficiency further. However, it is also possible that 108

weakening unions by forcing them to bargain plant-by-plant might improve market efficiency by reducing wages and thus increasing employment.

Answers to Even-Numbered Problems 2. The Brain Surgeon's Brotherhood faces an own-wage elasticity of demand for its labor that equals -0.1. The Dog Catcher's International faces an own-wage elasticity of demand for its labor that equals -3.0. Suppose that leaders in both unions push for a 20 percent wage increase, but have no power to directly set employment levels. Why might members of the Dog Catcher's International be more wary of the targeted wage increase?

Answer: Own-wage elasticity of demand = %(quantity demanded)/%(wage). In the case of the Dog Catchers this implies -3 = %(quantity demanded)/20%, thus employment will fall by 60% if they boost wages by 20 percent. In the case of the Brain Surgeons this implies -0.1 = %(quantity demanded)/20%, thus employment will fall by only 2 percent if they boost wages by 20 percent.

4. The following table gives the demand for labor at two different firms.

Wage Rate ($)

Demand (Firm ABC)

Demand (Firm XYZ)

3

24

28

4

23

26

5

22

24

6

21

22

7

20

20

8

19

18

9

18

16

10

17

14

The current wage rate in both firms is $7 per hour. A union would like to organize employees in one of the firms and bargain to raise the wage rate to $8 per hour. Calculate the wage elasticity of demand for each firm if the wage rate were increased from $7 per hour to $8 per hour. Which firm would the union be more interested in organizing? Why? Answer: For Firm ABC, the wage elasticity of demand is -0.38 (arc elasticity). For Firm XYZ, the wage elasticity of demand is -0.78 (arc elasticity). The union would be more interested in organizing Firm ABC, because the wage elasticity of demand is more inelastic, and thus wages could be increased with less loss of employment.

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6. There are two sectors of the construction industry that currently pay their employees the market-clearing wage. The demand for labor in each sector is MRPL = 12 – L, where L = the number (in thousands) of workers. The supply of labor in each sector is L = W – 2, where W = the wage rate (dollars per hour).

A union organizes in one of the sectors, and it restricts supply to that sector by insisting that only those in the union are hired by firms in that sector (and it is difficult to get into the union).

When the employees in this sector unionize, the supply of labor in that sector changes to L = W – 4. a. What is the wage rate in both sectors before unionization? How many employees will be hired in each sector? b. What is the wage rate in the unionized sector? How many employees will be hired in the unionized sector? c. If the unemployed workers in the newly unionized sector spill over into the nonunion sector, what will be the wage rate in the nonunion sector? How many employees will be hired in that sector? d. What is the union relative wage advantage? What is the true absolute effect?

Answer: a. The wage will be $7 in each sector, and five workers will be hired in each sector. b. In the unionized sector, the wage will be $8, and four workers will be hired. c. Moving the additional worker from the unionized sector to the nonunion sector lowers wages in the nonunion sector to $6 (and 6 workers are hired). (This assumes that all workers are identical, and so the new labor supply curve in the nonunion sector can be inferred to be L = W – 6.) d. The relative wage advantage is (8-6)/6 = 0.33, or 33%. The true absolute effect is (8-7)/7 = 0.14, or 14%.

Suggested Essay Questions 1. In the mid-1970s, the teachers' union of a large American city was told that the city's financial difficulties made it necessary to cut payroll costs for teachers by 10 percent. The city gave the teachers' union a choice: it could accept a 10 percent cut in the salaries paid to teachers and suffer no employment losses, or it could keep salaries constant and accept a 10 percent cut in employment levels (and a corresponding ten percent increase in class sizes). Generalizing from the political model of strike activity given in Chapter 13, in which the major actors are employers, workers, and union leaders (elected by majority rule), please perform the following tasks: a. Predict and explain the union's decision, assuming that its collective bargaining agreement with the city specifies that any layoffs will occur among those teachers most recently hired. b. Explain whether the decision in (a) would have been different if the collective bargaining agreement had specified that all layoffs would occur on a random basis, independent of seniority, teaching field, or any other teacher characteristics.

Answer: (a) If layoffs occur only among the most recently hired, it is possible for each union worker to calculate whether he or she is among the group to be laid off. Therefore, 90 percent of 110

all union members will know that they will not be laid off, and 10 percent know for sure that they will be. Because the union leaders who had to make this decision are elected by majority rule, it is a safe bet that they would act in the interests of the majority (who would not be laid off) and would therefore choose to maintain current salaries and accept layoffs of 10 percent. (b) If layoffs are to be made randomly, then each union member has a 10 percent chance of being laid off if salaries are held constant. Alternatively, members could accept a 10 percent cut in their salaries with the assurance that they would not be laid off. In either case, in advance of the decision that must be made by the union, each worker would face a 10 percent decrease in expected wages. In this case, it is much more likely that the union would choose to accept salary cuts than cuts in employment. A simple political model of union decision making could not predict for sure that unions would accept salary cuts in this case, although they probably would if their workers were risk averse. However, compared to the case in which layoffs are made among those most recently hired, the chances of the union's deciding to accept employment cuts are much lower.

2.

A union in industry X supports a local community proposal to give large property tax reductions to companies, while a union in industry Y opposes the proposal. Can it be concluded that the union in industry X is selling out to management and risking harm to its members? Explain.

Answer: Even though property tax reductions reduce the effective price of capital, the union in industry X is not necessarily selling out. Rather, the labor demand conditions in industry X may be fundamentally different than in industry Y. The fear that workers have about property tax reductions is that employers will have increased incentives to substitute capital for labor. If it is relatively easy to substitute capital for labor in industry Y, while it is very difficult in industry X, then one explanation for the differences in political stances can be understood.

Further, property tax reductions offer the possibility of a scale effect that would be helpful to labor. Industry X, for example, may be more capital intensive and/or face a more elastic product demand schedule than industry Y so that an investment tax credit could be expected to enhance the demand for labor more in industry X than in Y. Similarly, the union in industry X may believe it is likely that a local property tax reduction would attract other employers in the same industry to the area. If so, the differing political stances of the two unions can again be understood in the context of attempts to improve the position of their membership.

3.

The head of a large national union is trying to decide where he should concentrate his efforts at organizing a union. He perceives three options: firm A, firm B, or firm C. The three firms are identical except that: a. Firm A faces a perfectly elastic (horizontal) supply curve of labor and a rather inelastic demand curve for its output. b. Firm B behaves as a monopsonist (faces an upward-sloping supply curve of labor) and faces a perfectly elastic (horizontal) demand curve for its output. c. Firm C faces a perfectly elastic supply curve of labor and a perfectly elastic demand 111

curve for its output.

This union head would like to know where a new union will pay off most in terms of large wage gains and small reductions in numbers of workers. Rank the three options from best to worst, giving reasons for your ranking.

Answer: Firms A and C both face perfectly elastic labor supply curves; this implies that they operate in competitive labor markets and initially take the wage rate as given (see the figure on the left below).

Suppose that, in the absence of a union, the wage/employment combination for such firms would be a point like (WO,EO.). If a union enters and succeeds in raising wages to W1, the firm will respond by reducing employment to El . The reduction in employment will be larger the larger is the wage elasticity of the labor demand curve. Since Firm C faces a more elastic output demand curve than Firm A, other things equal, Firm C's labor demand curve will be more elastic.

Hence, the union will perceive that Firm A offers it a more favorable opportunity than Firm C; the employment loss associated with any given wage increase will be smaller in the former case.

Firm B, however, offers the union the best opportunity. In the absence of a union it faces an upward-sloping supply curve of labor (see the figure on the right). We know from Chapter 3 that a monopsonist will determine employment by equating the marginal cost of labor (MCL) to labor's marginal revenue product (MRPL), and then pay the wage rate that the supply curve indicates is required to attract that many workers. This results, for example, in a wage/employment combination of (W0B, E0B).

We know from Chapter 3 that in this situation it is possible to increase wages without any reduction in employment (see the discussion of minimum wage effects under monopsony).

Indeed, the union could increase its members' wage to WlB and maintain its members' employment at E0B. Moreover, any wage that was set between W0B and W1B, would result in the employment of union members increasing above E0B. 112

4. Consider the following quotation: The theory of compensating wage differentials is based on the assumption that workers are able to command higher wages in higher risk jobs. While I believe that this is true in such unionized sectors as ironworkers, construction workers, and lumber and sawmill workers, I have found the opposite to be true in nonunion, nonorganized industries. In the nonunion chemical industries, as well as in such industries as soap making, etc., it has been my experience that the most dangerous jobs were handled by the lowest paid, least- educated and usually minority workers. I am concerned about this because of the steady decline in the percentage of jobs that are covered by union contracts in this State over the past 20 years.

Please answer the following two questions about the above quotation: (a) Why might the presence of unions help to create compensating wage differentials for risk? (b) If the lowest paid, least educated workers in the nonunion sector do the dangerous work, does this suggest that compensating wage differentials in the nonunion sector do not exist? Why or why not?

Answer: (a) The generation of compensating wage differentials requires information and mobility. Unions may encourage compensating wage differentials through the provision of information to their members or through collective action (which can serve as a substitute for worker mobility). (b) The fact that wages in dangerous union jobs may be higher than wages in dangerous nonunion jobs does not necessarily indicate the nonexistence of compensating wage differentials outside the union sector. It may simply be that all union jobs pay more than comparable nonunion jobs, independent of risk level. Further, what is really important in assessing the existence of compensating wage differentials is whether dangerous jobs in either sector pay more than nondangerous jobs done by employees of comparable age, experience, and skills. Dangerous and low-paying sectors may exhibit compensating wage differentials if the wages that workers in these sectors could obtain in safer employment are even lower! In short, a sophisticated analysis that controls for all factors that influence pay must be used to make judgments about the existence of compensating wage differentials.

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CHAPTER 14 - UNEMPLOYMENT This chapter defines the unemployment rate and discusses its strengths and weaknesses as a measure of economic welfare. Further, it emphasizes that while the unemployment rate is a stock concept, there is an underlying set of flows into and out of that stock. Thus, different demographic groups may have different unemployment rates because of different propensities to quit or be laid off from jobs.

Next, we discuss four general types of unemployment: frictional, structural, demand deficient, and seasonal unemployment. In the section on frictional unemployment we discuss search theory and the effects of unemployment benefits on job search. When analyzing structural unemployment, occupational and geographical imbalances, government policies, and efficiency wages (including the "wage curve") are discussed. The section on demand deficient unemployment analyzes wage rigidity, the financing of unemployment benefits, and policies and adjustments found in Europe.

The chapter also treats the issue of "full employment." The structure of unemployment rates across demographic groups is presented, and we then discuss effects of the changing age, race, and sex composition of the labor force on the full employment rate of unemployment.

List of Major Concepts 1. The unemployment rate is the number of unemployed people seeking work divided by the number of people who are in the labor force. While this measure has a number of serious drawbacks, it remains a useful indicator of labor market conditions.

2. While one can think of a stock of unemployed persons, this stock is constantly changing, focusing only on the stock masks the highly dynamic nature of labor markets.

Unemployment rates are affected by layoffs and quits, new hires and recalls, retirees from and new entrants into the labor market. As these flows change relative to each other, the unemployment rate changes in predictable ways.

3. Frictional unemployment occurs because labor market information is imperfect. It takes time even in the best of markets for unemployed workers and employers with job vacancies to find each other. Government efforts to improve the rapidity of the job-matching process could reduce the extent of frictional unemployment.

4. A period of unemployment can be looked upon as a period when job search can be undertaken, and the extent to which someone will spend time searching for work depends upon the expected benefits and costs of continuing search.

5. Since the receipt of unemployment insurance benefits reduces the costs of extra time spent searching for work, the more generous these benefits are, the longer unemployed workers

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will tend to search for jobs. Thus, more generous unemployment insurance benefits may be expected to increase the duration of unemployment.

6. Structural unemployment occurs when flows of workers into and out of particular labor markets -- defined by skill or geography -- are impeded. Government efforts to subsidize mobility and/or job training would serve to reduce the incidence of structural unemployment.

7. Structural unemployment is also associated with firms' decisions to pay efficiency wages; in such cases, some workers without jobs "wait" for jobs in the high-paying sector and do not seek jobs in lower-paying firms.

8. Efficiency wages may underlie the "wage curve" found in almost all countries studied; this curve plots a negative relationship between the regions' wage rates and their unemployment rates.

9. Demand-deficient unemployment occurs when the aggregate demand for labor declines in the face of downward inflexibility of nominal or real wages.

10. There are several reasons for the downward inflexibility of money wages, including the preference of unions for layoffs over wage cuts, the asymmetry of information between employers and employees, firm-specific training, risk aversion of older workers, concerns about status, and implicit contractual agreements that after an initial period, when the risk of layoff is high, yearly earnings of workers will stabilize.

11. The government's tax treatment of most unemployment insurance benefits and its failure to perfectly experience-rate the unemployment insurance charges levied on employers lead to a higher layoff rate than would otherwise prevail.

12. In Europe, cyclical fluctuations in labor demand are more likely to be manifest in adjustments in hours, not employment levels. One reason for the greater adjustments in hours of work may lie in the wider use of partial unemployment compensation benefits in Europe.

13. Seasonal unemployment may be associated with changes in the weather or with model changeovers, but it is also affected by downward rigidity of money wages and the government's unemployment insurance program.

14. The full-employment rate of unemployment (i.e., unemployment in "normal" times) appears to have changed in recent years, in part due to the changing proportion of women, teenagers, and ethnic minorities in the labor force.

Answers to Even-Numbered Review Questions 115

2. Government officials find it useful to measure the nation's "economic health." The unemployment rate is currently used as a major indicator of the relative strength of labor supply and demand. Do you think the unemployment rate is becoming more or less useful as an indicator of labor market tightness? What other measures might serve this purpose better?

Answer: There are many problems with using the aggregate unemployment rate as an indicator of labor market tightness. It provides no information about the number of individuals who are not actively searching for work because they were unsuccessful in the past. It tells us nothing about whether the employed are working at jobs commensurate with their skill levels. It does not distinguish between unemployment of a skilled adult and unemployment of an unskilled new entrant into the labor force. It tells us nothing about the number of workers who are employed. Finally, it is sensitive to the generosity of some social programs, like the unemployment insurance system.

Over time, the growth of social programs and the changing age-gender-race distribution of the labor force probably have made the aggregate unemployment rate less useful as an indicator of labor market tightness. Rather than looking for a single indicator, our attention should focus on a number of indicators including the age-gender-race distribution of unemployment and employment rates, turnover rates (such as quit and layoff rates), and measures of earnings growth. Viewed in total, this set of variables provides a more complete description of labor market tightness.

4. Is the following assertion true, false, or uncertain? "Increasing the level of unemployment insurance benefits will prolong the average length of spells of unemployment. Hence, a policy of raising UI benefit levels is not socially desirable." Explain your answer.

Answer: The social desirability of raising unemployment insurance (UI) benefits depends on a number of factors. From an efficiency perspective, the costs of higher UI benefits are the prolonged spells of unemployment they induce (they encourage unemployed workers to search longer). The benefits of higher UI benefits are the better job matches they induce, as they provide unemployed workers with the resources to continue to search for jobs more commensurate with their skill levels. If individuals find higher-paying jobs that match their skills more closely, output will increase and the probability that these workers will quit their jobs in the future will decline. The empirical magnitudes of these various effects must be evaluated before one can decide if it is desirable to raise UI benefits.

One might also consider the equity, or income distribution effects, of raising UI benefits, Existing evidence suggests that UI benefits accrue, in large part, to workers from middle income and upper-income families. Raising UI benefits would affect the distribution of personal income, and policy makers need to consider this effect as well. In sum, the social desirability of the policy is uncertain.

6. “With the growth of free trade, Mexican employers have sought to reduce union control over 116

internal labor markets, and they have eliminated promotion by seniority, rules against subcontracting, and restrictions on the use of temporary workers – all in the name of greater flexibility.” Would you expect greater employer flexibility in hiring and assigning workers to increase or decrease unemployment in Mexico? Explain.

Answer. The level of unemployment in any country is a function of how fast workers flow into unemployment as compared to how fast they flow out. The above changes in Mexican employment conditions will probably tend to increase flows into unemployment, but by allowing employers to be more flexible, they lower the costs of creating new jobs. Hence, flows out of unemployment will tend to increase as the pace of job creation is enhanced. Even the flows into unemployment will be reduced, however, if the changes permit labor costs to be more flexible in a downward direction during periods of falling demand.

8. One student of the labor market effects of free trade argues that the government should offer “wage insurance” to workers who lose jobs because of free trade. Under this proposal, the government would replace a substantial portion of lost earnings if, upon re-employment, eligible workers find that their new job pays less than the one they lost. This wage insurance would be available for up to two years after the initial date of job loss. Would this wage insurance program reduce unemployment?

Answer. Wage insurance should cause unemployed workers to take offers they would normally have rejected, thus increasing the flows out of unemployment and into jobs – which, by itself, would reduce unemployment. Two factors might serve to increase the flows into unemployment, however, which could increase the level of unemployment. First, if workers take jobs hastily (the clock starts ticking upon job loss), they may be poorly matched with their employers – and may quit or be fired after the insurance runs out. Second, employers may be less reluctant to lay off workers, knowing that they have wage insurance for two years after layoff.

Answers to Even-Numbered Problems 2. Suppose that initially the Pennsylvania economy is in equilibrium with no unemployment: Ls = -1,000,000 + 200W and Ld = 19,000,000 – 300W, where W = annual wages and L = number of workers. Then structural unemployment arises because the demand for labor falls in Pennsylvania but wages there are inflexible downward and no one moves out of state. If labor demand falls to Ld = 18,000,000 – 300W, how many workers will be unemployed in Pennsylvania? What will be its unemployment rate?

Answer: Find the initial wage and employment level by solving as below: -1,000,000 + 200W = 19,000,000 – 300W, so 500w = 20,000,000, and W = $40,000 With W = $40,000, L = 7,000,000. Next, find the gap between Ls and Ld at W = $40,000 after the labor demand curve shifts: 117

Ls = -1,000,000 + 200x40,000 = 7,000,000 Ld = 18,000,000 - 300*40,000 = 6,000,000 This gap, Ls - Ld, shows that unemployment equals 1,000,000. The unemployment rate is (1,000,000/7,000,000)x100 = 14.3%.

4.

The following table gives data on characteristics of inhabitants in Anytown, USA. a. Identify the number of people employed, the number of people unemployed, and the number of people in the labor force. b. Calculate the labor force participation rate, the employment rate, and the unemployment rate, using official definitions.

Number (in Thousands) of People

Characteristic

Population

500

Population 16 years or older

400

Persons employed full-time or part-time

200

Persons unemployed and actively seeking work

20

Persons who have quit seeking work due to lack of success 10 Part-time workers seeking full-time jobs

30

Answer: a. Employed: 200. Unemployed: 20. People in the labor force: 220. b. Participation rate = 220/400 = .55 or 55%. Employment rate = 200/220 = .91 or 91%.

Unemployment rate = 20/220 = 0.09, or 9%. Discouraged workers are not part of the labor force, and persons seeking full time jobs do not count toward unemployment when they already have part-time jobs.

6. On July 24, 2007, the federal minimum wage was increased from $5.15 per hour to $5.85 per hour. Consider the effect of this increase on an unemployed job seeker. Using a job-search model, what is the effect on the probability of finding an acceptable job in any given period?

How does this increase affect the expected duration of unemployment and the expected wage (once employed)?

Answer: Considering only the effects on job search unemployment, the increase in the minimum wage should have no effects on workers with a reservation wage above the minimum wage, but the minimum wage increase, assuming that it was effective, does increases the number of people 118

seeking work while reducing jobs available. All other things equal, this will reduce the probability of receiving a job offer and thus increase the duration of unemployment. However, if we assume that there is no change in the reservation wages of workers, the minimum wage eliminates the possibility of some lower-wage job offers, and thus increases the probability that a given job offer will be acceptable (to workers with a reservation wage greater than or equal to the new minimum wage). For workers with a lower reservation wage than the new minimum wage, the probability of a job offer being acceptable is now equal to 1, eliminating search-related unemployment for workers of this type (although probably increasing unemployment due to other reasons). The expected wage will increase for workers with a reservation wage below the new minimum wage, and the effect on other workers is unclear, because while the value of wage offers may not be different for such workers, the probability of receiving a job offer of any type may decrease.

Suggested Essay Questions 1. Evaluate the following quote: “Without some kind of government transfer program (like Unemployment Insurance) the labor market would have no mechanism by which to ensure that the average yearly earnings of comparable workers in jobs with frequent layoffs are roughly equal to those in jobs that never lay off workers.”

Answer: This statement is not necessarily true because in the absence of Unemployment Insurance a compensating wage differential could arise. Workers would seek to avoid jobs with high layoff risk, especially because the lack of government transfers means their income would fall dramatically during periods of unemployment. The existence of compensating differentials, of course, would depend on the amount of information and choice available to workers in the labor market.

2. In 1988 the United States passed the Worker Adjustment and Retraining Notification Act (WARN), which required employers of 100 or more workers to give employees and local governments a 60-day notice before they shut down or make large-scale layoffs. Analyze how such advance notice would be expected to affect the unemployment rate.

Answer: In theory, advance notice has ambiguous effects on unemployment. It can be expected to reduce unemployment by giving workers opportunities to search for new jobs while still employed. Similarly, it also gives them time to apply for retraining programs, which can also reduce the time spent out of work. Finally, it gives workers time to try to prevent their displacement by offering wage or other concessions to their employers.

Advance notice, however, can also serve to increase unemployment. Plants that are in trouble and realize that they might have to close, might choose to give advance notice even though a final decision to close had not yet been made. By announcing the expectation of closure or large-scale layoffs, the employers may risk losing their best (most mobile) employees and lowering the morale of those left behind – which further increases the chances of having to close. Likewise, giving notice may discourage banks or suppliers from supplying new credit, which again makes it more difficult to solve the plants’ problems. Further, by increasing the costs of closing, 119

advance notice inadvertently discourages new plants from opening, thereby retarding employment growth.

3. In the 1970s Sweden adopted several new labor market policies affecting layoffs. Three were notable: (1) Plants that provided in-plant training instead of laying off workers in a recession received government subsidies; (2) All workers had to be given at least one month's notice before being laid off, and the required time in the average plant was two to three months; (3) Laid-off workers had to be given first option on new jobs with the former employer. What probable effects would these policies, taken as a whole, have on wages, employment, and unemployment in the long-run?

Answer: Policy number one clearly increases the incentives of firms to retain workers during a recession. Therefore, this policy will probably reduce unemployment associated with demand deficiency. If the training that is subsidized is useful and geared to market demands, then the substitution of training periods for periods of unemployment may reduce structural unemployment as well. That is, firms could train their workers to fill newly created jobs for which their current work force was not trained, or it could use the subsidy to provide training to its workers that other firms might find useful. This latter policy might be pursued by firms whose labor demand was shrinking and who might find it more profitable to induce employees to quit rather than undergo the expense of laying them off.

Requiring advance notice of layoff to employees raises labor costs because firms are no longer free to lay off workers the instant marginal productivity slips below the wage rate. While the short-run effects of this may indeed inhibit layoffs, the longer-run effect is that the rehiring of labor when the market improves will be discouraged. That is, by raising the costs of labor, the firm will be induced to scale down its operations and to substitute capital for labor. The slowing down of the post-recession recall of laid-off workers and the possibility of reduced labor demand could cause unemployment to rise (or remain) higher than it otherwise would. Of course, this conclusion would change if wages were to fall when this new "fringe benefit" of advance notice was mandated.

A requirement that laid-off workers be given first option on any new jobs with the former employer might prevent such employers from hiring younger, less experienced workers, and could cause the composition of unemployment to change. That is, the unemployment rate for older workers might fall and the unemployment rate among younger workers might be expected to rise as a result of this policy. By constraining firms to hire older, displaced workers from declining departments in their expanding departments, the requirement raises labor costs and will tend to cause employment growth to be smaller than it would otherwise be. This, of course, could contribute to unemployment in the long-run.

4. The present value of benefits in many pension plans are larger if a person retires before the normal retirement age. In short, there is a large inducement for many private sector workers to retire early. What effect will increasing the inducements to retire early have on the unemployment rate of older men? Fully explain your answer, making use of the assumption that retired workers withdraw from the labor force and do not seek or obtain other jobs.

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Answer: It is possible that increased inducements for early retirement will increase the unemployment rates of older workers. The reason for this is that they may induce older workers who are currently employed to withdraw from the labor force earlier than they otherwise would, thereby increasing flows from employment to "out of the labor force." When flows from employment to out of the labor force are increased, other things equal, the unemployment rate will rise because there is a fall in the labor force without a corresponding fall in unemployment.

It is possible, of course, that the older workers deciding to retire early are predominantly those who have just been laid off -- perhaps permanently -- by their employers. They may believe that, rather than continuing to search for work, they would be better off accepting their pension and dropping out of the labor force. Obviously, the more generous their pension is prior to normal age of retirement, the greater is the likelihood that they will drop out of the labor force after layoff. Thus, it is impossible to say whether more generous early retirement benefits tend to increase or reduce the unemployment rate of older men.

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CHAPTER 15 - INEQUALITY IN EARNINGS This chapter is intended to accomplish two purposes: to analyze changes in earnings inequality after the 1980s and to review major concepts of economic theory introduced in prior chapters. It begins with a section on measuring inequality and then moves to one that describes changes in the 1980s and early 1990s along various dimensions: the occupational distribution, relative wages, hours of work, and earnings dispersion within narrowly-defined human capital groups.

The underlying causes of growing inequality are then grouped into supply factors, institutional changes, and demand-side influences. Empirical studies are surveyed, with the conclusion that demand factors were dominant in the 1980s (especially computer-related technological changes that affected the mix of productive factors, leading to increased relative demand for educated workers). The appendix discusses the derivation of Lorenz curves and Gini-coefficients.

List of Major Concepts 1. Earnings inequality is a function of the dispersion of the earnings distribution, and this dispersion can be measured in various ways, which differ in the ease with which they can be completed and widely understood.

2. The most widely-used measures involve ranking the population and analyzing earnings by percentile (comparing either shares of the total received by a group or the earnings levels at percentile boundaries).

3. Earnings distributions for both men and women became "stretched" in the 1980s, more because wages of those in the upper end grew relative to others' than to a movement of jobs from the middle of the distribution to either end.

4. The most notable change in earnings for both men and women was the increase in the relative earnings of more-educated workers; for men this increase occurred mainly because earnings of the less-educated fell in real terms, while for women it was associated mainly with the increased real earnings of more-educated women.

5. The returns to experience rose modestly, but only for the less-educated.

6. Changes in the relative hours of work played no role in the growth of inequality.

7. Earnings also became more dispersed within human-capital groups.

8. Growing disparities could result from labor supply, institutional, or labor demand changes.

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9. The fact that skilled employment grew faster than unskilled employment in the 1980s appears to rule out supply changes as the dominant factor underlying the growth of inequality.

10. Such institutional factors as a "frozen" minimum wage and declining unionization could have played a role in the growing inequality, but they apparently played a minor one.

11. Both product demand changes and changes in the mix of productive factors contributed to growing inequality, with the latter changes the dominant force in the growth of educationrelated differentials.

12. The growth of contingent-pay plans might underlie the increased dispersion within humancapital groups, but definitive work has yet to be done.

13. (Appendix) The Lorenz curve and Gini coefficient are related measures of disparities that are based on groups' shares among the total.

Answers to Even-Numbered Review Questions 2. Assume that the "comparable worth" remedy for wage discrimination against women will require governmental and large private employers to increase the wages they pay to women in female-dominated jobs. The remedy will not apply to small firms. Given what you learned earlier about wages by firm size and in female-dominated jobs, analyze the effects of comparable worth on earnings inequality among women. (For a review of relevant concepts, see Chapter 12.)

Answer: The comparable worth remedy will have contradictory effects on the dispersion of earnings if it is applied only to large private or governmental employers. The reason is that the employers to which the comparable worth remedy will apply are the highest-paying employers, but the jobs to which it will apply are among the lowest-paying jobs. Raising the wages of the lowest-paying jobs will tend to equalize the distribution of earnings, but because the remedy applies only to the highest-paying firms, there may be offsetting tendencies. In particular, there may be downward pressure on wages in female-dominated jobs in the small business sector as employment shifts from sectors experiencing large wage increases to "uncovered" sectors. Thus, it is possible that the lowest-paying jobs with the lowest-paying employers will actually experience reductions in wages that could widen the dispersion of earnings. In summary, women in the very lowest part of the income distribution might experience wage reductions, while those slightly above them will experience wage increases; the more dominant of these two tendencies is difficult to forecast.

4. Proposals to tax health and other employee benefits, which are not now subject to the income tax, have been made in recent years. Assuming that more highly paid workers have

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higher employee benefits, analyze the effects on earnings inequality if these tax proposals are adopted. (For a review of relevant concepts, see Chapter 8.)

Answer: If employee benefits are subjected to the income tax, the receipt of compensation in the form of "in-kind" or deferred benefits becomes less attractive. Workers now receiving a substantial fraction of their overall compensation in the form of benefits may decide that they would prefer to have reduced benefits and receive a higher fraction of their pay in cash earnings.

Assuming overall (pre-tax) compensation levels are not changed by this new law, its main effect will be to shift the compensation of highly-paid workers away from benefits and toward even higher levels of cash earnings. If by the "earnings distribution" we mean (as we did in the text) cash earnings, then the effect of this benefits tax will be to widen the dispersion of earnings in society. Widening the dispersion of earnings, however, is offset by a narrowing of the dispersion of employee benefits received, with the result that the overall distribution of total pre-tax compensation might remain essentially unchanged. (The distribution of post-tax compensation, however, is more equal than before, owing to the increased taxes paid by highlycompensated workers.)

6. Discuss the role of geographic mobility in decreasing or increasing the dispersion of earnings.

(For a review of the relevant concepts, see Chapter 10.)

Answer: Geographic mobility is, at least in part, a response to earnings inequality across geographic areas. People tend to move from areas with low opportunities (wages) to places where they believe they can improve their earnings, at least in the long-run. Thus, geographic mobility should tend to equalize earnings across areas -- driving up wages in low-wage areas (as workers move out) and driving down wages in high-wage areas. While geographic mobility may do little to shrink the gap between the wages of highly-educated workers and those of high school dropouts say it does serve to reduce the disparity of earnings within human-capital groups.

8. One economist has observed that by age 20, the cognitive and noncognitive skills of people are set in such a way that those who are not good at learning new skills or concepts cannot be helped much by education or training programs. Assuming this observation is true, use economic theory to analyze its implications for the issue of earnings inequality in the world today.

Answer: If this is correct, some workers cannot be helped by education and training programs, and thus, all other things equal, cannot improve skills in a way that will increase earnings (and thus any earnings increases would have to be the result of something like an increase in demand for workers of their given skill level). This implies that it may not be possible to improve income inequality through training for some groups, and thus only income redistribution programs are likely to have much effect for groups of this type.

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Answers to Even-Numbered Problems 2. Suppose that the wage distribution for a small town is given below.

Sector

Number of Workers

Wage

A

50

$10 per hour

B

25

$5 per hour

C

25

$5 per hour

Then a minimum wage law is passed that doesn't affect the market in high-wage sector A, but boosts wages to $7 per hour in sector B, the covered sector, while reducing employment to 20. Displaced workers in sector B move into sector C, where wages fall to $4.50 per hour as employment grows to 30. Has wage inequality risen or fallen? Explain.

Answer: There are several ways to measure inequality. On the one hand, the share of income going to the bottom half of the income distribution has risen (from $250/$750 = .333 to $275/$775 = .355), thus wage inequality has fallen by this measure. On the other hand, the 80th20th percentile wage ratio has risen (from $10/$5 = 2 to $10/$4.50 = 2.22). There is no unambiguous answer to this question.

4. Calculate the coefficient of variation for the workers listed in Problem 1.

Answer: The coefficient of variation is the square root of the variance divided but the mean. The mean is $34,400, and the standard deviation (square root of the variance) is 10,403, so the coefficient of variation is 0.325, or 32.5%.

Suggested Essay Questions 1. Would a higher minimum wage promote more wage equality? Discuss thoroughly.

Answer. As discussed in Chapter 4, one possible effect of a higher minimum wage is for the “spillover effect” to cause lower wages in the uncovered sector. In this case, wages rise for some low-wage workers, but fall for others – and the effects on wage inequality are ambiguous. (Of course, there are different ways of measuring wage inequality, and different results could be obtained by different measures. For example, if workers covered by a new minimum wage were at the 20th percentile of the wage distribution, while those who are uncovered are at the 10th, an 80-20 measure would show improvement, but a 90-10 measure would indicate greater inequality.)

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2. Countries X and Y both have agricultural and industrial sectors. Historically, they have levied tariffs on each other’s exports, which have had the effect of reducing trade between the two countries. X and Y now agree to drop these tariffs. Will greater trade between the two countries lead to increased real incomes in each country? Will greater trade lead to increased real wage equality within each country?

Answer. As discussed in Chapter 4 and its appendix, moving from restricted to free trade will have effects similar to technological change (in that the principle of comparative advantage will lead to more efficient production of goods and services). Technological change will increase real incomes in both countries, which can now take advantage of cheaper goods and services.

However, technological change does not imply anything about changes in wage equality.

Comparative advantage may call for more of one kind of worker in a given country to be used, and less of another, depending on the ratio of marginal product to wages for the two kinds of workers in X and Y (clearly, these sectoral shifts do not depend on wage levels alone).

3. (a) Why might we expect higher rates of economic growth in a country to be associated with more rapid increases in earnings inequality within that country? (b) During the 1980s, Korea experienced a very high rate of economic growth but also experienced a reduction in earnings inequality? How might this be explained?

Answer: (a) Rapid growth requires workers (and employers) to adapt to new conditions, and some do this much more readily and better than others. Those who adapt most quickly experience faster earnings growth. Workers who are more educated may be better at learning (and therefore adapting), so the better-educated are generally favored by environments that require change; therefore, the earnings disparities across educational groups grows. However, within various educational groups, some will be better at adapting than others, so the earnings disparities within groups also grows. (b) In Korea, it is possible that economic growth permitted an expansion of the educational system and led to a relatively rapid increase in the number of well-educated workers. If the growth of the number of educated workers was faster than the growth in demand for them, earnings disparities across educational groups could fall.

4. Consider the following quotation: “Immigration (legal and illegal) of unskilled workers to the United States is the dominant cause of growing American earnings inequality.” What would you look for in labor market data to assess whether this quotation is true?

Answer: If this statement is true, the falling relative wages of unskilled workers in the United States would be associated with a rightward shift in their supply curve that dominates any shift in the labor demand curve. Such a large relative shift of the supply curve, however, would drive the employment of unskilled workers up relative to the employment of other workers. Thus, if this statement is true, we should see the falling relative wages of unskilled workers but relative growth in their employment levels.

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CHAPTER 16 – THE LABOR MARKET EFFECTS OF INTERNATIONAL TRADE AND PRODUCTION SHARING This chapter discusses the effect of trade and globalization of production on labor markets. The increase in world trade and reduction in protection of domestic industries has changed both goods and services available but also the meaning of a good that is “American”, due to the prevalence of imported components and supply chains that are global rather than local.

Are domestic workers harmed by lower-wage workers in other countries? This chapter attempts to answer these questions using tools developed earlier in the text and both positive and normative approaches.

List of Major Concepts 1. Trade, whether for individuals, firms, or nations, is based on comparative advantage and mutually beneficial exchanges.

2. Specialization and exchange benefits both trading partners if labor and capital are freely mobile, but if mobility is limited, the resulting unemployment of resources can offset the gains from trade.

3. Labor market effects are different by sector: in export sectors, the demand for labor increases, and thus wages and employment rise. In import sectors, the demand for labor falls, and wages and employment fall.

4. Greater trade may increase national income, increasing the demand for all goods and services, and to the extent that prices of imports fall, the change in real wages will be less in import sectors (greater in export sectors) than the change in nominal wages.

5. The availability of alternate supplies of labor (at lower wages) in other countries has a crosswage effect on the demand for domestic labor, and depends also on the ratio of wages to marginal productivity in both countries.

6. Substitution effects reduce domestic employment and are greater where the supply of domestic workers is more elastic and where domestic and foreign workers are more substitutable.

7. Scale effects result from the fall in product prices, which increases the quantity of the product demanded, and in theory might increase domestic employment. It is more clear that employment is likely to rise for workers that are complementary to foreign workers and when product demand is more elastic.

8. The demand for domestic labor is also likely to become more elastic, which may explain decreases in union bargaining power.

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9. Empirical estimates of job losses in the United States due to trade and to offshoring of jobs are quite small, but adjustment costs may be significant for those who do lose their jobs.

10. Trade theory implies that wages will converge across countries given sufficient time, but this process is extremely slow and is only likely to occur in sectors where the location of output is not important to the final product; the production of most services cannot easily be relocated.

11. Since international trade does involve losers, normative considerations require compensation of the losers from trade. This could involve subsidizing retraining, income support programs, or subsidized employment.

Answers to Even-Numbered Review Questions 2. Company X, a profit-maximizing employer that makes picture frames, is expanding and needs to pick a location for its new plant. It is considering two sites: one in Texas and one in Mexico, where wages are roughly one-quarter of what they are in Texas. Use economic theory to analyze the factors Company X will take into account when making its decision.

Answer: The primary factor that the firm needs to consider is the ratio of wages to marginal productivity in both countries. Mexico may have wages that are ¼ of what they are in Texas, but if productivity is more than four times lower, it is better to build the plant in Texas. (The firm may also have other considerations as well.)

4. Television commentator A makes the following statement: “Economic theory shows that reducing the barriers to international trade will, in time, make everyone in society better off.”

Comment.

Answer: Economic theory does predict that net social welfare will increase by removing barriers to trade. However, even though the gains to the winners exceed the losses to the losers, there are losers within society who may need to be compensated. Additionally, the adjustment costs may be sufficiently large that they might outweigh the gains from trade in the short run.

6. American television commentator C makes the following statement: “Reducing the barriers to trade with low-wage countries will expose our workers to competition from millions of lowpaid workers in the developing world. The result will be that American wage levels will plunge downward until they equal the wage levels in China and other poorer countries.” Comment using economic theory.

Answer: First, it is not wages that are most important but the ratio of wages to marginal productivity.

If wages in other countries are low but productivity is also low, then domestic workers may not really be competing with foreign workers. Secondly, while it is true that wages should roughly converge over time for similar jobs when the location of the output produced is not important, all other things equal, they will converge to a level somewhere between the low wage and the current U.S. wage, and the reduction in the real wage will be less than the reduction in the nominal wage due to lower import prices. Finally, that wage convergence will take considerable time and will not occur in sectors, such as many services, where the location of production is important.

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Answers to Even-Numbered Problems 2. Country C can produce 200 tons of wheat or 50 million automobiles per year. Country D can produce 500 tons of wheat or 125 million automobiles per year. The production possibilities curve for each country is linear. a. What is the opportunity cost of wheat in each country? What is the opportunity cost of automobiles in each? b. Which country has a comparative advantage in producing wheat? Why? c. Should these two countries trade? If not, why not? If so, which country should produce wheat and which country should produce automobiles?

Suggested Essay Questions 1. The production possibilities curve for the United States is linear and allows it to produce a maximum of 500 million units of clothing or 300 million units of food. The production possibilities curve for France is also linear and allows it to produce a maximum of 250 million units of clothing or 150 million units of food. Which good will the United States export to France?

Answer: Neither. The two countries have the same opportunity cost, so neither has a comparative advantage in either good.

2. One observer of the North American Free Trade Agreement (NAFTA) claims that, contrary to expectations, jobs in Mexican agriculture have been destroyed while jobs in the industrialized cities of northern Mexico have expanded. Assuming the facts on job loss and employment gains are accurate, are they consistent with economic theory?

Answer. Free trade allows countries to specialize in producing goods and services that have the lowest internal opportunity cost (that is, to specialize in goods for which they have a comparative advantage). If we think of two generalized goods (agricultural goods and manufactured goods), a country becomes more efficient in the production of manufactured goods will, by the definition of opportunity cost, become less efficient in the production of agricultural goods. If Mexico has a comparative advantage in the production of manufactured goods, it must have a comparative disadvantage in the production of agricultural goods. Thus, the assumed facts in the question are quite consistent with economic theory.

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