Solution Manual for Development Economics, Theory, Empirical Research, and Policy Analysis Julie Sch by Ace Test Banks

Chapter 1

Solutions Manual for Development Economics: Theory, Empirical Research, and Policy Analysis Julie Schaffner The Fletcher School, Tufts University December 2013

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Chapter 1

Chapter 1: Introduction Discussion Question 1: Many development actors have rallied around the United Nations’ Millennium Development Goals (MDGs), which are listed in Table 1.4 (see text). a. What do the MDGs indicate about the relative emphasis placed by supporters on the following: • Income versus nonincome indicators of well-being • Well-being improvements for the poor versus the nonpoor • Immediate versus longer-term improvements b. What might explain the emphasis in the MDGs on defining measureable targets? c. The MDGs have little to say about the process or policies through which the targets might be achieved. What are the potential benefits of remaining silent about the processes that will deliver MDG success and the policies development actors should employ in their efforts to achieve the MDGs? Do you see any potential costs? See Collier and Dercon (2006). [Discussion of the MDGs may be used to get students thinking about the many dimensions of development performance that development objectives might emphasize, and the difference between development objectives (i.e. values and priorities) and development methods (i.e. policies and approaches that might be used to achieve the objectives).] a. The MDGs seems to place strong emphasis on income, education and health as important for well-being, and to place strong emphasis on improvements for people living on less than $1.25/day relative to people who are less poor (but still very poor by developed country standards) and the non-poor. The goals seemed to emphasize short- and medium-run improvements over longer-term improvement, because they set targets for 2015. b. An emphasis on measurable targets might have several purposes. It might help focus efforts on successful outputs rather than on quantities of “inputs” to development efforts, thereby increasing interest in monitoring, evaluation, effectiveness, midcourse corrections, and redesign. It might also help focus diverse actors’ attention on similar objectives, possibly aiding cooperation. c. Focusing primarily on objectives rather than methods has the advantage of leaving the development community free to search for the best ways to achieve the objectives (perhaps acknowledging that there is no consensus about how best to do this). A possible cost of saying little about methods, pointed out by Collier and Dercon (2006), is that it might lead some development actors to pursue the objectives in the most direct and obvious ways, which need not, ultimately, be the most effective ways. For example, development actors might attempt to achieve the first goal only in the most direct way – by giving cash to poor households – instead of also trying to raise the incomes of the poor indirectly by, for example, strengthening property rights (thereby possibly encouraging investment and increasing the demand for lowskill labor in a long-lasting way). Notice also that the quantitative targets (right column of Table 1.4) are neither pure statements of objective nor precise and complete statements about policy. For example, the third target is

Chapter 1

to ensure that all boys and girls complete a full course of primary education. This reflects the value that everyone should have a real opportunity for primary education, and perhaps the belief that education is useful for sustained improvements in income and well-being, but it also implies the belief that policymakers should work toward the goal of expanding education by concentrating on efforts to get all children into school and to get them to remain in school through the official number of years of primary school. Unfortunately, the experience of the last 15 years is that even great success in getting all kids into and through primary school doesn’t mean they obtain real primary education. The quality of teaching and learning has plummeted and many children leave primary school without even becoming literate. The Collier and Dercon (2006) piece raises other provocative discussion questions, such as: Does the international community’s push to focus on absolute poverty reduction in developing countries have normative justification, given that it seems to override the social choices of democratically elected governments in developing countries?

Chapter 2

Chapter 2: Well-Being Discussion Question 3: Consider two approaches for assessing household living standards and well-being. The first involves selecting a random sample of households within a region and using long, detailed questionnaires to elicit comprehensive information about income, consumption, and living standards more generally. The second involves a very short questionnaire that is administered to every household in a community, which includes only questions that are easy to answer and may be used to construct simple indices of households’ living standards (e.g., questions about how many rooms respondents’ homes have and whether the household head is literate). For what purposes is each method best suited? (Purposes might include identification of regions that merit priority in poverty reduction efforts, academic research on poverty, and assessment of eligibility for an emergency cash transfer program.) How could analysis of the results of the first approach be used to give practical guidance regarding the design of the second approach? Long questionnaires administered to random samples of the population could be useful for identifying which regions are poorer than others. The long questionnaires allow reasonably accurate measurement of good well-being indicators (e.g. consumption expenditure per capita) and the random samples might allow good inferences about regional poverty rates without the expense of a full census. Data from long questionnaires and random samples might also allow economists to study the determinants of poverty and the effectiveness of various policies for reducing poverty. Short questionnaires administered to everyone in a community, by contrast, might be useful as part of a proxy means test when implementing a targeted poverty reduction program. Analysis of the first kind of data might allow researchers to construct a good short questionnaire to use in proxy means testing. With a random sample of answers to a long questionnaire that includes both good measures of consumption expenditure per capita and a variety of shorter questions, researchers could identify a set of simple questions that together are good predictors of per capita consumption expenditure and poverty levels. They could also produce an equation or rule for taking the answers to the simple questions and using them to determine whether a household is probably poor or not by a more accurate measure. Practitioners could then collect data only on the easier questions, and use the rule or equation to determine who is poor (and thereby eligible for the program by the proxy means test). Problem 1: Suppose we know that a policy did not produce any change in a household’s real per capita consumption expenditure. List at least five ways the policy might nonetheless have improved the household’s well-being. That is, suggest at least five stories regarding how the household’s circumstances might have changed, and how the household responded to those changes, that are consistent with the household’s well-being rising even while its per capita consumption expenditure remains constant. Good answers to this question reflect the use of the analytical framework of Chapter 2, and point clearly to changes that would raise well-being even while not raising consumption expenditure. Answers such as “receiving access to a better agricultural technology” (without richard@qwconsultancy.com

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Chapter 2

some sort of qualification) are off track, because the most obvious way through which such a change would raise well-being is by increasing income and consumption expenditure. Here are some possible answers: • •

•

The policy may have increased income (by providing a cash transfer or information about a new agricultural technology, or through many other types of intervention), but the additional income was put into saving rather than consumption expenditure. It may have improved the profitability of income generating opportunities, but the household took advantage of the opportunity to work less and earn the same income – enjoying more non-work time. We might see this in: o more leisure o children going to school rather than working It may have improved the household’s current well-being along non-income dimensions such as o reduced pollution o better health It may have reduced the household’s exposure to future risk or fluctuations, or improved the household’s ability to cope with risk and fluctuations (without changing current income), by creating o infrastructure that reduces flood risk o a public works program that households can access in the future if they need it o improved access to credit that households could use to smooth consumption in the future o new opportunities to purchase insurance It may have improved the household’s investment opportunities or ability to take up investment opportunities, for example through o improved access to school for children

Problem 2: Suppose you are attempting to choose a measure of living standards for use in determining which households most need assistance. Discuss the relative merits of the following possible measures of living standards: • Real income per capita within the household over the last two weeks • Real income per capita within the household over the last 12 months • Real consumption expenditure per capita over the last month • Per capita meat consumption over the last month • Indicators of whether a household has a dirt floor, uses water from an improved source, and sends children to school • Individual measures of height (for age), weight (for age), and recent illness Measure Strengths Weaknesses Real income per capita • This is a summary measure of a • It is not sensitive to variation within the household household’s ability to purchase in households’ capacity to over the last two weeks goods and services that is obtain goods and services that adjusted at least crudely for are not sold in wellvariation in need across functioning markets (e.g.

Chapter 2 households. •

•

• Real income per capita • within the household over last 12 months

If measured well, it provides an • even better measure of per capita capacity to purchase • goods and services than the previous measure, because it is less subject to fluctuations across months or seasons. •

•

Like income per capita, it is a • good summary measure of a household’s capacity to • purchase goods and services. It is even better than income per capita measured over a short recall period if people can smooth consumption, because it may fluctuate much less than income from month to month. Often it is thought to be measured more accurately than

Real consumption expenditure over the last month

•

health care). It does not account for the hours of work required to obtain the given level of income. It adjusts for differences in need only imperfectly. It adjusts for differences in numbers of household members but not, for example, in their health-related needs. When measured over just two weeks, it may provide a poor measure of the household’s usual capacity to purchase goods and services, because income fluctuates and households may be able to smooth consumption. It is insensitive to differences in households’ prospects regarding future income and consumption. It is a household-level measure that does not allow study of the distribution of well-being within the household. It is costly and difficult to measure. It has the same weaknesses as above. It may also fail to identify households that suffer severe deprivation for short periods within a year. It is difficult to measure accurately, because people have limited recall capacities. It has similar weaknesses as for the first measure. It fails to register improvement when households use rising income to increase saving and investment rather than consumption.

Chapter 2

Per capita meat consumption over the last month

•

Indicators of whether a • household has a dirt floor, uses water from an improved source, and sends children to school •

• Individual measures of • height (for age), weight (for age) and recent illness. •

•

income. If meat consumption is a steady • fraction of income or consumption expenditure, then it would have comparable strengths to those measures. It also has the merit of measuring a living standard of direct interest to policymakers concerned about nutrition. • It is easier to measure than total consumption expenditure.

These measures may do a better • job than income or consumption expenditure at measuring households’ living • standards along very important dimensions. To the extent they reflect assets rather than income, they may also have more to say about likely future well-being than a current income measure. They are easier to measure than income or consumption expenditure. These measures shed light on • health, which is of direct interest in the assessment of well-being. They allow study of the comparative well-being of men/women, young/old within households (unlike all the other measures mentioned above). Because they reflect health assets, they shed light on future prospects as well as the current well-being.

Because meat is a luxury, meat consumption may fluctuate more than total consumption expenditure. Meat consumption over a short period may, therefore, give a poor indication of usual living standards. Some households may choose not to eat meat for religious or cultural reasons; a meat consumption measure might understate their level of wellbeing. They are hard to aggregate into a single index for identifying who is deprived. Again, people with similar capacity to obtain goods and services may choose not to acquire some of these things because of differences in preferences.

They may not vary even when non-health dimensions of living standards vary a great deal.

Chapter 3

Chapter 3: Economic Growth Discussion Question 1: Read Collier (2007), Chapter 1. What does the author mean by “the bottom billion”? How does the author make his argument that achieving faster rates of economic growth must be the priority in development for the countries where the world’s “bottom billion” live? What do you think of this argument? Collier’s “bottom billion” includes the billion people living in a set of very poor countries that have not been growing and that he believes are stuck in one of four poverty traps: the conflict trap, the natural resource trap, the landlocked with bad neighbors trap, and the bad governance trap. (Notice that they are not the poorest billion people in the world; they are the billion people living in the countries with lowest average income.) He argues that we should be more concerned about growth in these poorest countries—and less concerned about immediate poverty reduction there – for perhaps two reasons. First, without growth the size of the pie is extremely small in these countries; so growth will be necessary for raising them out of widespread poverty. Second, he asserts that growth is more important than immediate poverty reduction for giving people hope, and hope encourages good people to stay (rather than emigrate) and try to contribute. With a reference to Cuba, he also seems to assert that if too much attention is paid to poverty and inequality, these countries will get stuck being countries with equal but very low incomes (perhaps because the incentive effects of the poverty reduction policies will cause investment and growth to stagnate). One might respond that these arguments for de-emphasizing immediate poverty reduction are not quite complete or fair, for several reasons. First, it is not clear that concentrated growth, which is not accompanied by poverty reduction, would inspire the kind of hope Collier believes necessary for many people. Second, even if we agree that growth is a necessary condition for development in the short and medium run, we may disagree about the relative (un)importance of getting today’s children into school or protecting them from waterborne diseases. That is, we might be willing to slow down the attainment of middle class status down the road (by accepting a lower growth rate) in exchange for preventing more children now from dying unnecessarily. On another subject: It is also useful to question his assertion that, among the 5 billion people in the developing world, only his “bottom billion” really merit international concern. Three quarters of today’s global poor (defined using the $2 per day poverty line) in fact now live in middle income countries, including India and China, and are not included in his bottom billion. These poor families continue to live in deep poverty, and helping to eliminate their poverty will continue to be a major challenge for decades. Discussion Question 2: As poor economies grow, the share of production that passes through formal markets rises as subsistence farmers become more integrated into markets and improved law enforcement reduces black market activity. Would this process tend to raise or lower the measured rate of economic growth? Would the measured rate of economic growth tend to understate or overstate the true rate of economic growth?

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Chapter 3

If countries measured GDP only by valuing goods and services that pass through markets, then if growth is accompanied by an increase in the share of goods and services passing through markets, the measured rate of growth would exceed the actual rate of growth. In practice it is harder to say, because countries use diverse methods for adjusting their GDP statistics for the existence of production that does not pass through markets. Problem 1: If GDP per capita grows from an initial level of 𝐺0 to the level 𝐺𝑡 after 𝑡 years have passed, then the average annually compounded rate of economic growth over the period 𝑟 is the growth rate 𝑟 (expressed as a percentage) that solves the equation 𝐺0 (1 + 100)𝑡 = 𝐺𝑡 Rearranging this expression, we find that 1 é ù t æ ö G ê t r = êç ÷ -1úú *100 G êëè 0 ø úû

The rule of 72 says that if a country grows at an annually compounded rate of 𝑟, then we can approximate the number of years it will take for the country’s GDP per capita to double (𝐷) using the calculation: 𝐷 = 72/𝑟 . To calculate doubling time exactly, notice that the number of years 𝐷 that it takes to double an initial income per capita of 𝐺0 for a country 𝑟 growing at rate r solves the equation 𝐺0 (1 + 100)𝐷 = 2𝐺0 . Dividing both sides by 𝐺0 , taking the natural logarithm of both sides, and rearranging, we derive this formula for determining doubling time exactly: D=

ln(2) ln(1+ r /100)

It just so happens that for growth rates in the relevant ranges for studies of economic growth, the right-hand side of this equation is a function of 𝑟 that is well approximated by the function 72/𝑟. The following table lists real per capita GDP for selected countries in 1960 and 2000 (in U.S. dollars). a. Calculate the average annually compounded rates of economic growth for each country to fill in column 3 in the table. b. Use the rule of 72 to calculate the approximate number of years it would take for GDP per capita to double in each country, assuming it continues to grow steadily at the rate you reported for part a. Record your answers in column 4. c. Use the formula presented above to calculate more exactly the number of years it would take for GDP per capita to double in each country, assuming it continues to grow steadily at the rate you reported in part a. Record your answers in column 5. a., b., and c. Country

(1) GDP per capita 1960 (U.S. Dollars)

(2) GDP per capita 2000 (U.S. Dollars)

(3) Average Annually Compounded

(4) Doubling time using “Rule of

(5) Doubling time using exact

Chapter 3

Bolivia China Ghana Taiwan

2431.39 448.13 411.86 1443.61

2929.19 891.39 1392.20 19183.93

Growth Rate 72” 1960-2000 (Percent)

calculation

0.47 1.73 3.09 6.68

148 40 23 11

153 42 23 11

Notice that the “rule of 72” approximation does a pretty good job for growth rates in this range.

Problem 2: Suppose a firm’s production function is given by F(L, H, K;A),where L,H, and K are the current quantities of labor, human capital, and physical capital employed in production, and A is an index of the current level of technology. For each of the following changes, indicate whether it would raise, lower, or leave unchanged: (a) the average product of labor (APL) in the firm and (b) total factor productivity (TFP) within the firm. • an increase in K, holding L, H, and A constant, while the firm continues to operate on its production function o (a) raises APL (b) leaves TFP unaffected • an increase in L, holding H, K and A constant, while the firm continues to operate on its production function o (a) reduces APL (b) leaves TFP unaffected • an increase in A, holding L, H and K constant, while the firm continues to operate on its production function o (a) raises APL (b) raises TFP • an increase in output that represents a movement toward operation on its production function, while holding L, H, K and A constant o (a) raise APL (b) raises TFP Problem 3: According to the growth accounting equation discussed in Box 3.1, gy = gA + α gk + (1-α)gh,, where gy, gk, and gh, are growth rates of GDP per capita, capital per worker, and human capital per worker, and α is the share of capital income in total GDP. The first four columns of the following table give values for gy, gk, gh, and α. a. Fill in the fifth and sixth columns of the table with the growth attributed to physical and human capital accumulation. These may be calculated as αgk and (1-α)gh, respectively. b. Fill in the seventh column of the table, plugging the values of gy, gk, gh, and αinto the growth accounting equation and backing out gA. c. Fill in the final column of the table by calculating the fraction of overall growth (gy) that is attributed to TFP by the growth accounting framework. (That is, divide gA by gy and multiply by 100.) a., b., and c. gy

Growth attributable to Physical capital

Growth TFP attributable growth to Human capital

TFP share in growth

Chapter 3 5.2

4.0

2.0

1.2

1.4

2.6

5.2

4.0

3.0

1.2

2.1

1.9

5.2

4.0

2.0

1.6

1.2

2.4

d. Discuss the potential for inaccurate estimates of gh and α to render misleading estimates of the importance of TFP growth. Estimates of TFP growth rates are calculated as a residual, after accounting for growth in physical and human capital. Thus, any inaccuracy in the measurement of these two parameters, which help quantify the growth that is “explained” by growth in physical and human capital, leads to inaccuracy in the estimate of TFP growth. Comparing rows 1 and 2, we see that if growth in human capital is overestimated, TFP will be underestimated. Comparing rows 1 and 3, we see that if the physical capital share is overestimated, and if physical capital has been growing more rapidly than human capital, then again TFP growth will be underestimated. Problem 4: In this problem you will derive the growth accounting equation discussed in Box 3.1. Assume that the aggregate production function takes the form y(t) = A(t)k(t)αh(t)1-α where y, k and h represent GDP per capita, physical capital per worker and human capital per worker, and α is a technological parameter. We assume that A, k and h are changing over time for unspecified reasons, and use the functions A(t), k(t) and h(t) to describe their levels at dy dk dh any point in time t. Derivatives of these functions with respect to time, dt , dt and dt , describe how fast they are growing (in absolute terms) at any point in time. Their percentage growth dA dk dh rates are g A = dt /A, g k = dt /k and gh = dt /h. Because Y is a function of A, k and h, it, too, is a dy

function of time, with percentage growth rate g y = dt /y. a. Take the derivative with respect to time t of both sides of the aggregate production function equation. dy(t) dt

dA(t) dt

dk(t)

dh(t)

k(t)αh(t)1-α+α dt A(t)k(t)α-1h(t)1-α+(1 − α) dt A(t)k(t)αh(t)-α

b. Divide both sides of this new equation by y, so that the left hand side becomes gy. gy=

dA(t) dt

k(t)αh(t)1-α+α

dk(t) dt

A(t)k(t)α-1h(t)1-α+(1 − α)

dh(t) dt

A(t)k(t)αh(t)-α

c. Show how to transform the equation you just derived into the following: gy = gA + αgk + (1-α)gh Substitute in A(t)k(t)αh(t)1-α for y(t) in the denominator of each right hand side term. In each of the three terms you can then cancel like terms in numerator and denominator to get the

Chapter 3

indicated relationship. Problem 5: Consider two firms that produce the same output. The marginal product of labor in each firm is a declining function of the quantity of labor employed there. In Firm 1, the marginal product of labor 𝑀𝑃𝐿1 is described by the function 𝑀𝑃𝐿1 = 40 – 2L1 , where L1 is the quantity of labor employed in Firm 1. In Firm 2, the marginal product of labor is described by 𝑀𝑃𝐿2 = 30 – 𝐿2 , where 𝐿2 is the quantity of labor employed in Firm 2.

30 25

MPL2

MPL1

a. Graph these functions in two graphs, side by side. Let your horizontal axes measure units of labor in the range of 0 to 20, and let your vertical axes measure the marginal product of labor in the range of 0 to 45 units of output.

10 labor

b. Suppose 𝐿1 = 6 and 𝐿2 = 8. What is the marginal product of labor in Firm 1? What is the marginal product of labor in Firm 2? Explain why the total quantity of output produced by the two firms together would rise if one unit of labor was moved from Firm 2 to Firm 1. 𝑀𝑃𝐿1 =40-2*6=28 𝑀𝑃𝐿2 =30-8=22 Taking away one unit from firm 2 would reduce output by 22, while adding it to firm 1 would increase output by 28. c. At what levels of 𝐿1 and 𝐿2 do the marginal products of labor equal 20 in both firms? If these are in fact the quantities of labor employed in the two firms, what is the average product of labor in each firm? (Hint: The average product of labor is just the total product or total output divided by the quantity of labor employed. The total product is equal to the area under the marginal product of labor curve.) You have just shown that it is possible for the average products of labor to differ across firms (or sectors) even when the marginal products of labor are equal. 𝑀𝑃𝐿1 equals 20 when 𝐿1 =10 𝑀𝑃𝐿2 equals 20 when 𝐿2 =10 The shaded rectangle in the below graph has area 10*20=200. The shaded triangle has area .5*10*20=100. The total product in firm 1 is 300, and the average product is 300/10=30. Comparable calculations find that for firm 2 the area under the curve is 10*20+.5*10*10=250, and the average product is 25.

20 10 0

MPL1

Chapter 3

10 labor

Chapter 4

Chapter 4: Economic Growth Theory in Historical Perspective Discussion Question 1: The Harrod–Domar model exhibits the knife-edge property that growth is consistent with continuously full employment only if (s/k)-d just happens to equal n. This knife-edge property is eliminated in the simple neoclassical model, which is characterized by continuously full employment. Discuss the importance of assuming variable rather than fixed proportions production technology for working this change. With a fixed proportions production technology, producers with a given quantity of capital can employ only so many workers. This number of jobs may fall short of the number of workers (as assumed in the Harrod-Domar model). Even if the excess supply of workers drove down the wage, employers would have no way to adjust their production choices to hire more workers (using their current capital stocks). They might be encouraged to expand production by investing, but their ability to do so is constrained by the saving rate. With a variable proportions production technology, by contrast, employers can respond to lower wages by increasing their use of labor relative to capital. Even while holding the capital stock constant, they will hire labor until the value of the marginal product of labor equals the wage. Whoever is willing to work at that wage will find employment. Discussion Question 2: For each of the bodies of growth theory described in this chapter, state whether production technologies are characterized by constant or increasing returns to scale. Where production technologies are characterized by increasing returns to scale, state whether the increasing returns to scale are present only at the aggregate level (while individual producers continue to work under the assumption that their technology is characterized by constant returns to scale), or whether increasing returns to scale are also present and important at the level of the individual firm. What roles do these assumptions play in shaping the predictions of the models? Harrod-Domar model: Constant returns to scale. This, together with the assumption of abundant labor, means that the growth rate of output is the same as the growth rate of capital. Lewis model: No potential to increase scale in the traditional sector and in fact no reduction in output if labor input is reduced. Constant returns to scale in the modern the sector. This implies that as labor is drawn from the traditional to the modern sector, total output rises. Solow models: Constant returns to scale. This, together with diminishing marginal returns to individual inputs, means that as the ratio of capital to labor rises, the impact of further increases on output per person falls. This is crucial to the result that there is no growth in steady state. Growth as by-product of human capital investment: Increasing returns to scale at the level of the entire economy. This creates the potential for investment that increases the capital stock (per worker) to be less productive in poor countries (where capital-labor ratios are lower) than in rich countries. Poor countries might tend toward a steady state with low levels of capital and income per worker, while rich countries tend toward the better steady state. The richard@qwconsultancy.com

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Chapter 4

increasing returns also come about through an externality, meaning that government might have a role to play in encouraging more of the relevant investments. Poverty trap models: In at least some versions, increasing returns at micro and macro levels are important. Increasing returns at the micro level might imply that investment is not profitable unless producers expect to face a large enough market. This, in turn, might mean that any one investment is profitable only if many other producers also invest. Discussion Question 3: Discuss the role of empirical research (including simple empirical observations) in driving the evolution of growth theory. Observations of success in the USSR and of the depression in the U.S. encouraged early capital fundamentalism and structuralism. New data on the economic behavior of poor households, new studies of human capital and earnings, new growth accounting studies, and new observations about growth encouraged a shift to models that also incorporated human capital and technology as proximate sources of growth and to models in which decisionmakers are responsive to changing incentives and in which markets work well. Observations of diverse growth experiences among poor countries, and the attempt to make models that treat technical change in more realistic ways, led to models in which growth does not necessarily happen ideally in the absence of intervention. Problem 1: As discussed in the text, the assumptions of the Harrod– Domar model may be summarized by the equations 1

Y = (𝑣) K Y = (1) K v

(4.A) (4.B)

and

K = sY – dK (4.C) where the notation is as defined in the text. (Equations 4.A and 4.B are two ways of stating the same assumption, but both expressions are useful to remember in the derivations you will be required to do below.) a. Demonstrate that equations 4.B and 4.C together imply the following result regarding the growth rate of GDP. (Notice that the text offers guidance about how to derive this equation.) •

Y s = -d v Y Plugging equation 4.C into equation 4.B, we get 1 𝑌̇ = ( )(𝑠𝑌 − 𝑑𝐾) 𝑣 Dividing by Y we get 𝑌̇ 𝑠 𝑑 𝐾 = − ( )( ) 𝑌 𝑣 𝑣 𝑌

Chapter 4

Recognizing that 1/v = Y/K, we can do some cancelling in the second term and get: 𝑌̇ 𝑠 = −𝑑 𝑌 𝑣 b. Show that equations 4.A and 4.C together imply the following result regarding the growth rate of K. •

K s = -d v K From part a we know that 𝑌̇ 𝑠 = −𝑑 𝑌 𝑣

From equation 4.A we know that K = vY and 𝐾̇ = 𝑣𝑌̇

Dividing by K, we get 𝐾̇ 𝑣 = 𝑌̇ 𝐾 𝐾

Recognizing that v=K/Y, we get 𝐾̇ 𝐾1 𝑌̇ = 𝑌̇ = 𝐾 𝑌𝐾 𝑌 Plugging in the result from part a, we conclude that 𝐾̇ 𝑠 = −𝑑 𝐾 𝑣

Problem 2: Consider the neoclassical growth model with technical change, and its diagrammatic summary in Figure 4.3. Suppose the rate of population growth n increased. Which element of the graph (i.e., the k*(n+d+g) line or the sf(k*) curve) would change and in what way? Draw such a change into a graph like the one in Figure 4.3. When the rate of population growth increases like this, what happens to the steady-state level of income per capita? What happens to the steady-state rate of growth in income per effective worker? What is the immediate impact on the rate of growth in k*? What is the immediate impact on the rate of growth of GDP per capita? Using intuitive, plain language, explain why the increase in the

Chapter 4

population growth rate has the short-run impact on growth that you just described and why that short-run impact eventually fades away. If n increased, the straight line in Figure 4.3 would rotate up, still starting at the origin but having a steeper slope. The steady-state level of capital per worker and GDP per capita falls. The steady state growth rate is still the rate of technical change. Initially, if the economy was in steady state equilibrium at the higher level of GDP per capita, the increase in the population growth rate world slow the rate of capital accumulation, causing the rate of capital growth to fall below the rate required to keep everyone equipped at the initial level of capital per worker. Growth would slow below the rate of technical change, but as the ratio of capital to effective labor falls, the growth rate would pick up, until the economy reaches the new steady-state equilibrium. Intuitively, the increased rate of population growth makes the economy fall short of equipping all new workers with the initial level of capital per effective worker (while also replacing depreciated capital). Capital per effective worker falls, tending to reduce per capita income. Growth probably remains positive even so, because technology is also improving. Problem 3: Suppose the aggregate production function takes the form Y = A(K) F(K,L) β where A(K)=K describes an external, economy-wide effect of K on A, F(K,L)=LαK1-α and 0< α<1. a. Demonstrate that if you double both K and L while holding the initial value of A constant (i.e., ignoring the external effect of K on A), Y doubles. If Y(L,K)=ALαK1-α, then Y(2L,2K)=A(2L)α(2K)1-α = 2α+1-α ALαK1-α = 2Y(L,K) b. Demonstrate that if you double both K and L, taking into account the external effect of K on

A, Y more than doubles. If Y(L,K)=KβLαK1-α, then Y(2L,2K)= (2K)β(2L)α(2K)1-α = 21+β KβLαK1-α = 21+βY(L,K)>2Y(L,K) c. Derive an expression for the marginal product of capital while ignoring the external effect

of K on A. That is, holding A constant (rather than treating it as a function of K), take the derivative of the aggregate production function with respect to K. Show that if K increases while L holds constant, this marginal product of capital falls. If Y(L,K)=ALαK1-α, then ∂Y/∂K = (1-α)ALαK-α, and because K is raised to a negative power, this derivative gets smaller as K rises. d. Derive an expression for the marginal product of capital, taking into account the external

effect of K on A. Show that if K increases while L holds constant, the marginal product of capital can fall or rise, depending on the values of α and β. If Y(L,K)=KβLαK1-α, then ∂Y/∂K = (1-α+β)LαK-α+β. If β>α, then K is raised to a positive power, and this derivative is increasing in K. Problem 4: Critical to the construction of some models of macro poverty traps is the assumption that the profitability of setting up a modern, high-productivity establishment in

Chapter 4

any one sector depends positively on the size of the market the establishment will face (which in turn is taken to depend positively on the number of other sectors in which modern, highproductivity establishments have set up). In this problem you will examine a very simple technology for modern production, involving a fixed cost of setup, in which profitability of setting up indeed depends positively on the number of units of output the firm anticipates being able to sell. Suppose that modern production can take place only after incurring a fixed cost of F units of labor. Once that cost is incurred, each unit of additional labor produces α>1 units of output. The price of a unit of labor is 1. Suppose the price of a unit of output is 1 also. Let Q be the quantity of output the potential investor anticipates selling. a. Derive an expression for the producer’s profits (i.e., revenue minus labor costs) as a function of Q, F, and α. Profit is equal to revenue minus cost. Revenue is equal to price times quantity sold. With price equal to 1, this is just Q. Cost is the fixed cost of F plus the variable cost of 1 for each unit of labor required. If each unit of labor produces α units of output, then each unit of output requires 1/α units of labor, and the variable cost is (1/α)Q. Thus profit is Q-F-(1/α)Q = (1-1/α)Q – F. b. Making use of this expression, show that if F = 0 (meaning that there are no fixed costs)

then setting up is profitable regardless of the level of Q. If F is 0, then profit is (1-1/α)Q = [(α-1)/α]Q, and this is positive, no matter what positive value Q takes, because α>1. c. Now assume F>0. Derive an expression for the minimum level of Q at which production is

profitable. How does this minimum profitable scale change as F increases? As α increases? If profit is (1-1/α)Q – F, then to find the level of Q at which profits are zero (just turning from negative to positive), we set that expression to zero and re-arrange. When (1-1/α)Q – F=0, Q = F/[1-1/α]. As F increases, this minimum profitable scale increases (because 1> 1/α). As α increases, 1-1/α increases and the break-even level of Q falls.

Chapter 5

Chapter 5: Poverty, Inequality, and Vulnerability Discussion Question 1: Consider giving one dollar to a poor person, keeping in mind that among a country’s poor people, some have much lower incomes than others. Consider each of the aggregate poverty measures defined in the text, and assume that per capita household income is the measure of individual-level well-being they summarize. For each measure, discuss how the impact on the measure would differ depending on whether the additional dollar were given to a person who is just barely poor (with income just below the poverty line) or to a person who is very poor. For the headcount ratio: If you gave one dollar to the least poor person (i.e. the person with the highest income that qualifies as poor), this indicator might show improvement, because a dollar might raise that person over the poverty line. If you gave the dollar to the poorest person, though, this indicator would not show improvement, because that would not raise the income of the poorest person above the poverty line. For the total income gap: This measure would change the same way, whether you gave the dollar to the most poor or least poor person. For the average proportional income gap: If you gave a dollar to the poorest person, this would go down. If you gave a dollar to the least poor person, the dollar might raise the person over the poverty line, and thus take the person out of the calculation of the average. It is possible that this measure would get worse. For the poverty gap index: If you gave a dollar to the poorest person this would go down. Whether you give a dollar to the most poor or least poor person, this would reduce the measure by the same amount. For the P2 measure: If you gave a dollar to the poorest person, this would fall by more than if you gave the dollar to the least poor person. Problem 1: This problem provides a brief review of summation notation, using an example related to the distribution of incomes in a population. Order the individuals in the population from 1 to N, with individual 1 being the poorest person and individual N being the richest. An individual’s index is his rank number in this ordering. For example, the fifth-poorest person has person index 5. Let Yi be the income of person i. In summation notation, the Greek letter Σ (capital sigma) denotes a sum. More specifically, the expression ∑N i=1 𝑌i , which is read as “the sum from i = 1 to N of Y-sub-i,” can be defined as follows: N i=1Yi = Y1 + Y2 + ...+ YN . a. Using summation notation, write down a formula for the mean (or simple average) of income in this population. The mean is equal to the total income in the population, ∑N i=1 𝑌i , divided by the number of people in the population, N. Thus we could write the formula this way: (1/N) ∑𝑁 i=1 𝑌𝑖 . richard@qwconsultancy.com

0|Pa ge

Chapter 5

b. Consider the expression

1 q ( z − Yi )  z q i =1 where z is the income poverty line and q is the index of the individual with the highest income who remains under the poverty line. State in plain language the calculation this expression describes and offer an intuitive interpretation of the statistic that results from this calculation. The expression to the right of the summation sign is person i’s proportional income gap. When we sum this from 1 to q, we are summing up these proportional income gaps only among the poor. When we then divide by q, which is the number of the poor, we are taking the average, among the poor, of the proportional income gaps. Problem 2: The following table lists the incomes for all individuals in each of three very small countries (just 10 people each). Incomes are listed in currency units (CUs) per week. The official poverty line is 10 CUs per week. Incomes in Currency Units Per Week Country 1 Country 2 8 3 8 3 8 9 8 9 8 12 8 12 12 12 12 12 12 12 12 12

Individual 1 2 3 4 5 6 7 8 9 10

Country 3 6 6 6 6 6 12 12 12 12 12

a. Fill in the following table. Poverty Measure P0 (Headcount Ratio)

Country 1

Country 2

.6 .12 .024

P1 (Poverty Gap Index) P2

Country 3

.4 .16 .10

.5 .20 .08

b. Fill in the following table. For each poverty measure, enter into the table the country rankings from most poor (1) to least poor (3) according to that measure. Country 1 Ranking according to P0

Country 2

Country 3

Chapter 5 Ranking according to P1 Ranking according to P2

a. Write a brief essay on differences among the three poverty measures in the values underlying them and how these differences in values lead to differences in poverty rankings in the case of the three countries described in the tables. A good paragraph here: • starts with a synthesizing topic sentence that is specific and content-filled rather than vague. • makes explicit reference to the details of Countries 1, 2, and 3. • gets across clearly that the HR is sensitive only to differences in prevalence, the P1 is sensitive to differences in both prevalence and average depth, and the P2 is sensitive to differences in prevalence and average depth and the fraction of the poor with incomes well below the average income of the poor. It is not the case that each is sensitive only to differences along one dimension. Here’s one possible paragraph: Whether we find Country 1, Country 2 or Country 3 to have the most poverty depends on our choice of poverty measure, because the P0, P1 and P2 poverty measures differ in the weights they place on the prevalence, average depth and extremes of poverty in the populations to which they are applied. The P0 measure determines poverty rankings purely on the basis of the numbers of people who are officially poor, regardless of how poor they are. By this measure, Country 1 has the most poverty, because the largest fraction of the population is poor there, even though they are not very poor. The P1 measure determines rankings in a way that exhibits concern not only for the number of the poor but also for the average depth of poverty. By this measure, poverty is greatest in Country 2, in which fewer people are poor than in Country 1, but in which the average severity of poverty is greater. The P2 measure is sensitive not only to the number of poor and the average severity of poverty, but also to variation around that average level of poverty, and thus to the existence of extremely poor people among the poor. By the P2 measure, Country 2 is the most poor, even though it has the smallest number of poor people, and even though the average depth of poverty is the same as in Country 3, because it contains some people who are much more deeply poor than the poor found in the other countries. Problem 3: Draw a diagram like that in Figure 5.1, including an initial income schedule. For each of the following cases, draw a new income schedule such that the shift from the initial schedule to the new one is associated with each of the following changes: • Reduction in the headcount ratio but increase in average depth of poverty among the (remaining) poor To show a reduction in the headcount ratio, the new income schedule (in red) must rise above z to the left of the initial q. The red schedule shown here reflects greater average depth of

Chapter 5

poverty among the poor, because the income schedule starts lower and is lower for a large fraction of the population that is poor. Income Yi YN

•

N Rank order i from poorest to richest

Constant headcount ratio but reduction in poverty gap index

For the headcount to remain constant, the income schedule must cross the z line at the same i. For the poverty gap index to fall, even while the headcount stays the same, the average depth of poverty among the poor must fall; so the average height of the Y schedule to the left of q must rise. Income Yi YN

•

N Rank order i from poorest to richest

Constant headcount ratio and poverty gap index but reduction in the P2 measure.

For the headcount ratio and poverty gap index to remain the same, the Y schedule must cut the z line at the same q, and the average height of the Y schedule to the left of q must stay the same. For the P2 measure to fall, the incidence of deepest poverty must fall. This requires that the Y schedule start at a higher level but have a lower slope throughout enough of the range to the left of q.

Chapter 5

Income Yi YN

N Rank order i from poorest to richest

Problem 4: The table below describes the distributions of income in two states (A and B) and in two subregions (rural and urban) of each state. Every individual in these states lives in a household of size one and has an income of exactly 100, 200, or 10,000 dollars per year (so it is easy to describe the distributions and calculate poverty statistics). The first two sections of the table present the numbers and percentages of individuals in each region at each income level. a. Fill in the two rows of poverty statistics in each of the last two sections of the table. For the first of these sections, use a poverty line of $201. For the last use a poverty line of $101.

Population (# of people) No. of people with Income of: $100 200 10,000 Percent of Population with Incomes of: $100 200 10,000 Poverty statistics Using poverty line Of $201: • Headcount ratio(%) • Total Income Gap($)

State A Urban 10,000

Total 20,000

State B Urban 10,000

Rural 10,000

Rural 90,000

Total 100,000

0 2,000 8,000

0 6,000 4,000

0 8,000 12,000

0 2,000 8,000

45,000 0 45,000

45,000 2,000 53,000

0 20 80

0 60 40

0 40 60

0 20 80

50 0 50

45 2 53

2000

6000

8000

2000

4,545,000

4.547,000

Chapter 5 Poverty statistics Using poverty line Of $101: • Headcount ratio (%) • Total Income Gap($)

45.000

45,000

b. Suppose attention is restricted to headcount ratio statistics employing a poverty line of $201, and representatives of State A are attempting to argue that their state should be given priority in the allocation of poverty alleviation funds. Would they prefer to employ statistics calculated at the state level (columns 3 and 6) or subregion level (1,2,4, and 5)? Why? Pretty clearly, they would like the sub-region level, because while their overall headcount ratio (using this poverty line) is lower, their rural headcount ratio is the worst of any subregion. They would probably rather get some funding for their rural areas than no funding for their entire state. c. Suppose attention is restricted to headcount ratio statistics calculated at the subregion level, and representatives of State A are still attempting to make the same argument. Would they prefer to employ a poverty line of $201 or $101? Why? They’d prefer the 201 poverty line, because by the lower poverty line they don’t even have any poor. The lower poverty identifies the rural area of State B as the only location with deep poverty. d. Suppose attention is restricted to poverty statistics calculated at the subregion level and employing a poverty line of $201, and representatives of State A are still at it. Would they prefer to use headcount ratio statistics or total income gap statistics? They’d prefer headcount statistics, simply because that is a statistic that is not sensitive to scale. State B is just plain bigger, so even if the ratio and depth of poverty were the same, the total income gap would be larger. e. Given that no single statistic captures everything that matters about poverty, what practical reasons might policymakers have for defining budget allocation rules based on a single simple statistic? In particular, why not just say: “Our civil servants know poverty when they see it; just give them discretion to allocate the funds as they see fit.”? Here’s a possible answer: Policymakers may prefer to settle for using an imperfect rule rather than giving discretion to policy implementers, because this may help prevent corruption and favoritism and help reassure the public that funds are being allocated in a fair and non-corrupt way. When implementers have discretion over the distribution of valuable resources, they may be tempted to allocate funds in ways that bring private or political gain for themselves or for their favorite groups, rather than pursuing the larger good. For example, they might claim that poverty is greater in their home states, thereby identifying an excuse for sending large fractions of funds there. Even if they exercise good judgment, diverse states or ethnic groups might get the

Chapter 5

impression that they had shown favoritism, and unrest might result. The use of rules might reduce both favoritism and the appearance of favoritism. Furthermore, implementers might be tempted to divert some resources into their own pockets. When well-publicized rules determine how many funds each state should receive, individual states are better empowered to hold the implementers accountable. Problem 5: The first column in the following table describes the initial incomes of all 10 people in a very small country. The official poverty line in this country is 15. a. Fill in the table in the following way. For the first 10 rows, in the second and third columns, fill in the income each person would have if each person’s income exactly doubled or tripled, respectively. Then fill in the remaining rows, making use of the income information found in the first 10 rows. Person

1 2 3 4 5 6 7 8 9 10 Total income Average income Headcount ratio Average income among the poor

Initial Income

1 1 1 7 7 7 19 19 19 19 100 10 .6 4

Income After DistributionNeutral Doubling 2 2 2 14 14 14 38 38 38 38 200 20 .6 8

Income after DistributionNeutral Tripling 3 3 3 21 21 21 57 57 57 57 300 30 .3 3

b. Plot a Lorenz curve describing the distribution of income in the first column. How would the Lorenz curves for the distributions in the second and third column compare to this one? Explain.

incshr

100

Chapter 5

100

popshr

The Lorenz curves for the second and third column should be the same, because when all incomes rise by the same percentage, the income shares belonging to given shares of the population remain the same. c. Imagine that economic growth brings a change in incomes from the situation described by the first column to the situation described by the second column in just one year. What rate of economic growth would this imply? Describe in words what happens to the incomes of those who were officially poor at the beginning of the period. Is the improvement for the poor in this case picked up better by changes in the headcount ratio or changes in the average income among the officially poor? The rate of growth would be 100 percent. The incomes of the poor double, but they are still below the poverty line, so the headcount ratio does not change. The average income among the poor measure would pick up the improvement better. d. Now imagine that economic growth brings a change in incomes from the situation described by the first column to the situation described by the third column in just one year. What rate of economic growth would this imply? Describe in words what happens to the incomes of those who were officially poor at the beginning of the period. Is the improvement for the poor in this case picked up better by changes in the headcount ratio or changes in the average income among the officially poor? The rate of growth is 200 percent. The incomes of all those who were initially poor triple, causing half of them to rise above the official poverty line. The headcount ratio falls. But, because those who were least poor before the change exit poverty, the average income among

Chapter 5

those who remain poor falls. In this case the headcount ratio seems to do a better job of picking up the change in poverty. e. Study the absolute income increases enjoyed by various members of the economy over the course of growth from the first column to the second or third column. Comment on the statement: “If the distribution of income (as measured by the Gini coefficient) remains constant during growth, then everyone in the economy shares equally in the growth.” The table illustrates what is happening when the Lorenz curve, and thus the Gini coefficient, remains constant. All incomes grow at the same percentage rate. But the incomes of those who start out with more also rise by more in absolute terms. We wouldn’t necessarily say that all are sharing equally in growth.

Chapter 6

Chapter 6: Consumption, Time Allocation, and Production Choices Discussion Question 3: Discuss the claim, “For a consumer with a utility function satisfying the assumptions of basic consumer choice theory, at least one good must be a normal good, but no good need be inferior.” Consider an initial budget line and an initial consumption point (F,N) on that budget line. When the budget line shifts out (as the result of an increase in income), there are no points on the new line for which the quantities of both F and N are less than their original values. If the consumer’s preferences really do reflect that “more is always better,” then we know the consumer will consume on the new budget constraint. For some points F is smaller and N is greater than for the original consumption point, for others N is smaller and F is greater, and for some both F and N are greater. But there are no points on the new budget constraint for which both F and N are smaller than in the initial choice. Discussion Question 4: Show that to determine the real quantities F and N consumed by the consumer whose preferences are shown in Figure 6.1a, it is enough to know the two ratios Y/pn and pf /pn. We do not need to know all three quantities Y, pf , and pn independently. Knowing only Y/pn and pf/pn, we know an intercept and a slope, and therefore can completely trace out the budget line. Discussion Question 5: Define a consumer’s true utility to be the utility she would associate with consumption choices if she had complete understanding of the consequences of those choices for her health and nutrition. Define her perceived utility to be the utility she associates with consumption choices in her current state of imperfect knowledge regarding these consequences. Assume that because she lacks complete knowledge of health and nutrition consequences, she tends to undervalue the consumption of vitamin-rich vegetables relative to the consumption of other items. Using a diagram similar to that in Figure 6.1a, demonstrate that when she maximizes her perceived utility she fails to maximize her true utility. Other At this point she is on the highest achievable perceived preferences indifference curve, but she is not on the highest possible true Y/Po preferences indifference curve.

Perceived preferences or preferences under incomplete information

“True” preferences or preferences under full information

Y/Pv

richard@qwconsultancy.com

Veggies

0|Pa ge

Chapter 6

Discussion Question 6: Suppose a labor supplier allocates time to only two activities, work and home time, and has a total of 80 hours available per week to be allocated across these two activities. Show that under the assumptions of basic labor supply theory the following two circumstances would lead a labor supplier to make the same time allocation choice. a. The labor supplier receives 20 pesos in nonlabor income and is offered a wage of 5 pesos per hour of wage labor. b. The consumer is offered 420 pesos for a contracted work week of 80 hours but may buy time off (to allocate to home time) at a price of 5 pesos per hour. In basic labor supply theory, one way to show that two situations would lead an individual to make the same choice is to show that the two situations imply identical budget constraints in an indifference curve diagram. That is the case here. In situation a, we are told that the individual is given 20 in nonlabor income and has 80 hours to dispose of. This means he can choose 80 hours of home time and 20 pesos of nonlabor income (the corner of the budget constraint). For each hour of home time he gives up to work, he can increase consumption expenditure by 5 pesos, indicating a slope of -5. If he spends all 80 hours working, he’ll earn labor income of 80*5=400. Together with nonlabor income he could spend 420 on consumption while consuming no home time. In situation b, we are told that if the individual spends all 80 hours working (no home time) he can consume 420 (same as in a). Each hour of home time he chooses to consume costs him 5 pesos in consumption expenditure, again implying a slope of -5. If he chooses to spend all 80 hours in home time, he gets 42080*5=20. Discussion Question 7: Using diagrams like the one in Figure 6.5, describe the kinds of changes to a woman’s labor supply choices that might be induced by her receipt of additional education. How might her budget constraint change? Why? How might her preferences change? Why? When a woman acquires education, she may become capable of taking jobs that pay higher wages, changing the slope of the budget constraint and increasing her “full income.” Education may also alter her attitudes toward work and consumption. For example, she may come to see women’s work outside the home as more acceptable. Discussion Question 8: What guidance does basic labor supply theory give us regarding the variables we should include in a regression examining the determinants of total household labor supply? The basic labor supply model suggests that when seeking to understand the determinants of total household labor supply, we should, at the very least, wish to control for non-labor income, wages faced by all members, and factors that are thought to create systematic differences in the relative priority households place on home time versus consumption expenditure, such as numbers of children and religion. Taking a broader view of the basic labor supply model, we might also wish to include the cost or availability of goods and

Chapter 6

services that are complements to or substitutes for home time. For example, a reduction in the cost of high quality child care may improve the relative attractiveness of working. Discussion Question 9: Consider a farmer who uses all of his available land to cultivate corn and beans, and assume that bean cultivation requires more labor per acre than corn production. Discuss the likely sign of the effect on corn production, bean production, and labor demand resulting from a reduction in the price of beans, an increase in the price of corn, an increase in the wage, and a reduction in the price of chemical herbicides. Explain your answers. Effect on: Effect of: Corn production Reduction in bean Corn production may price rise, if some land (or other input) that was previously devoted to beans is now more profitably devoted to corn.

Increase price

corn We expect an increase in corn production, as corn production becomes more profitable.

Bean production We expect a reduction in bean production as it becomes less profitable.

Farmers may devote to corn production some land (or other input) that was previously devoted to beans, reducing bean production.

Labor demand The bean price reduction represents an overall reduction in farm profitability, thus we’d expect a scale effect that reduces the demand for labor. Even if land and other inputs are shifted from beans to corn (rather than just being taken out of service), labor demand is likely to fall, because corn requires less labor per acre. The corn price increase represents an increase in overall profitability. We thus expect a scale effect that increases the demand for labor. If some land that was devoted to beans is now devoted to corn, however, this would tend to reduce the demand for labor (because corn requires less labor per acre). The net effect is uncertain, though we’d probably expect

Chapter 6

Increase in wage

The scale effect of the increase in the wage is to reduce production of corn and beans. Because beans require more labor per acre, the wage increase makes corn production more attractive relative to bean production, however. We’d expect corn production to fall by less than bean production. In the extreme, corn production could even rise while bean production contracts a lot. Reduction in price If the chemical of chemical herbicides are useful herbicides in corn cultivation, this may represent a price reduction that increases profitability and encourages more production. It is possible that the price reduction, by allowing cheaper substitution of chemicals for weeding labor, makes bean production more attractive relative to corn production. This could create a countervailing tendency for corn cultivation to fall.

labor demand to fall only in pretty extreme cases. The increase in the We expect an increase wage reduces the in the wage to reduce overall profitability of the demand for labor. producing any crop, tending to reduce bean production. Because beans require more labor per acre than corn, the increased wage is also likely to induce a change in composition away from bean production toward corn production. Both of these effects would tend to reduce bean production.

If the chemical herbicides are useful in bean cultivation, this may represent a price reduction that increases profitability and encourages more production. It is possible that the price reduction, by allowing cheaper substitution of chemicals for weeding labor, reduces the labor requirement disadvantage of beans relative to corn, encouraging a shift in the mix of crops toward beans. This might further increase the production of

The scale effect of the input price reduction would be to increase labor demand. If it stimulates a shift from corn toward beans, this might further tend to raise labor demand. But it would also create incentives for farmers to substitute chemical weed control for manual weed control. Labor demand might, therefore, fall.

Chapter 6

beans. Discussion Question 11: When studying any issue, economists instinctively identify the relevant decisions and decision makers, seek to understand the constraints and preferences that shape those decisions, work out the logically possible implications, and then undertake empirical research to determine which of the theoretical possibilities are important in practice. Suppose you are asked to study the likely effects on teacher and student performance of an effort to link teacher pay to how well their students perform on standardized tests. Which of the three basic models described in this chapter would serve as the best starting point for developing an appropriate analytical framework? Who is the most relevant decision maker? What is the most salient set of choices? What constrains those choices? What does the framework suggest regarding the possible impacts of the teacher performance-pay proposal? The most relevant decision maker here is the teacher, who must decide how to respond to the new incentive pay scheme. The relevant choices are teachers’ choices about how to use their time and energy, so the basic time allocation model would seem to be the most likely starting point. The framework reminds us that teachers have some kind of limit on the total time and energy they put into various activities. When the activities that are rewarded by the incentive scheme become relatively more attractive (because of the incentive scheme), teachers may shift some of their time and energy into doing more of the rewarded activities. It remains possible that they would take time out of non-rewarded activities, which may also be important for student learning. Whether the net effect is to bring improvement or deterioration in student learning is an empirical question. (See the discussions of performance contracting in Chapter 13.) Problem 1: Consider a consumer who chooses F and N to maximize U(F, N) = F.75N.25 subject to the budget constraint that Pf F + Pn N = Y. Making an appropriate substitution based on the budget constraint, this consumer may be construed as choosing F to maximize F.75[(Y – PfF)/Pn].25. a. Write down the first-order condition that must characterize the utility-maximizing choice F*. −.75 𝑌 − 𝑃𝑓 𝐹 ∗ .25 𝑃𝑓 ∗ .75 𝑌 − 𝑃𝑓 𝐹 ∗ ∗ −.25 . 75(𝐹 ) ( ) − .25 (𝐹 ) ( ) =0 𝑃𝑛 𝑃𝑛 𝑃𝑛 b. Rearrange this condition to derive an equation for the utility-maximizing F* as a function of Y, Pf, and Pn. 𝑌 F=.75𝑃 𝑓

c. According to this equation, how does the consumer’s choice of F* change as Y increases? As Pf increases? As Pn increases? F* rises as Y rises and falls as Pf rises. It is unaffected by Pn.

Chapter 6

d. Rearrange the condition one more time to derive an equation describing how the utilitymaximizing food expenditure share, (PfF*)/Y, relates to the model’s parameters. What do you learn from this expression? 𝑃𝑓 𝐹

= .75. This says that, no matter what, a consumer with these preferences always spends three quarters of her income on food. 𝑌

Problem 2: Draw three identical graphs with axes labeled as in Figure 6.1a. Draw into the three graphs identical budget constraints, with a point a located in the same place on the budget constraint (like point a in Figure 6.1). In all three graphs draw in the new budget constraint that would become relevant after an increase in income (of the same amount in all diagrams). Now draw different sets of indifference curves into the three diagrams to indicate the preferences of three different consumers, in which their preferences lead to the following outcomes: All three consumers choose to consume at point a when facing the initial budget constraint. The first consumer spends the entire increase in income on food. The second consumer increases food and nonfood consumption in the same proportion. The third consumer reduces food consumption after the income increase. Draw at least two indifference curves in each diagram, making sure that they satisfy all the properties required by the basic theory. In each diagram, the two (or more) indifference curves must be downward sloping and bowed toward the origin, and they must not look like they cross. Notice that we can use a horizontal line to mark the set of points along which nonfood consumption is constant, a vertical line to mark the set of points along which food consumption is constant, and a ray from the origin to market the set of points along which the ratio of nonfood to food is the same.

Nonfood

Y/Pn

Nonfood

Y/Pn

Y/Pf

Food

Y/Pn

Y/Pf

Food

Y/Pf

Food

Problem 3: Elasticities are useful measures, because we can roughly assess their size without reference to the units in which we measure goods consumption or price levels, simply by comparing their values to benchmarks of 1, 0, or −1. a. If the income elasticity of rice consumption equals 1, what happens to the ratio of rice consumption expenditure to total income when income rises (holding prices constant)? If the elasticity is greater (less) than 1?

Chapter 6

We are interested in the ratio of rice consumption expenditure to income, or prR/Y. If the income elasticity of rice consumption is 1, then whenever Y rises by α percent, rice consumption rises by α percent. Thus whenever the denominator of prR/Y rises by α percent, the numerator does the same, and the ratio remains constant. If the income elasticity of rice consumption is greater than 1 (less than 1), this ratio rises (falls) as Y rises. b. If the own price elasticity of rice consumption (R) is less than (greater than) −1, rice demand is said to be “price elastic”(“price inelastic”). When rice demand is price elastic (inelastic), does total expenditure on rice (pRR) rise or fall when the price of rice (pR) rises? We are interested in the total expenditure on rice, pRR. If the own price elasticity of rice consumption is less than -1 (so that rice demand is price elastic), then when pR rises by α percent, R falls by more than α percent, and the product pRR falls. If rice demand is price inelastic, then total expenditure on rice rises when pR rises. Problem 4: Draw a diagram like Figure 6.2a. Suppose this diagram illustrates the impact on a consumer of a general food subsidy’s reduction in the price of food (to the level associated with the dashed budget line). a. If the consumer still faced the initial prices, how much cash would she have to be given to be able to consume F2 units of food and N2 units of nonfood? Please answer using notation defined in the graph.

Non-food (N)

Y/pn

N2 N1

I1 F1 F2 Y/pf1

Y/pf2 Food (F)

I1 F1 F2 Y/pf1

Y/pf2 Food (F)

She would have to be given (F2-F1)pf1 + (N2-N1)pn. This is just the cost at initial prices of the extra amounts of food and nonfood that she consumes after the change.

Chapter 6

b. Show that your answer to part a is equal to F2(pf1 −pf2). After expanding the expression from part a, and then adding and subtracting F2pf2, the result may be re-arranged into F2(pf1-pf2)+(F2pf2+N2pn) – (F1pf1+N1pn). The latter two parenthetical expression are both equal to Y (because consumption choices just satisfy the budget constraint both before and after the change in price), and cancel out. c. Now suppose the consumer had been given F2(pf1 − pf2) in cash while continuing to face the initial prices. Draw the budget constraint she would face into your diagram, and explain why you draw it as you do. The equivalent cash transfer budget constraint must go through the point (F2,N2), because we have chosen a cash transfer that just allows the consumer to consume this combination. The slope must be the same as the initial budget constraint, however, because the consumer would face the initial prices. See the light gray line in the figure on the right above. d. Making reference to your graph and to any relevant assumptions of the model, demonstrate that if given the cash transfer described in part c, the consumer would consume less than F2 units of food but would achieve a higher level of utility than that associated with consumption of F2 and N2. The equivalent cash transfer budget constraint cuts through the indifference curve I2, which is just tangent to the budget constraint associated with the food subsidy. The cash transfer budget constraint therefore includes some points, to the left of (F2,N2), that lie on higher indifference curves. Under the equivalent cash transfer, therefore, the consumer would achieve higher utility, but would consume less food. Problem 5: Draw and label completely a diagram describing a consumer’s choice regarding consumption of rice and other items when she has Y rupees of income and faces prices Pr and Po in rupees per unit of rice and other items. Construct the new budget constraint she would face if she were offered the opportunity to purchase a limited quantity R of rice at a subsidized price Ps, which is lower than Pr. You may assume that R is less than Y/Pr.

Chapter 6

It is still the case that if the consumer spends all of her income Y on other goods, she would be able to consume Y/Po units. Her cheapest source of rice is now the subsidized distribution, so as we trace out her budget constraint, we must recognize that she will buy the first R units at the subsidized price. Starting from the budget constraint intercept on the horizontal axis, where she is consuming only other goods, if she gives up one a first unit of other goods, she would use the proceeds to purchase rice at the subsidized price. The first portion of her budget constraint (starting from the intercept on the horizontal axis) would, therefore, have steeper slope than the original. As she continues to give up other goods and use the proceeds to purchase rice, she will eventually exhaust the R units to which she is entitled. After that, if she gives up additional units of other to purchase more rice, she will have to do this at the market price. The remainder of the budget constraint, therefore, has slope equal to the slope of the original budget constraint. Problem 6: Consider a manufacturer who produces cloth using low-skill labor, high-skill labor, and several other inputs. According to basic producer theory, what do we know (or not know) about the signs of the scale effect and input substitution effect on the demands for lowskill labor associated with each of the following changes: a. A reduction in the wage for low-skilled labor, b. A reduction in the cost of an input that is a complement to low-skill labor, c. A reduction in the cost of an input that is a substitute for low-skill labor, d. Low-skill labor-using technical change, and e. Low-skill labor-saving technical change.

Reduction in wage for low-skill labor Reduction in cost of input that is a complement to lowskill labor Reduction in cost of

Regarding demand for low-skill labor Sign of input Sign of scale effect substitution effect + + +

Chapter 6

input that is a substitute for low-skill labor Low-skill labor-using technical change Low-skill laborsaving technical change

Problem 7: Suppose every farmer in a region cultivates one acre of land, but their plots differ in quality. The quantity of output they produce, Y, as a function of the labor they devote to cultivation, L, is given by the production function Y = eαQLβ , where Q measures land quality and 0 < β < 1. The price of output is p, the wage is w, and farm profits are given by pY − wL. Take Q as given and treat L as a variable input. Derive an expression for the profitmaximizing value of labor input, L*, as a function of Q. According to this expression, how does the value of labor input per acre vary across farmers with different land quality? 1

L* = (

𝛽𝑝𝑒 𝛼𝑄 1−β 𝑤

)

This indicates that the profit-maximizing quantity of labor per acre rises as the quality of the land rises.

Chapter 7

Chapter 7: Households Discussion Question 1: Consider a rural community composed of the following groups: • • • • • •

Subsistence farmers who produce corn only for their own consumption, using no purchased inputs, and who neither buy nor sell labor Wage labor households who earn income only by working for wages (either in agriculture or nonagriculture) and who purchase corn Small commercial farmers who produce corn for their own consumption and for sale, using only family labor, and who do not sell any labor Large commercial farmers who produce corn for their own consumption and for sale, using hired labor, and who do not sell any labor Nonfarm business households who buy corn and sell nonfarm services and who neither buy nor sell labor Incapacitated households who beg from their neighbors, sometimes receiving gifts of food and sometimes gifts of cash, which they use to buy corn

Discuss the likely effects of an increase in the price of corn on the well-being of the diverse groups within this community. You might wish to differentiate between short-run and longrun effects. The key idea here is to apply the general finding that a price increase benefits households that are net buyers of the item, hurts households that are net sellers and has no direct effect on households that are nonparticipants (unless the price change is large enough to shift them into buying or selling). In the short run, the households may be affected only by the price increase. In the longer run, the price increase may stimulate production and labor demand, raising wages, generating a second round of effects. Subsistence farmers: They do not participate in markets and will not, therefore, be directly affected by changes in the price of corn or the wage, unless the price or wage changes are so large that they encourage them to start participating in markets. Wage labor households: The increase in the price of corn hurts them, by reducing their real purchasing power. If the increase in corn price drives up labor demand and wages, then in the long run they might not be hurt as much and might even be helped, as their wage income rises. Small commercial farmers: They are net sellers in the corn market and do not participate in the labor market. They would be helped by the corn price increase. Large commercial farmers: They would be helped by the corn price increase, but this benefit would be diminished if the corn price increase drives up wages. Nonfarm business households: They are net corn buyers and don’t participate in labor markets, so they would be hurt by the corn price increase.

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Chapter 7

Discussion Question 2: Consider the model, developed in the text, of decision making by a wage labor household. Which variable within that model increases if the household receives a cash transfer from a government program? What does the model tell us about the likely impact of this change on the household’s consumption of food, nonfood, and home time and its labor supply? Assuming that home time is a normal good, what happens to the household’s actual labor income? Does the cash transfer translate peso for peso into increases in household consumption expenditure? If we find evidence that cash transfers reduce labor supply and thus raise total income by much less than the size of the transfer, must we interpret this as a policy failure? In the model of the wage labor household, the variable that increases as the result of a cash transfer is nonlabor income, M. An increase in M would likely increase consumption of food, nonfood and home time, because we suspect all of these are normal goods. The household’s labor income falls as the household consumes more home time. The cash transfer does not translate peso for peso into increases in household consumption expenditure, because the cash transfer’s increase to nonlabor income is partially undone by the reduction in labor income. When households respond to increased nonlabor income by reducing labor supply, we can see them as putting the cash transfer to use in the way that most raises their well-being. If our policy goal is to raise well-being, this is great. If our policy objective is to raise income or food consumption, this is not so great, but we have to question why we think we know better than the recipients about how to put the resources to good use. Discussion Question 3: What would happen to a wage labor household’s consumption choices if pf , pn, M, and w all rose by the same percentage? If they all rose by the same percentage, nothing would change in real terms. The wage and non-labor income would each still be able to buy the same real quantities of food and nonfood as before. Discussion Question 4: When participation in markets is costless and buying prices equal selling prices, we may treat farm households as first maximizing profits and then maximizing utility subject to their full income budget constraint (which depends on the level of maximized farm profits). In this model, changes in M have no impact on input use and output choices on the farm because they are irrelevant to the maximization of farm profits. Is the same always true in the model with positive costs of carrying out labor market transactions? Consider each panel of Figure 7.1. For the situation described in each panel, discuss whether a change in M would or would not affect the farm household’s choices regarding agricultural production. If home time is a normal good, we might expect an increase in M to raise the HLS schedule. In panels a and b (when the household is participating in the labor market), this has no impact on the household’s choice regarding labor to use in farm production, which is determined by the VMPL schedule and a wage line. In the third diagram, however, this change would lead to a reduction in labor used on the farm and thus a reduction in agricultural production.

Chapter 7

Discussion Question 5: Why might road improvements in a rural rice-producing area, which make daily travel between farms and town easier and cheaper, lead to an increase in the price elasticity of rice supply to the market? By reducing the transfer costs associated with participating in local labor markets, road improvements might induce more local farm households to participate in the labor market. As we saw in the text, households that participate in labor markets may increase production more in response to a price change than households that do not participate in labor markets. Discussion Question 6: Suppose you are asked to predict the approximate impact on the real purchasing power of the poorest and richest 10 percent of a country’s households of a 20percent increase in the price of maize. What data would you wish to collect and what calculations would you make? I would look for a household survey that allows me to estimate the average quantities of household maize production and maize consumption (and thus net purchases or sales) of households in the lowest and highest 10 percent of the population. I could get a crude sense of the purchasing power impacts by looking at the sizes and signs of the net maize sales calculations for the two groups. I might wish to recognize, though, that even among the “poorest 10 percent,” some households might be wage laborers, while others are maize farmers. I might, therefore, which to disaggregate the data further and look at net purchases and sales of maize within smaller subgroups. Discussion Question 7: Drawing on all models of household decision making discussed in this chapter (whether unitary or non-unitary), brainstorm a list of ways that a development organization might try to improve the relative treatment of women and girls within households. Even the unitary model suggests some ways that policymakers might try to improve the relative treatment of women and girls within households. They might use advertising campaigns, or other ways of altering norms, to change households’ unitary decision makers’ preferences regarding the treatment of girls and women. They might raise income (in the hope that consumption by girls and women are more strongly normal goods than consumption by boys and men). They might create subsidies that are tied specifically to expenditures on girls. For example, they might wave school fees only for girls, or offer scholarships only for girls. Cooperative bargaining models suggest that policymakers should brainstorm about how to improve women’s fallback positions and bargaining power. They might try to reform property rights laws, so that women do not lose access to land if they divorce. They might try to improve employment opportunities for women. Sen’s version of the cooperative bargaining model suggests that policymakers might wish to focus on changing women’s understanding of their own interests, perhaps by creating opportunities for them to meet with each other.

Chapter 7

Separated spheres and mental accounts models suggest that policymakers might wish to design policies that introduce new resources into women’s mental accounts rather than men’s. They might also try to alter community norms regarding spheres of control and legitimate uses of income from various sources. Problem 1: Using notation defined in the text, a wage labor household’s income M + wS must equal its consumption expenditure pf F + pnN. Let’s call the household’s initial level of income and consumption expenditure Y. If the household were to make no changes in S, F, or N while pf rises by ρ percent and w rises by ερ percent, a difference between its consumption expenditure and its income equal to pf(1+ρ/100)F+pnN−(M+w(1+ερ/100)S) would emerge. Show that as a percentage of the initial Y, this equals ρ(f – εω), where f is the fraction of Y initially spent on food and ω is the fraction of Y it derives from wage labor. We start with the size in pesos of the gap that opens up between required expenditure and income: pf(1+ρ/100)F + pnN – (M + w(1+ϵρ/100)S) We re-express this as a fraction of income, Y, and simplify, as follows: 𝜌 𝜀𝜌 𝑝𝑓 𝐹 + 𝑝𝑓 𝐹 100 + 𝑝𝑛 𝑁 − 𝑀 − 𝑤𝑆 − 𝑤𝑆 100 𝑌

𝑝𝑓 𝐹 𝜌 𝑤𝑆 𝜖𝜌 − 𝑌 100 𝑌 100

where we use the fact that pfF+pnN – (M+wS) = Y – Y = 0 to simplify the numerator of the first expression. Multiplying by 100 to turn this from a fraction to a percentage, and substituting in f=pfF/Y and ω=wS/Y, we get fρ-ωϵρ = ρ(f-ϵω). Problem 2: Consider a model of farm household decision making in which there are no costs of participation in markets, and buying and selling prices are identical. On the production side of the model, the household is endowed with capital K, a level of technology A, and a food production function Q = b(L, I, K; A), where L is labor input, I is fertilizer, and Q is food produced, and the function b(.) is a standard production function, increasing in all its arguments and exhibiting diminishing marginal productivity in L, I , and K. It faces output price pf, wage w, and fertilizer price q. On the consumption and time allocation side of the model, the household is endowed with nonlabor income M and total time T and seeks to maximize utility U(F, N, H), which is a function of food consumption F, nonfood consumption N, and home time H. It allocates S units of time to work, whether on the farm or in the market, for the wage w, where H + S = T and it must satisfy the budget constraint that pfF+pnN=M+wS+(pfQ−wL−qI), which says that its expenditures on consumer goods must equal the sum of nonlabor income, labor income, and farm profits. We argued in the text that such a household will first choose L, I, and Q to maximize farm profits and then choose F, N, and H to maximize utility subject to the budget constraint pfF + pnN + wH = M + wT + (pf Q* − wL* − qI*), where the term in parentheses is maximized farm profits. The household takes

Chapter 7

as exogenous the variables K, A, q, w, pf, pn, M, and T, and it must choose the utilitymaximizing values of L, I, Q, F, N, H, and S. a. Which of the exogenous variables influence the household’s production-side choices? The exogenous variables relevant for maximizing profits are K, A, q, w (as the price of labor), and pf (as the price of output). b. Which of the exogenous variables influence the household’s consumption and time allocation-side choices (either directly or indirectly)? All exogenous variables influence the consumption and time allocation choices. The variables in the answer to a affect the consumption side by altering maximized farm profits. As households maximize utility on the consumption side, they are influenced by the level of maximized farm profits, as well as pf , pn, w, M and T. c. Discuss what the model predicts regarding the effects of an increase in A and an increase in M on all endogenous variables, as well as on NMS=Q−F and NLS=S−L. When considering a change in A or M, you should hold all other exogenous variables constant. Do not, for example, speculate about how market prices pf and pn might change in response to the change in A or M. Increase in A: • Technical change increases profit-maximizing output Q and maximized farm profits. • Its effects on farm labor use L and purchased input use I depend on the nature of the technical change. • The increase in maximized farm profits tends to increase F, N and H, and decrease S, if F, N and H are normal goods. • With Q and F both rising, the effect on NMS is ambiguous. • The reduction in S would tend to reduce NLS. If the new technology is more demanding of labor on the farm, this would reduce NLS further. It is possible, however, that the new technology is less demanding of labor, causing L to fall and leaving the net effect on NLS ambiguous. Increase in M: • This leaves the “production side” unaffected, so L, I and Q remain the same. • An increase in M tends to increase consumption of normal goods F, N and H, and decrease labor supply L (if H is normal). With F rising and Q constant, NMS falls. With L constant and S falling, NLS falls. Problem 3: A wage labor household is a special case of a farm household, in which the household produces no food and employs no labor in its own production activities. Defining all notation as in the chapter, do the following: a. Write a simple equation describing the relationship between m and f when a household produces no food. f is expenditure on food as a fraction of income, so

Chapter 7

f = pfF/Y. m is the ratio of the household’s net marketed surplus, valued at the market price of food, to toal consumption expenditure (which equals income) so m = pf(Q-F)/Y. When Q=0, the second expression becomes m= - pfF/Y, so f = -m when Q=0. b. Write an equation describing the relationship between n and ω when a household employs no labor. n is the ratio of the household’s net labor supply (valued at the market wage) to total income, so n=w(S-L)/Y. ω is the fraction of income a household derives from wage labor, so ω = wS/Y. When L=0, the first expression becomes n=wS/Y. So when Q=0, ω=n. c. Demonstrate that the formula for the approximate percentage increase in a farm household’s purchasing power arising out of an increase of ρ percent in the price of food and ερ percent in the wage, ρ(m + εn), has exactly the same implications for the effect of the price and wage changes on a wage labor household’s purchasing power as the formula for the approximate percentage reduction in a wage labor household’s purchasing power, ρ(f – εω). The farm household’s purchasing power rises by ρ(m + εn). If this is a farm household with Q and L equal to zero, this reduces (making use of parts a and b) to ρ(-f+ εω). This is the same thing as saying that purchasing power falls by ρ(f-εω). Problem 4: Consider the three graphs in Figure 7.1, which depict three situations in which a farm household might find itself. a. What assumptions are common to the three situations? The three diagrams are based on the common assumptions that: • the household produces only the cash crop and consumes only food • the household maximizes utility U(F,H) • the household produces cash crop according to a given production function • the price of food is 1, the farm takes cash crop price as given and takes the wage as given

Chapter 7

•

the household is endowed with given quantities of non-labor income and time. b. What assumptions differ across the three situations?

They differ in their assumption regarding how the level of the market wage (plus or minus transfer costs) compares to the household’s autarky value of labor. c. What does the HLS schedule represent? What would happen to the HLS schedule in any panel if the household’s nonlabor income endowment (M) increased? Explain. The HLS schedule is essentially a household-level labor supply schedule, which indicates the wage the household would have to be offered to just compensate for giving up another unit of home time. If the non-labor income endowment M increased, and if H is a normal good, then at any wage the household would want to supply less labor. This suggests a leftward shift of the HLS schedule. d. Analyze what would happen in each of the three panels to the utility-maximizing levels of S*, L*, and Q*, and to the household’s sales and purchases of labor, as a result of the increase in the household’s nonlabor income endowment (M). In all three panels, the HLS schedule shifts back (if H is normal). In the first two panels, (assuming the change is not too large) this leaves total labor use on the farm L unchanged, but reduces S and reduces sales of labor or increases purchases of labor. In the third panel, the autarky value of labor time rises as the intersection with the HLS schedule moves up and back along the VMPL schedule. The household supplies less labor and also uses less labor on the farm. Unless the change is large, the household continues not to participate in the labor market as buyer or seller. Problem 5: Consider a household composed of a husband and a wife. The husband cares only about the household’s tobacco consumption, T, and obtains utility of V(T). The wife cares only about the household’s food consumption, F, and obtains utility of U(F). V(T) and U(F) are both functions with positive first derivatives and negative second derivatives. The husband brings income Y into household, and the wife brings in income Z. The husband is the household’s sole decision maker, who maximizes the simple sum of his own and his wife’s utility, V(T)+U(F), subject to the budget constraint pT+qF=Y+Z, where p and q are the perunit prices of tobacco and food. Show that the household pools income by showing that the effect on F of an increase in Y is the same as the effect on F of a comparable increase in Z. The husband maximizes V(T) + U(F) subject to pT+qF=Y+Z. Substituting in from the budget constraint, this is the same as maximizing 𝑌 + 𝑍 − 𝑝𝑇 ) 𝑉(𝑇) + 𝑈 ( 𝑞 with respect to T. The first order condition for finding the optimal T is 𝑝 𝑌 + 𝑍 − 𝑝𝑇 ). 𝑉 ′ (𝑇) = 𝑈 ′ ( 𝑞 𝑞

Chapter 7

Y and Z enter this expression identically. A one-peso increase in either one would lead to the same change in optimal T. To find optimal F we subtract the optimal T from Y+Z. Here, too, a one-peso increase in Y or Z would have the same effect. Problem 6: A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z > Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. a. Derive expressions for Ch and Cw as functions of Z, Yh, and Yw. (Hint: Substitute Z − Ch in for Cw in the maximand. You may then maximize the resulting expression with respect to Ch alone.) From the text we know we can find the solution by maximizing (Ch-Yh)(Cw-Yw). Making the suggested substitution, this becomes (Ch-Yh)(Z-Ch – Yw). Taking the derivative of this with respect to Ch, setting it equal to zero and re-arranging, we find that in the solution Ch=(Z+Yh-Yw)/2. From the budget constraint we know that Cw=Z-Ch, so Cw=(Z+Yw-Yh)/2. b. What do Ch and Cw equal if Yh =Yw =0? If Yh and Yw were both zero, then both Ch and Cw would equal Z/2. They would split income evenly. c. What do Ch and Cw equal if Yh = Yw (but this quantity is not equal to zero)? If Yh=Yw, then Ch and Cw are both equal to Z/2. Again, they split income evenly. d. The surplus associated with cooperation is S = Z − Yh − Yw. Show that each spouse consumes his or her fallback income plus half the surplus in the Nash cooperative bargaining solution. From above we know that Ch = (Z+Yh-Yw)/2. If the husband consumed his fallback income plus half the surplus, he’d consume Yh + (Z-Yh-Yw)/2 = (2Yh+Z-Yh-Yw)/2 = (Z+Yh-Yw)/2. The two expressions are equal. Similarly, Cw=(Z+Yw-Yh)/2. If the wife consumed her fallback income plus half the surplus, she’d consume Yw + (Z-Yh-Yw)/2 = (2Yw + Z – Yw –Yh)/2 = (Z +Yw-Yh)/2, which equals the above expression.

Chapter 8

Chapter 8: Domestic Markets for Goods and Services Discussion Question 1: Use diagrams like those in Figure 8.2 to explain the statement: “If transfer costs were zero it would be difficult to explain why grain markets in some communities remain in autarky—neither importing nor exporting—over long periods, during which prices change at home and in external markets.” If there were no transfer costs, the LEP and LIP would both equal the external market price, and would be equal to each other. Suppose the solid local supply and local demand schedules in the diagram below describe an initial set of supply and demand conditions. The only way for these conditions to be consistent with autarky (i.e. no importing or exporting) is for the LEP and LIP, which are the same, to be equal to the price associated with the intersection of the local supply and local demand schedules. If the supply or demand schedule shifted up or down, while the LIP=LEP line held constant, importing or exporting would emerge. For example, if the demand schedule shifted to the position of the dashed schedule, importing would occur. The local market would remain in autarky only if the external market price just happened to rise to the level associated with the new intersection of local supply and demand schedules. Price per bag of carrots

LEP=LIP

Bags of carrots

Discussion Question 2: Suppose a development organization discovers that agroclimatic conditions in a poor rural community are ideal for producing a food that commands a high price in urban markets. The costs of producing a kilogram of the new crop are similar to the costs of producing a kilogram of traditional local crops, but the urban price of the new crop is double the price of the traditional crop. Will local production of the new crop necessarily increase local farm households’ profits and income? Why might a shift from production of a traditional to a new crop fail to raise incomes? What does the transfer-cost discussion have to say about the kinds of investment that might be required before farmers and urban buyers both perceive the potential to profit from trade in the new crop?

richard@qwconsultancy.com

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Chapter 8

The profitability of selling in the external market depends not only on the price there, but also on the transfer costs associated with selling there. Producing the higher value crop for sale in the external market may not be profitable, because the transfer costs may be too high. Many types of investment may be required before production of the new crop becomes profitable, including investment in learning how to grow the new crop, investment in infrastructure adequate for transporting the new crop safely to market, investment in the development of relationships with buyers, and collective investments in facilities for sorting, packaging and making bulk shipments. Discussion Question 3: Consider a rural community in which many households produce rice, and consider an agricultural extension program that causes some but not all local farmers to adopt new, more productive technologies. a. In diagrams like those in Figure 8.2, what schedules or lines would shift, and in which directions, as a result of the agricultural extension program? If the rice market in this community is in autarky equilibrium (both before and after the introduction of the extension program), what happens to the price of rice? The agricultural extension program would shift the local supply schedule down and to the right, tending to reduce the price of rice. b. Employing common sense, as well as the tools of the first half of Chapter 7, identify the diverse socioeconomic groups within the community that are likely to be affected by the extension program and related price changes in different ways. Which groups are likely to gain? Which groups are likely to lose? The farmers who adopt the new technology benefit from increased profits, because the new technology is more productive. As their supply increases, they tend to drive down the price of rice, if the market is in autarky equilibrium. This mitigates (but does not reverse) their gain. The price reduction also helps net buyers of rice, but hurts net sellers of rice who did not adopt the new technology. Discussion Question 4: Read Williamson (2000), which discusses different notions of what is meant by the “Washington consensus.” Create a list of the various policy agenda items that are included as components of the Washington consensus within any school of thought. For each item, consider whether it has more to do with letting currently existing markets (shaped by current transfer costs) operate without direct government intervention (in the form of taxes on or regulation of transactions); reducing government involvement in production and marketing; or undertaking investment to reduce transfer costs and increase the geographic scope and sophistication of markets. Tax reform, interest rate liberalization, trade liberalization, liberalization of FDI flows and deregulation have to do with reducing taxation, subsidization and regulation of market activities. Privatization has to do with removing government from production and marketing activities. Investments in infrastructure and securing property rights are investments intended to improve the functioning of markets by reducing transfer costs. Much attention is given to

Chapter 8

“getting the government out of markets,” but over the years growing attention has been paid to helping markets work better by investing to reduce transfer costs. Problem 1: Using diagrams like those in Figure 8.2, discuss the potential impacts on the local price and local quantities of corn produced, consumed, imported, and exported of each of the following changes: a. An inflow into Small Village of refugees who bring wealth with them but do not have access to farm land General assumption: We assume that the changes are all small enough that the market does not shift from one kind of equilibrium (e.g. importing, exporting or autarky) to another. Assuming that the refugees bring wealth with them but do not have farm land, their entry would increase the demand for corn forthcoming at any price, shifting the demand schedule to the right, but leaving the supply schedule unchanged. In panel a (export equilibrium) this leaves the local price and the local quantity produced unchanged, but increases the quantity consumed and reduces the quantity exported. In panel b (importing equilibrium) this leaves the local price and local quantity produced unchanged, but increases the local quantities consumed and imported. In panel c this causes the local price and the local quantity produced and consumed to rise. b. A reduction in the price of fertilizer A reduction in the price of fertilizer would directly cause the local supply schedule to shift out, as farmers become willing to supply more corn at any price. In panel a, this leaves price and local quantity consumed unchanged while increasing the local quantities produced and exported. In panel b this leaves price and the local quantity consumed unchanged, increases the local quantity produced and reduces imports. In panel c it reduces the local price and increases the local quantity produced and consumed. The reduced price of fertilizer also raises farm incomes, tending to shift the local demand schedule to the right. The rightward shift of the demand schedule is likely to be smaller than the rightward shift of the supply schedule, because only a fraction of any increased income would be spent on a single food item. Thus the qualitative results remain the same as when we considered only the supply shift. c. The construction of better paths connecting outlying Village center

homesteads to the Small

The construction of better paths connecting outlying homesteads to the Small Village center would reduce the transfer costs associated with participation in the market by outlying households within the local market area. Local supply and local demand might both shift to the right as households that were not much participating in the market as buyers or sellers now participate more. It is unclear what the net effects would be. Small changes would lead to changes in local prices only in the case of autarky equilibrium.

Chapter 8

d. The construction of a better road connecting Small Village to Big City. The construction of a better road connecting Small Village to Big City would reduce the transfer costs associated with imports and exports. In panel a, this would raise the LEP, increase the local price, increase the local quantity produced, reduce the local quantity consumed and increase the quantity exported. In panel b this would lower the LIP line, increase the local quantity demanded, reduce the local quantity supplied and increase imports. In panel c this may have no effect at all. Only if the shifts are large enough to shift the market into importing or exporting equilibrium will it make a difference. Problem 2: Elaborate on the discussion of cash and food transfers found in the text. a. Using diagrams like those in Figure 8.5 explain how and why cash and food transfers affect prices and quantities in local food markets that are in autarky equilibrium. In autarky equilibrium: • The cash transfer shifts the local demand schedule to the right and leaves the local supply schedule unchanged. This raises local price and the local quantity produced and consumed. • The food transfer creates a new total supply schedule that lies to the right of the local supply schedule by the quantity of food brought in and distributed locally. (At any price, the same quantity of supply is still forthcoming from local suppliers, plus the additional quantity brought in by the program is also available, fulfilling some of the demand.) The food transfer also raises the incomes of the recipients, however. If food is a normal good, this will increase their demand for food. As we learned in Chapter 6, however, it is likely to increase their demand for and consumption of food by less than the quantity distributed. Thus the size of the horizontal shift to the right of the demand schedule is smaller than the horizontal shift to the right of the supply schedule. Local price declines, local quantity produced declines, but the local quantity consumed rises. b. Using diagrams similar to those in Figure 8.5, but modified to reflect importing equilibrium conditions, explain how and why cash and food transfers affect prices and quantities in local food markets that are in importing equilibrium. In importing equilibrium: • Again, a cash transfer shifts the local demand schedule to the right and leaves the local supply schedule unchanged. The local price and the local quantity supplied do not change. The local quantity demanded and the volume of imports rises. • The food transfer creates a total supply schedule that lies to the right of the local supply schedule by the quantity of food shipped in. The local demand schedule

Chapter 8

shifts to the right by less. The local price and local quantity supplied do not change. The local quantity demanded and imported increase. c. Discuss how the effects of cash and food transfers change as the local supply schedule becomes more inelastic, assuming that the local market is in autarky equilibrium. In autarky equilibrium, if the local supply schedule becomes more inelastic: • The cash transfer causes greater increase in price and smaller increase in local quantity produced and consumed. • The food transfer causes greater reduction in price and smaller reduction in local quantity produced. d. Discuss how the effects of cash and food transfers change as the local supply schedule becomes more inelastic, assuming that the local market is in importing equilibrium. In importing equilibrium, if the local supply schedule becomes more inelastic: • The impacts of the cash and food distributions do not change. e. How would you expect the elasticity of local food supply to differ in the short run and long run? What implications does this have for debates about the relative merits of cash and food distributions? I would expect the elasticity of local food supply to be more elastic in the long run than in the short run, because over a longer run there is time to alter how much land is under cultivation, how many inputs to use, etc. This suggests that if we look only at the short run during an emergency, food distributions might tend to look superior for markets in autarky equilibrium, but that if the government continues to distribute food over a long time period, it may indeed discourage local food production, and food distributions look less attractive relative to cash distributions. Problem 3: Draw a market diagram for a local rice market where buyers and sellers face an external market price that is higher than the local price, but in which high costs of importing and exporting cause the local market to remain in autarky. Suppose a road already exists between the local community and the external market, but costs of importing or exporting remain high because no external traders have set up routine business activities in the local market and no locals have set up routine business dealings in the external market. In the initial diagram, the EP and LIP lines should be above the autarky price (i.e. the price associated with the intersection of the local supply and demand schedules), but the LEP must lie below the autarky price, so that producers have no incentive to export.

Chapter 8

a. Draw what would happen to this diagram in the short run (during which costs of importing and exporting remain unchanged) if the external market price for rice rises, but the local market for rice remains in autarky. The external trade price band (and the LEP in particular) would rise, but the LEP would remain below the autarky price. This induces no change in the local market. b. Explain why this change might stimulate private investment in the development of transport and marketing businesses that could reduce costs of exporting from the local community to the external market. Investments in exporting businesses would bring down transfer costs and allow local farmers to take advantage of higher prices in the external market. When the price in the external market rises, this potential return rises. Thus, investments that were not profitable before might now look profitable. c. Draw into the diagram and discuss what would happen if investments reduce transfer costs enough to make exporting attractive. The investments would reduce transfer costs and raise the LEP above the autarky price, causing the local market to begin exporting. d. In light of your answers to parts a through c, discuss possible differences between short-run and long-run responses of local prices in outlying areas to price changes in central markets. The answers to parts a through c suggest that while in the short run local prices in a market in autarky might not respond to changes in external prices, in the longer run they might begin to respond as investments allow new market connections to develop. Problem 4: Suppose that farmers in Small Village may use their land to cultivate either traditional green beans, for which transfer costs to the external market are moderate, or supermarket carrots, for which transfer costs to the external market are initially very high, and they fully cultivate all available land. The external market price for a kilogram of supermarket carrots is significantly higher than the external market price for a kilogram of traditional green beans. a. Draw two well-labeled diagrams depicting the Small Village markets for green beans and supermarket carrots, with the market for green beans in autarky equilibrium and the local market for carrots in an equilibrium in which local farmers supply no supermarket carrots and local consumers demand no carrots. The horizontal axes measure green beans and supermarket carrots in kilograms. The vertical axes measure the prices in pesos per kg. The external market price is higher in the carrot diagram than in the bean diagram. The LEP, however, is lower in the carrot diagram than in the bean diagram. In the bean diagram, the LIP is above the autarky price and the LEP below, so that the market is in autarky equilibrium. The trickiest part here is to figure out where/how

Chapter 8

to draw in the local supply and demand schedules in the carrot diagram. Because there is no exporting and no sale to the domestic market, we know that the local export price must be below the lowest price local farmers would accept to supply any carrots. Thus the local supply schedule must start at a point on the vertical axis above the local export price. Because there is no importing and no local consumption, we know that the local import price must be above the highest price that consumers would be willing to pay, and thus above the point on the vertical axis at which the demand schedule starts. Finally, because there is no production for local consumption, we know that the highest price consumers are willing to pay (where the demand schedule hits the vertical axis) must be below the lowest price that suppliers would accept (where the supply schedule hits the vertical axis). Hence the local supply schedule in the diagram starts above both the local demand schedule and the LEP line. Price of Green Beans Price of Supermarket Carrots (Pesos per kg.) (Pesos per kg.) . LS

LIP EP EP

LEP LEP

LD Green Beans (Kg)

Supermarket Carrots (Kg)

b. Suppose that joint investments by supermarkets and NGOs reduce the transfer costs associated with exporting supermarket carrots to the external market (while leaving transfer costs on exports of traditional green beans unchanged). Depict in your diagram a reduction in transfer costs large enough to induce farmers in Small Village to begin producing and exporting supermarket carrots. What happens to the price (net of transfer costs) that farmers could expect to bring home from producing and exporting supermarket carrots? The LEP line in the carrot diagram rises to a level that is higher than the price associated with the intercept of the supply schedule on the vertical axis. The net price local farmers could expect to bring home has risen. c. What might happen to the local supply schedule for traditional beans in response to this change in the local market for supermarket carrots? Explain.

Chapter 8

As farmers begin to find carrot production profitable, they may shift some land out of bean production into carrot production. The increase in the price of carrots shifts the bean supply schedule to the left. This would tend to raise the local price of beans in autarky equilibrium. Price of Green Beans Price of Supermarket Carrots (Pesos per kg.) (Pesos per kg.) . LS

LIP EP EP

New LEP

LEP LEP

LD Green Beans (Kg)

Supermarket Carrots (Kg)

Chapter 9

Chapter 9: Labor Markets Discussion Question 1: Suppose a household survey asks all workers to report the pay they received last week. List as many reasons as possible as to why their reports of pay last week might vary across workers. Which of these reasons for reported wage differences provide reason for the higher-reported-wage workers to be better off than the other workers, and which are consistent with higher- and lower-wage workers being equally well off? The discussion of working conditions and employment contracts points to many reasons why workers might report different pay in a given week but still be equally well off as other workers with the same skills: • some accept lower wages in exchange for better working conditions • some receive in-kind payments and report only their cash wages • some receive wages that are steadier over the year – in slack seasons their wages look higher than others’ and in peak seasons they look lower, but they are just as well off • some are paid under incentive schemes that lead them to work harder and they are compensated for the harder work The discussions of mobility barriers and human capital acquisition point to reasons why some workers have better compensation than others: • they live in different locations and there are geographic mobility barriers • they work in different firms and there are mobility barriers even across jobs • they are in higher- and lower-wage sectors within segmented labor markets • they have different skills Discussion Question 2: Suppose two firms produce clothing of identical value according to the same production function. Firm 1 provides workers with good working conditions and pays them $W per day, while Firm 2 provides workers with bad working conditions. Workers find employment in the two firms equally attractive only when Firm 2 pays a compensating differential of $D per worker per day. Firm 1’s provision of nicer working conditions raises its costs by $C per worker per day relative to Firm 2’s costs. Both firms maximize profits by setting the VMPL in clothing production equal to the marginal cost of labor (which includes the wage and any costs of providing good working conditions). a. If labor markets are perfectly competitive, what wage must Firm 2 pay? $(W+D) b. Assuming that the total supply of labor to the two firms is fixed, under what conditions would this labor be allocated across the two firms in the way that maximizes the value of production by the two firms? Maximization of the total value of clothing produced by the two firms requires that the VMPLs in the two firms be equal.

richard@qwconsultancy.com

0|Pa ge

Chapter 9

c. Now suppose that D>C. Compared to the allocation of labor across firms that maximizes the value of clothing production, is too much or too little labor allocated to Firm 1? If the cost of providing good working conditions is $C per worker per day, then the total cost of a day of labor for Firm 1 is $W+$C, and it hires until the VMPL equals this quantity. Firm 2 must pay a wage of $W+$D, and it hires until the VMPL equals this quantity. With D>C, the two firms are setting their VMPLs equal to different values. The VMPLs are, therefore, not equal, and labor is not allocated across the two firms in the way that maximizes the value of production. More specifically, with the VMPL higher in Firm 2, too little labor is employed there and too much in Firm 1. d. If we think of the firms as producers of both clothing and workplace amenities to be enjoyed by their workers, might we nonetheless consider this equilibrium efficient? Efficiency requires that the marginal contribution to the total value of production be the same for all labor uses. The current allocation might be considered efficient (at least conditional on the current capacities of the two firms to generate workplace amenities). For efficiency, what must be equalized across firms is the marginal contribution to the total value of production, including the production of clothing and the production of workplace amenities. The value of the marginal clothing produced by Firm 1 is lower than in Firm 2, but each hour of labor there also produces amenities worth $D. The total value of the marginal product of labor (taking into account both clothing and workplace amenities) is, therefore, the sum of $W (which is the level to which it sets the value of the marginal clothing produced by labor) and $D. This is the same as the $W+$D to which Firm 2 sets its VMPL (which comes only from clothing). Discussion Question 3: Suppose a developing country government is considering new legislation that would mandate the provision of sun screen and eye-shielding hats to agricultural workers who work out of doors. You are asked to write a memo on whether or not this legislation is likely to generate more benefits than costs. What are some of the questions you would wish to research before offering your opinion? The discussion of workplace regulations in the text suggests the following questions: • How well do workers understand the implications of sun exposure for their health and the protective benefits of sunscreen and hats? • Are the relevant labor markets competitive? • Might employers be able to provide sunscreen and hats to workers at lower cost than the cost the workers would pay if they obtained them on their own? • Were the workers already receiving protective gear from employers? If not, were they receiving compensating differentials for sun exposure before the program? If labor markets are competitive and workers understand the implications of sun exposure, then employers not providing gear would have to pay a compensating differential equal to what it costs workers to provide themselves with protective gear or bear the potential risks

Chapter 9

(whichever is lower). If employers are able to provide sunscreen and hats to workers more cheaply than the workers could supply themselves (and markets are competitive and workers understand the implications of sun exposure), then employers might already find it in their profit maximizing interest to supply the protective materials. Providing the materials is cheaper than paying the wage premiums required to compensate workers for having to pay for the gear themselves. If the cost to employers of providing the gear is greater than what the gear is worth to workers (and if markets are competitive and workers understand the implications of sun exposure), then workers would be receiving a compensating differential in jobs without protective gear. If the legislation moves employers to provide gear, competition would drive the wage for workers in those jobs down, leaving workers no better off than in the absence of the regulation. It might even leave them worse off, if employers’ cost of providing the gear is greater than the value to workers, so that the increased cost associated with providing gear is greater than the reduced wage. In this case the marginal cost of labor rises and employers might choose to employ fewer workers. If workers do not understand the implications of sun exposure, then it becomes possible that the legislation could increase the provision of protective gear without driving wages in the affected jobs down, tending to raise the well-being of workers. The legislation would also raise the marginal cost of labor, tending to reduce labor demand. This could reduce the wage for all workers in this market as a second round effect. Discussion Question 4: Suppose the government sets up a workfare program, which stands ready to give program jobs to anyone who comes forward to participate in the program. (The compensation rate is low, because the aim is to attract participation only by the most needy households.) While the main objective of the program is to provide jobs and income to needy households, program designers also hope to beautify roads and other public spaces by employing program participants in collecting trash. Initially the program offers to pay workers a fixed number of pesos for an 8-hour work day. What concerns might you have regarding the use of the fee-for-time contract structure? What alternative contract forms might you put forward for consideration? If the program pays only for participants’ time, either the workers will face low-powered work incentives or program managers must spend resources on supervising participants (to keep them working). Paying participants a piece rate – such as paying them a certain amount per 100 meters of cleaned road – would provide higher-powered work incentives. Rather than having to supervise them every minute, only quick inspection of the road would be necessary. Discussion Question 5: Draw figures like those in the three panels of Figure 9.2, labeling them appropriately so that the first panel represents agricultural demand for low-skill labor, the second represents manufacturing demand for low-skill labor and the third panel describes total national demand. a. Show what happens in this set of diagrams when investment in manufacturing equipment increases the demand for low-skill labor in that sector. Discuss how the

Chapter 9

analysis reflects the assumption of costless mobility of workers between agriculture and manufacturing. The investment raises the demand schedule in the manufacturing sector diagram. It also raises the total demand for labor. Perfect mobility means that if wages started to rise in manufacturing, employers in agriculture would have to raise their wages in tandem to retain workers. In the new equilibrium all workers will be paid the same wage and the total quantity supplied must equal the total quantity demanded. At that equilibrium wage, some workers have moved from agriculture to nonagriculture and some workers have entered the labor force (as indicated by the movement up along total supply schedule). b. How do the impacts of the manufacturing investment change if the supply of lowskill labor becomes more inelastic? How does the change in elasticity affect the distribution of the benefits of labor demand growth across those initially employed and those who are brought into the labor market as a result of growth? If the supply becomes more inelastic, then the wage rises more (implying greater benefits for workers already employed) and fewer workers are drawn into employment. c. How do the impacts of the manufacturing investment change if the manufacturing demand for labor becomes more inelastic? If the demand becomes more inelastic, then the same upward shift would yield a smaller increase in the wage. If the wage remained constant while the demand schedule shifted up, a smaller excess demand for labor would emerge if the demand schedule were more inelastic, and a smaller increase in the wage would suffice to restore equilibrium. d. How do the impacts of the manufacturing investment change if the agricultural demand for labor becomes more inelastic? If the demand for labor in agriculture becomes more inelastic, then again the wage rises by less. Discussion Question 6: Consider a remote rural community where workers face very high costs of migrating out to obtain work elsewhere, and suppose that a single large landowner owns all the land and is the only source of employment. If the costs of commuting and migration are high enough, this employer may have monopsony power, lacking any effective competition for local workers. Such an employer can push wages down below the level that would obtain if the local labor market were competitive. What might prevent the employer from pushing wages down to zero? How might the employer’s use of monopsony power in the local labor market (which allows him to push wages below the competitive level), combined with his power in local politics, affect the community’s potential to grow through road construction or the setup of new local manufacturing enterprises? If the employer pushed the wage down to zero, workers might stop working (perhaps trying to get by cultivating small plots of land they own or can use) or might work but become

Chapter 9

malnourished and unproductive. Under the conditions described in the question, it is in the employer’s profit-maximizing interest to prevent the entry of employers who would compete with him for workers. He might, therefore, use his political power to set up regulations that are unfriendly to new investors. Problem 1: Re-read the discussion of Green Revolution impacts on rural labor markets in Chapter 6. That section presents a puzzle. The Green Revolution seemed to increase rural wages but reduce agricultural employment. This is difficult to explain as the result of a shift only in the agricultural demand for labor. The section argues that to understand these changes we must incorporate the rural non-farm sector into our analysis. Draw figures like those in the three panels of Figure 9.2, labeling them appropriately so that the first panel represents agricultural demand for labor in a particular rural community, the second represents nonagricultural demand for labor in the same community, and the third represents the total demand for and supply of labor in the community. Draw in new agricultural and nonagricultural labor demand schedules (representing shifts of both schedules) that might follow from the introduction of Green Revolution technologies and that lead to a new equilibrium in which local wages have risen and agricultural employment has fallen. Please assume that the Green Revolution technologies are labor using. In what direction must the non-farm labor demand schedule shift for the net result of the two demand schedule shifts to yield the indicated outcome (i.e. higher wages and lower quantity of labor employed in agriculture). What are the impacts of such changes on non-agricultural employment and total employment? What must be true of the Green Revolution technology, and of its impacts on markets for goods produced by the non-farm sector, to generate agricultural and non-agricultural demand shifts like this? Consider first what must happen to the demand schedule in agriculture. We are told that the technical change is labor using, so we must draw the new (dashed) agricultural demand schedule up and to the right of the original. What would happen if this were the only change? The total market demand for labor would also shift up and to the right. The wage would rise. Total employment would expand as some workers are drawn into the labor market by the higher wage. The higher wage would reduce the quantity of labor employed in nonagriculture (in a movement up along the nonagriculture demand schedule). The increased wage also causes some movement up and back along the new agricultural demand schedule, but the net result is to raise employment. (We know that total employment has risen and nonagricultural employment has fallen, so agricultural employment must have risen.) So if the only thing that shifts is the agricultural demand, we would have higher wages and higher agricultural employment. What shift of the nonagricultural demand for labor would help us explain why higher wages were accompanied by lower employment in agriculture? The answer is that the nonagricultural demand for labor must also have shifted up and to the right, and this shift must have been big enough to drive wages so high that along the new agricultural demand for labor the quantity of labor demanded (at that higher wage) is lower than the initial level of agricultural employment. Here’s the logic: There is no shift in the total labor supply schedule. So if the new equilibrium involves higher wages it must also involve higher total employment. The only way higher total employment can be reconciled with lower

Chapter 9

agricultural employment is if non-agricultural employment expanded more than agricultural employment contracted. We illustrate such a set of changes in the graph below. Pesos per day

Pesos per day

D VMPL1

Agricultural Employment

VMPL2

Non-agricultural employment

L1+ L2

Total employment

The analysis thus far suggests that an outward shift in the local nonagricultural demand for labor must have been important. How might the Green Revolution have caused the nonagricultural demand to shift out? Green Revolution developments in agriculture must have increased the demand for nonagricultural goods (maybe inputs, maybe consumer goods), driving up the price of those goods, thereby encouraging an expansion of the rural nonfarm sector. Problem 2: Consider four types of intervention that might be used to reduce the costs imposed on workers by unemployment and the threat of unemployment: a) the creation of a job search assistance program that gathers information about vacancies and job seekers and helps workers and employers find good matches, b) an unemployment insurance program that provides monetary assistance for several months to workers who are fired (funded out of general government revenue), c) a regulation requiring employers who dismiss workers to pay the workers lump sum severance payments, and d) a regulation requiring employers to gain government approval for dismissing workers. Discuss the likely or possible impacts of each intervention on each of the following outcomes: i) the rate at which employed workers are fired, ii) the rate at which employed workers quit, iii) the extent to which firing causes workers and their families to make drastic cuts in consumption, iv) the length of time in unemployment of those who have lost jobs, v) the length of time that first-time job seekers remain unemployed, vi) the typical quality of match between worker and employer, and vii) overall labor productivity. Explain.

Fire rate

Job search assistance (JSA)

Unemployment insurance (UI)

JSA could increase the fire rate if it makes finding new

With UI in place, some employers might find it easier to

Severance payment requirement (SPR) SPRs reduce fire rates by employers who want to avoid

Approval for dismissal requirement (ADR) ADRs make it more time consuming and costly to fire,

Chapter 9

workers easier.

Quit rate

JSA could cause the quit rate to rise if it makes finding new jobs easier.

Consumption JSA could cuts for fired reduce the workers consumption cuts, if it makes unemployment period shorter. Length of JSA could unemployment reduce the spells length of unemployment spells by helping workers find

fire workers who won’t be made destitute. If, however, workers’ better financing for job search leads to better matches between workers and employers, fire rates might decline. It is not obvious that the quit rate would be affected, because quitters don’t get UI benefits.

making severance payments.

and would thus tend to reduce fire rates.

Quit rates might fall, because workers prefer to be fired rather than quit.

UI would prevent workers from having to cut consumption so much.

Severance pay would help fired workers maintain consumption.

Quit rates might rise as employers try to convince workers to quit rather than having to fire them. On the other hand, if ADRs are enforced in only some jobs, workers with those jobs might have additional bargaining power and better compensation, which might make those workers more reluctant to quit. ADRs would not obviously help the workers who do get fired.

UI might encourage longer spells, because it reduces the overall cost to the worker of

On the one hand, severance pay might help workers find new jobs quicker by

It is not obvious that ADRs would affect the length of unemployment spells.

Chapter 9

jobs faster.

searching rather than taking a new job.

relaxing liquidity constraints that hinder job searches. On the other hand, workers may be better able to finance longer job search.

Length of first JSA should job search reduce the time it take for new workers to find jobs.

UI would not help first time job seekers.

Match quality

UI could improve match quality by allowing workers to search longer.

If the severance requirement makes employers more reluctant to hire (reducing the demand for labor), it might be harder for market entrants to find jobs (or it might just reduce the wages for the jobs they find). On the one hand, SPRs would give employers stronger incentive to search longer, to make sure matches are good before committing. On the other hand, average match quality might decline because employers would have a harder time firing once they realize that a

JSA could help workers and employers find better matches by providing them with more and better information.

Like SPRs, ADRs might make employers more reluctant to hire, and this may affect first time job seekers’ job prospects.

ADRs might have similar effects as SPRs.

Chapter 9

worker is a poor match.

Problem 3: Draw figures like the three panels of Figure 9.2, labeling them appropriately so that the first panel represents labor demand by large firms, the second represents labor demand by small firms, and the third represents the total supply and demand for labor by large and small firms combined. a.Depict an initial equilibrium in which the market for low-skill labor is perfectly competitive. Analyze the impact of a minimum wage law that sets a legal minimum above the competitive equilibrium level and enforces it perfectly for all employers, both large and small. (To “analyze” here means to “depict the change in your graphs and discuss the impacts on total employment, on employment in each sector, and on the earnings of any relevant class of worker.”) Imposing the minimum wage Wmin in the diagram below (and really enforcing it for all firms) causes profit-maximizing employers of both sizes to move up and back along their labor demand schedules and reduce employment. Total employment falls. But the higher wage also stimulates a higher quantity supplied (moving up and to the right along the total supply schedule). Thus we get unemployment, in the sense that there are some people who would like to work or would like more hours of work at the going wage, but cannot find that work. The quantity of unemployed labor in this sense is given by the length of the segment U. Workers who retain their jobs are made better off, but some workers lose employment and are worse off.

wmin

b. Again depict an initial perfectly competitive equilibrium. Analyze the impact of a minimum wage law that sets a legal minimum above the competitive equilibrium level, but is enforced only for large employers. The minimum wage is enforced for the large firm sector. The quantity of labor employed in that sector falls until the VMPL in that sector (the height of the demand schedule) is equal to the new, higher wage. At any wage below that level in the rest of the market, the large firms would just continue to employ that same quantity of labor. This implies that, at any wage

Chapter 9

below the minimum wage, the total demand for labor now has the same slope as the demand for labor in the small firm sector (because as the wage falls further nothing happens to the quantity demanded in the large firm sector). The large firms’ reduced interest in hiring thus shifts the total market demand schedule to the left. This reduces the wage in the “uncovered” part of the labor market (i.e. the part for which the minimum wage regulation is not enforced). Looking at where this new lower wage hits the demand for labor schedule in the small firm sector, we see that employment there has increased. Total employment has fallen, because the reduced wage causes a movement down and to the left along the supply schedule.

c. Draw a new set of figures depicting an initial equilibrium in which labor markets are segmented, with large employers paying wages above the competitive market level for “efficiency wage” reasons. (You may assume that the “efficiency wage” does not change throughout this problem.) Discuss the implications of this labor market imperfection for as many labor market outcomes as can be analyzed in these graphs. We can use the same diagram as for part b. The two parts refer to two reasons why the wage may be forced up to a level above the market-clearing wage, but only in the large firm sector. As a result: • the wage is higher than it would have been in the large firm sector • employment is lower in the large firm sector than it would have been • employment is higher in the small firm sector than it would have been • wages are lower in the small firm sector than they would have been • total employment is smaller than it would have been • some workers have exited the labor market, some have moved from large firm sector to small firm sector d. Continuing in the graphs you drew for part c, analyze the impacts of a minimum wage law that sets the legal minimum wage to a level that is higher than the wage associated with perfect competition (the “competitive wage”) but lower than the efficiency wage paid by large firms, and is enforced only for large firms. Would large firms appear to be in compliance with the law? What impact would the law have on labor market outcomes? This is a case in which you might think that the minimum wage is being enforced for large employers, because they are paying more than the minimum wage and are paying more than

Chapter 9

small employers pay. They appear to be in compliance with the law. They would have paid those wages anyway, however, thus the new minimum wage law doesn’t have any impact.

e. Draw a set of figures identical to those you drew for part c. Analyze the impacts of a minimum wage law that sets the legal minimum wage to a level that is higher than the efficiency wage paid by large employers and is enforced only for large employers. This basically just aggravates everything that the original efficiency wage introduced. Employment falls further, while the wage rises higher, in the large firm sector. The wage falls more and employment rises more in the small firm sector. Total employment falls more as more people get discouraged about the low wages. (They might still be hoping for the large firm jobs, but the people with the premium large firm jobs aren’t going to quit and create openings very often!) The interesting point of this exercise is that minimum wage legislation may in fact raise wages for workers who were already earning more than others, while reducing the wages for people who were already earning less.

Problem 4: In this problem we consider an employer who knows that he can get workers to work harder, and produce more “effective labor” per hour of work, if he pays them higher wages. More specifically, letting w be the wage in dollars per hour and e(w) indicate the number of effective units of labor produced per hour of labor, the employer believes that the e(w) function looks like the one illustrated in the diagram below, having positive but diminishing slope. We could describe any ray from the origin in the diagram by an equation

Chapter 9

of the form e=sw, where s is the slope of the ray. This tells us that at any point along a ray, the ratio of w to e, w/e, must be equal to the same number, 1/s. a. What are the “units” of the number w/e? minimize this number?

Why might an employer wish to

The units of w/e are dollars per hour over effective labor per hour or dollars per effective unit of labor. The employer would be minimizing the cost per unit of effective labor by minimizing this. b. To minimize w/e, while respecting the constraint that e=e(w), the employer must find a point along the e(w) schedule at which w/e reaches its lowest value, and thus where s=e/w reaches its highest value. Show how you might find this cost-minimizing level of w in the diagram. The wage associated with this point is this employer’s “efficiency wage.” e e(w)

Efficiency wage w

We want to find the point along the e(w) schedule at which w/e is lowest, and thus at which s (the slope of a ray from the origin) is highest. This will be where a ray from the origin is just tangent to the e(w) schedule. Problem 5: Suppose ln(w)=a +bS+e, where ln(w) is the natural logarithm function, w is a worker’s wage in dollars per hour, S is the years of schooling the worker has completed, and e is a random error capturing the idea that even among workers with the same years of schooling, workers vary in ability and receive diverse wages. a. Show that b = [∂w/∂S]]/w, where ∂w/∂S is the partial derivative of w with respect to S. If ln(w) = a + bS + e, then, taking the derivatives of both sides with respect to S, we get (1/w) [∂w/∂S] = b On the left hand side we have applied the chain rule and used the fact that the derivative of ln(x) is 1/x. Re-arranging, this is what we were asked to show. b. Technically, the derivative ∂w/∂S tells us the rate of change in w per unit of S for “ very small ” changes in S, but we might think of the value of ∂ w/ ∂ S as approximating the amount by which w would increase for every 1 year increase in S. Making use of this approximation, what does the expression you derived in part a tell you about how to interpret values of b? (You may think of the w in the denominator as

Chapter 9

representing the initial level of w.) How should we interpret an estimate of b equal to .09? The expression in part a suggests that we can interpret the coefficient as telling us the ratio of the change in wage (associated with increasing S by one unit) to the initial wage. A value of .09 would mean an increase in the wage of 9 percentage points. c. Given that you spend one year in school to increase S by one, but might reap the resulting increase in w for many years in the labor market, would you think of an estimate of b equal to 0.15 as indicating a large or small effect of S on w? Explain. I would think of .15 as indicating a pretty high return. Even if you have to give up an entire year of earnings at the initial low wage level to gain a year of schooling, you would then get 15 percent higher earnings for many years. That’s like getting a consistent 15 percent return on a financial investment. We’d consider that pretty high.

Chapter 10

Chapter 10: Investment and Financial Markets Discussion Question 1: Suppose farmers may choose to invest in one or the other of two irrigation systems: a low-tech system or a high-tech system. The high-tech system costs more up front and requires more operation and maintenance expenditures, but it generates larger increases in crop yields and lasts longer. What differences across investors and locations might cause some farmers to choose the low-tech irrigation systems while others choose the high-tech systems? Even if all farmers experienced the same up-front costs and expected the same future benefits of the high-tech system, and even if some of them choose the high-tech system, some might choose the low-tech system because they are liquidity constrained. If the high-tech system exposes farmers to more risk, some might also fail to choose it even while others do if they are insurance constrained. An additional reason why some farmers might not choose the high-tech system even while others do, and even when all face the same up-front cost and same true future benefits, is that some farmers might lack information about the high-tech system or have incorrect information about it. Yet other reasons why some might not undertake the investment while others do point to reasons why the up-front costs may be higher for some farmers than others, or why the future private returns may be lower for some than others: • The high-tech system may work well only on certain kinds of terrain; on other terrains it might have lower average yield or more variable yield. • If purchased inputs are required to take advantage of the irrigation, which produces the benefit of greater yields, then where transfer costs are higher, so that input prices are higher and output prices lower, the relative profitability of the high-tech system will be lower. • The relative profitability of the high-tech system may also depend on whether farmers belong to good cooperatives that help them access technical assistance more cheaply or that help them bundle their extra product and get better bulk prices. • Because it takes longer to recoup the up-front costs of the high-tech investment than the low-tech investment, weak property rights in land might reduce the desirability of the high-tech investment more than the low-tech investment. This might lead farmers with weak property rights to choose the low-tech investment while farmers with stronger property rights choose the hi-tech system. • Some farmers may not have the skill the get the full potential returns from the hightech system. Discussion Question 2: Consider a potential investor who maximizes expected utility and consumes C in any state of the world if she does not invest. She faces a potential investment that pays net return R+e in good states of the world and pays R-e in bad states, where R>0 and 0<e<R. Good states occur with probability 0.5.

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Chapter 10

a. Use a diagram like Figure 10.1 to show that if u(F)=F, so that utility in any state is just a linear function of consumption in that state, then she chooses to undertake the investment, no matter what value e takes within its range. If the u(F) line is a straight line, then u(C+R) is the same as the height of the midpoint of a line connecting (C+R-e,u(C+R-e)) and (C+R+e, u(C+R+e)). As long as R is positive, the expected utility associated with undertaking the investment, u(C+R) is greater than the expected utility of not undertaking the investment, u(C). b. Draw a diagram in which u(F) is concave as in Figure 10.1, rather than linear. Draw a case – defined by values of R and e – in which the investor whose utility function you have drawn would choose not to undertake the investment. Using the diagram, explain why the investor chooses not to undertake this investment. The diagram must be drawn with some combination of (1) the u(F) graph sufficiently concave, (2) R sufficiently close to (though above) C, and (3) e sufficiently large that the height of the midpoint of the dashed line connecting the points on the graph indicating u(C+R-e) and u(C+R+e) is lower than the height of the graph at C, as in the figure below. This investor would choose not to undertake this investment, even though it raises consumption on average (from C to C+R), because the loss associated with the lower returns in bad states of the world reduce utility more than the increases in utility associated with the good states of the world. Utils

u(F) u(C) EU

C+R-e

C+R

C+R+e

Discussion Question 3: Use the simple model of private investment decisions exposited in this chapter to brainstorm a list of factors that might help explain why a particular family does not send its child to primary school. This question gets students figuring out for themselves much of what will go into the model of school enrollment decisions in Chapter 19. Discussion Question 4: Draw a diagram describing how the market for loanable funds would work if there were no transaction costs, no intermediaries and no problems of asymmetric information. The horizontal axis should measure the quantity of loanable funds supplied by

Chapter 10

savers and/or the quantity of loanable funds demanded by investors and others. The vertical axis should measure the interest rate charged of borrowers and paid to savers, which is the price of loanable funds. a. Why might the supply schedule be upward sloping? Why might the demand schedule be downward sloping? b. Imagine that all potential investment projects pay out their returns after one year, but that potential investors face projects with differing levels of returns. If the market achieves equilibrium at the intersection of the supply and demand schedules, what can you say about the sets of potential investors that do and do not undertake investment in equilibrium? How are the potential returns on their investment projects likely to differ? c. Imagine that the equilibrium you have drawn pertains to a population in which no one suffers from present bias. How would the diagram differ for a population that is in every way the same, except that some people exhibit present bias? d. Suppose that lenders are prohibited from charging interest rates above a ceiling level rc, which lies below the interest rate associated with the intersection of supply and demand. Use the diagram to explain how this gives rise to credit rationing. What can you say about the investment projects that are and are not undertaken under credit rationing? e. Now suppose that carrying out financial intermediation services cost a fixed rate c per dollar of loanable funds transferred from lender to borrower, and that intermediaries are competitive and always charge borrowers a rate rb that is equal to rs +c , where rs is the interest rate they must pay to savers. How could you illustrate the introduction of such intermediation costs into your simple diagram describing equilibrium in the market for loanable funds? What happens to the quantity of loanable funds exchanged through the market? To the set of investment projects undertaken? See the accompanying PowerPoint presentation for Chapter 10. Discussion Question 5: Many micro-finance organizations offer poor borrowers loans under joint liability arrangements. This means that borrowers must form groups of five, 10 or more members, in which each member bears responsibility not only for repaying his or her own loan, but also for repaying the loan of any group member who defaults. Lending under joint liability is sometimes considered a substitute for requiring collateral. What is the purpose of requiring collateral, and how might lending under joint liability fulfill a similar purpose? How might joint liability lending mitigate the problem of adverse selection? How might it mitigate the problem of moral hazard? Requiring collateral improves the expected profitability of lending for lenders in two ways. First, the lender can claim the collateral if the borrower defaults, guaranteeing at least partial repayment. Second, when borrowers have posted collateral they have more to lose if they default. This may reduce problems of adverse selection by causing some borrowers with high-risk projects not to seek loans. It may reduce problems of moral hazard by causing some borrowers to work harder to avoid default. As with requiring collateral, lending under joint liability can increase profitability for lenders by increasing repayment collection when a

Chapter 10

borrower defaults and might also reduce default by discouraging adverse selection and moral hazard. Under joint liability, each borrower in a group must help fulfill the repayment obligations of other borrowers who default (if they wish to remain in good standing). Like collateral, this provides some repayment of a loan even when the borrower defaults. It may also reduce problems associated with adverse selection of high-risk borrowers into the market, because group members who know they must help repay the loans of their group members may refuse to accept some high-risk borrowers into their groups. It may reduce problems associated with moral hazard if group members who are jointly liable are able to observe each other and pressure each other into working hard. Problem 1: Suppose that you save 10 pesos per month out of your non-interest income, you earn interest on savings of 5 percent per month, and you add all your interest income to your savings. How many months must you “save up” to accumulate 60 pesos? (You may assume that you deposit the 10 pesos plus interest saved during a month at the end of each month.) Holding all else the same, how many months must you save up to accumulate 60 pesos if you earn interest on savings of 10 per month?

Month

1 2 3 4 5 6

Interest rate of 5 percent per month Starting Deposit Deposit Ending Balance out of of Balance Income Interest Earned 0 10 0 10 10 10 0.5 20.5 20.5 10 1.025 31.525 31.525 10 1.57625 48.10125 48.10125 10 2.155063 55.25631 55.25631 10 2.762816 68.01913

Interest rate of 10 percent per month Starting Deposit Deposit Ending Balance out of of Balance Income Interest Earned 0 10 0 10 10 10 1 21 21 10 2.1 33.1 33.1 10 3.31 46.41 46.41 10 4.641 61.051

At a rate of 5 percent per month it takes 6 months to save up at least 60 dollars. At a rate of 10 percent it takes 5 months. Problem 2: The table to the right describes a 10-person economy. Each person in this economy has 1 dollar that he might save or consume. He saves only if he can obtain a return on savings at least as high as the rate indicated in the first column. Each person also has access to an investment project paying the return listed in the second column. He is willing to undertake the investment using his own savings only if the return on his investment is at least as high as the return he requires to make saving attractive. He is willing to undertake the investment using a loan from a financial intermediary only if the investment pays a return greater than or equal to the interest rate he must pay on the loan. He prefers to finance the investment out of his own savings rather than a loan (if available) only if the return he requires to render saving attractive is lower than the interest rate he must pay on a loan. a. Assume first that the costs of carrying out financial transactions are so high that no borrowing or lending takes place. As a result, the only way an individual can earn a return on savings is by investing in his own investment project. Which individuals will invest in this case? What is the average return on these investments undertaken?

Chapter 10

Individual

1 2 3 4 5 6 7 8 9 10

Save if return ≥ (percent) 5 5 5 8 8 8 10 10 20 20

Investment Who return invests, (percent) part a 5 x 8 x 9 x 5 5 5 9 10 x 9 15

Who Who saves, part invests, b part b x x x x x x x x x x x

Only an individual for whom the return to investing in his own project (in the second column above) is greater than or equal to the minimum rate at which he will save (in first column) will save and invest. See third column. The average return on those 4 projects is 8. (We use a simple average, because all projects are of the same size.) b. Now assume that financial intermediation is costless, that all savings are deposited with financial intermediaries and all investments are financed by loans from intermediaries. Because intermediation costs are zero and the market is competitive, the interest rate paid on savings is equal to the interest rate charged on loans. This interest rate adjusts to achieve equilibrium, in which the quantity of savings deposited with intermediaries just equals the quantity of loans extended by the intermediaries to finance investments. Describe the supply of savings deposits by listing possible interest rates and the quantities of deposits forthcoming at each interest rate. (That is, at each relevant interest rate, determine how many individuals would be willing to save.) Describe the demand for loans by listing possible interest rates and the quantities of loans demanded at each interest rate. (That is, at each relevant interest rate, determine how many individuals would be willing to undertake an investment if financed with a loan at that interest rate.) What is the equilibrium interest rate? At this rate which individuals save? Which individuals invest? What is the average return on investments undertaken? The supply of loanable funds schedule indicates the number of people who are willing to save at any interest rate. To be willing to save at an interest rate, their minimum acceptable interest rate must be less than or equal to that number. We get this schedule (which is upwardsloping, at it should be): Interest rate 5 8 10 20

No. savers 3 6 8 10

Chapter 10

The demand for loanable funds schedule indicates the number of investors who would want to borrow and invest at any going interest rate. To be willing to borrow and invest at an interest rate, an individual must have an investment project that pays at least that rate. We get this schedule (which is downward-sloping, as it should be): Interest rate 5 8 9 10 15

No. investors 10 6 5 2 1

The quantity supplied equals the quantity demanded at an interest rate of 8, thus this is the equilibrium interest rate. The fourth and fifth columns above indicate who saves and who invests at that rate. The average return on the investment projects undertaken here is 10. c. Consider a change from having no financial intermediation (part a) to having costless financial intermediation (part b). In what way does Person 1 gain from this change? Person 8? Person 10? What happens to economic growth? Why? Person 1: Previously had to invest in own low-return project, and now can earn more by saving (thereby investing in someone else’s higher return project). Person 8: Previously had to finance investment with own funds, and now can finance investment with lower cost funds. Person 10: Previously didn’t invest, but now, with lower-cost funds, does invest. Economic growth increases both because the volume of investment has increased and the average rate of return on the investments undertaken has increased. Problem 3: Consider an individual who faces two possible states of the world. With 20 percent probability he will face a bad state of the world, in which he must pay out $100 in health care expenses, while in the good state of the world he has no health care expenses. In either state of the world he earns income of $100 and consumes his income less his health care expenses. He is offered an opportunity to pay $20 up front (thereby reducing his consumption by $20 in either state of the world) for a health insurance contract that promises to pay him $100 to cover health care expenses in the bad state of the world. He seeks to maximize expected utility, where the utility he would derive in any state of the world is given by C 0.5, where C is his consumption in that state of the world.

Chapter 10

a. Calculate the expected value of his consumption, first assuming that he does not purchase insurance and then assuming that he does. If he does not purchase insurance, the expected value of his consumption is 0.8*100 + 0.2*0 = 80. If he purchases insurance, the expected value of his consumption is 0.8*80 +0.2*80=80. b. Calculate his expected utility, first assuming that he does not purchase insurance and then assuming that he does. Would he choose to purchase the insurance? If he does not purchase insurance, he consumes 100 in the good state and 0 in the bad state and achieves expected utility of 0.8*(100)0.5 + 0.2*(0)0.5 =8. If he purchases insurance he consumes 80 in either state and achieves expected utility of (80)0.5=8.94. His expected utility is higher if he purchases insurance, so yes, he chooses to purchase the insurance. c. Now suppose that an insurer sells health insurance contracts to 10,000 individuals. Each individual faces a 20 percent chance of experiencing a health shock that requires payment of $100 in health care expenses. Their risks are idiosyncratic. This implies that in any one year approximately 20 percent of them will be hit by health shocks. Each insurance contract requires an up-front payment of $20 and pays out $100 if the buyer experiences a health shock. Approximately how much will it cost the insurer to fulfill its promise of paying out $100 to every insurance contract buyer who experiences a health shock? With 10,000 individuals insured, the insurer can expect 10,000*0.2=2,000 of them to be hit by health shocks. Thus it will cost approximately 2,000*100=$200,000 to fulfill the insurance promises. d. If the cost of administering the insurance arrangement is $1 per contract holder, how large a premium would the insurer have to charge to cover its total costs (including payouts for medical expenses and administrative costs)? Would the contract holders be willing to pay this premium? The per-holder cost of fulfilling the insurance promises is 200,000/10,000=20. So to cover the costs of fulfilling promises and the administrative costs, the insurer would have to charge $21 of each contract holder. Assuming the contract holders are like those described earlier in the problem, the expected utility they associate with a contract that costs 21 and pays out 100 in the event of health shock is (79)0.5 =8.88. This is greater than the expected utility associated with not taking out insurance, which is 8. So yes, the contract holders would be willing to pay this premium. e. If the contract holders were risk neutral, and sought to maximize the expected value of consumption rather than expected utility, would they be willing to pay this premium?

Chapter 10

No. The expected value of consumption was the same (80) with or without insurance when the premium was 20. If the premium rises to 21, the expected value of consumption with insurance will fall below 20 and the individual will not wish to purchase insurance. Problem 4: Consider a person who expects to earn Y in the present (period 0) and 0 in the future (period 1), and who seeks to maximizes utility as given by the function: U(C0,C1)= u(C0) + βu(C1), where u(C) is a single-period utility function, C0 and C1 are quantities consumed in the present and future, and β is a parameter between 0 and 1. a. Suppose initially that u(C)=C (so that the single-period utility function is characterized by constant rather than diminishing marginal utility) and β=1 (so that this person does not discount the future). Would U(Y,0) be greater than, equal to, or less than U(Y/2,Y/2)? Under these conditions U(C0,C1) is just C0+C1. U(Y,0)=Y+0=Y and U(Y/2,Y/2)=Y/2+Y/2=Y, so utility is the same whether the person gets all of Y in the first period or gets half of it each period. b. Now suppose that u(C)=C and β=0.5. Would U(Y,0) be greater than, equal to, or less than U(Y/2,Y/2)? Explain in intuitive terms why your answer here differs from your answer in part a. Now U(C0,C1) is C0+0.5C1. U(Y,0)=Y and U(Y/2,Y/2)=Y/2+0.5*(Y/2)=.75*Y. Now U(Y,0) is greater than U(Y/2,Y/2). Having Y all in the first period is better than spreading Y over two periods, because utility diminishes when consumption is delayed. c. Now suppose that u(C) is the concave function described in the graph below, and β=1. Making use of a ray that that extends from the origin through (and beyond) the point [Y/2,u(Y/2)], identify the quantity U(Y/2,Y/2) in the graph. Would U(Y,0) be greater than, equal to, or less than U(Y/2,Y/2)? Demonstrate this in the graph. Explain in intuitive terms why your answer here differs from your answer in a. U(Y/2,Y/2) = u(Y/2)+u(Y/2) and is two times as high as u(Y/2). In the graph, the ray from the origin that goes through (Y/2,u(Y/2)) reaches this height where C=Y. U(Y,0) = u(Y)+u(0)=u(Y), which is less than U(Y/2,Y/2). In the graph U(Y,0) is the height of the u() function at C=Y. With β=1, there is no loss of utility from delaying consumption, and with u(C) concave, there is a benefit from smoothing consumption. Under these conditions it is better to spread Y over two periods rather than consume it all in the first period.

Chapter 10

Utils U(Y/2,Y/2)

u(C) U(Y,0)

Y/2

d. Continue to assume that u(C) is the concave function described in the graph, and let β=0.35. Would U(Y,0) be greater than, equal to, or less than U(Y/2,Y/2)? Now it appears that U(Y/2,Y/2) is less than U(Y,0). The discounting is sufficiently strong (relative to the degree of concavity of u(C), which indicates the strength of desire for consumption smoothing), that spreading out Y evenly over the two periods is worse than consuming it all in period 1. Utils When β=0.35)

u(C) U(Y,0) U(Y/2,Y/2) This vertical line lies the 0.35(Y/2) to the right of Y/2.

Y/2

Problem 5: A banker knows that when she offers loans at any interest rate below 5, the default rate is zero. For any interest rate I between 5 and 15, the default rate is given by the function D= .2×(I-5)+0.1×(I-5)2 When the interest rate is I and the default rate is D, the banker expects to collect average returns on lending of A=[(1+I/100)(1-D/100)-1] ×100. a. In a table, list integer values of I from 5 to 15. Calculate the default rate D and the average return on lending A associated with each interest rate. At which interest rate in your table is A maximized?

Chapter 10

I used a spreadsheet to calculate the following: I 5 6 7 8 9 10 11 12 13 14 15

D 0 0.3 0.8 1.5 2.4 3.5 4.8 6.3 8 9.9 12

A 5 5.682 6.144 6.38 6.384 6.15 5.672 4.944 3.96 2.714 1.2

When choosing among these integers, A is maximized when I is 9. b. Now suppose that many competitive bankers face this same relationship between interest rates and default rates. Explain why equilibrium in this credit market might be characterized by rationing. This market might be characterized by rationing because the quantity of credit demanded when I=9 may exceed the quantity of loanable funds forthcoming at that interest rate. With such excess demand, borrowers might offer to pay higher interest rates, but the relationship examined in part a indicates that lenders might not find it in their profit-maximizing interest to raise interest rates.

Chapter 11

Chapter 11: International Markets and General Equilibrium Discussion Question 1: Use Figures 11.1a and b to analyze the impacts of (a) a depreciation of the Indonesian exchange rate and (b) the introduction of a tax on shoe exports. (a) A depreciation of the Indonesian exchange rate would cause the external market price expressed in Rupiahs and the LEP to rise. The local price would rise. This would reduce the local quantity demanded and increase the local quantities supplied and exported. (b) The introduction of a tax on shoe exports would cause the LEP to fall (as the transfer costs of exporting rise). The local price would fall. This would tend to increase the local quantity demanded and reduce the local quantities produced and exported. Discussion Question 2: When residents of the United States take a safari vacation in Tanzania, Tanzania is said to “export tourism services” while the United States is said to “import tourism services.” Draw diagrams similar to those in Figure 11.1, modified to describe the Tanzanian safari tourism market and the world market for safari tourism services. Use the diagrams to brainstorm about the kinds of policy changes and programs that might be effective in increasing the volume of Tanzanian tourism service exports. A policy or program would increase the exports of safari tourism services if it raised the LEP or shifted the local supply schedule to the right. The LEP would rise with a reduction in the real exchange rate, a reduction in any tax on the export of safari services or a reduction in the transfer costs associated with selling safari services to foreigners. Bringing the transfer costs down might require investments in transport and communication infrastructure that make it cheaper for people to travel into and out of the country. Any improvements in infrastructure or institutions that reduce the local cost of production would shift supply out and encourage an expansion of safari service exports. This might include improvements in domestic transport infrastructure, reductions in taxes on gasoline (for the jeeps used in providing safari services), education and training programs that increase the supply and reduce the price of tour guides who have necessary skills, and reductions in tariffs on imported jeeps. Discussion Question 3: In the specific factors model, general equilibrium involves equilibrium in five markets. What are these five markets? Draw five market equilibrium diagrams (of the sort developed in Chapter 8) depicting equilibrium in all five markets, assuming that Home exports food and imports textiles. Suppose Home imposed a tariff on imports of textiles. Which of the five markets would be directly affected? Why and how would changes in this market (in response to the new tariff) bring change in the other markets? Why and how would changes in the other markets lead to new rounds of change in the first market? What do we learn from the specific factors model about what the new equilibrium will look like in each of the five markets after all rounds of change have worked themselves out and the system has attained the new general equilibrium? The five markets are the markets for food, textiles, labor, land, and capital. If Home imposes a tariff on imports of textiles, the textile market is directly affected. The tariff would tend to raise the local price of textiles, reduce the local quantity demanded and increase the local richard@qwconsultancy.com

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Chapter 11

quantity supplied of the import-competing good. This change in price could be expected to change the quantities supplied and demanded in other markets while holding the prices in those markets constant at any level, and thus to induce shifts in supply and demand schedules. With the price of textiles rising, the demand for labor would shift to the right, tending to raise the wage. The demand for capital would shift right, tending to increase the return on capital which is supplied perfectly inelastically. The rising wage reduces the quantity supplied of food, tending to reduce the quantity demanded of land (which is inelastically supplied), raising its price. The rising return on capital and the rising wage reduce somewhat the supply of textiles, tending to counteract the initial impact of the tariff. The specific factors model tells us that when all is said and done, production of textiles rises, production of food falls, the real return to land falls, and the real return to capital rises. It also tells us that the effect on the real return to labor is ambiguous. Discussion Question 4: Consider the PPF in Figure 11.2. Under the assumptions of the specific factors model, how would this PPF change as a result of investment that increases the stock of capital (while the stocks of land and labor remain fixed)? As a result of technical progress in the food sector only? Suppose the capital stock increases while world prices for the two goods hold constant. What would happen to the quantities of food and textiles produced and to the ratio of food to textile production? An increase in the stock of capital would cause the endpoint of the PPF on the horizontal axis to move further from the origin, while leaving the other endpoint unchanged. Technical progress in the food sector only would cause the endpoint on the vertical axis to move further from the origin, while leaving the other endpoint unchanged. As the increase in the capital stock causes the endpoint on the horizontal axis to move out, the slope of the PPF at any quantity of textiles will tend to become flatter. If prices remain constant, the point on the PPF at which it is just tangent to an isovalue line with slope given by world prices will tend to move to the right, increasing textile production more than food production. Discussion Question 5: Consider the country depicted in Figure 11.3. Suppose the rest of the world (from which this country imports textiles) experiences technical advance in textile production, and the rest of the world is “large” relative to world markets. How would you depict the results of this change in Figure 11.3, and what would be the implications for the country’s production, consumption, import and export quantities? Technical advance in textile production in the rest of the world would tend to drive down the world price of textiles, improving Home’s terms of trade. This would cause the relative world price line to become flatter. Home would consume on an indifference curve further from the origin. The relative value of their export product would have increased, leaving the country better off in terms of aggregate consumption. The country would produce more food and fewer textiles. It would import more textiles and export more food. Discussion Question 6: Consider a factor proportions model in which the two goods are textiles and chemicals, the two factors are unskilled labor and skilled labor, and chemical

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production is relatively skilled-labor intensive. What impact would an increase in the world price of textiles have on the wage differential between skilled and unskilled labor in the textile exporting country? Explain. An increase in the world price of textiles would tend to increase textile production and reduce chemical production. Because textile production is relatively unskilled-labor intensive, wages for unskilled labor would rise, while wages for skilled labor would fall, so the wage differential would fall. Discussion Question 7: Drawing on the specific factors model, the factor proportions model, and extended versions of these models in which we allow for internal transfer and mobility costs, create as long a list as possible of reasons why a particular poor household might fail to benefit from an increase in the price of the unskilled labor-intensive good. In the specific factors model, if unskilled labor is the mobile factor, the effect on the real wage for unskilled labor of an increase in the price of the unskilled labor-intensive good is ambiguous. If it is a sector-specific factor, unskilled labor would not benefit if it is employed in the sector that is not intensive in unskilled labor. In the simple factor proportions model, unskilled labor would benefits from an increase in the price of the unskilled labor-intensive good, regardless of the sector in which it is employed. Once we introduce transfer costs, unskilled laborers might not benefit if they live in communities that are cut off from goods markets by high transfer costs. When we introduce mobility costs, they might fail to benefit if the unskilled labor-intensive goods are produced in distant regions of the country, and the mobility costs render their local labor markets unintegrated with the distant markets. Problem 1: Draw a pair of diagrams comparable to those in Figure 11.1, but modified to depict the market for bicycles in a bicycle-importing country and the world market for bicycles. Use this diagram to determine what would happen to this country’s local price of bicycles, and to the quantities of bicycles the country produces, consumes and imports, in response to each of the following changes: • An increase in the world demand for bicycles An increase in the world demand for bicycles would shift the demand schedule in the world diagram to the right, tending to raise the world price of bicycles. This translates into an upward shift in the external market price and the LIP in the country market diagram. The local price rises, the local quantity demanded falls, the local quantity supplied rises, and imports fall. •

An appreciation of the country’s currency

An appreciation of the country’s current means that the same world price as denominated in dollars now translates into a lower world price denominated in the local currency. The world price line and the LIP fall. The local price falls, the local quantity demanded rises, the local quantity supplied falls, and the quantity of imports rises. •

An upgrading of the country’s port facilities

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An upgrading of the country’s port facilities would reduce the transfer costs associated with international transactions. This would tend to reduce the LIP. Again the local price would fall, the local quantity demanded would rise, the local quantity supplied would fall, and imports would rise. •

A reduction in local wages

A reduction in local wages, by reducing an important cost of production, would shift the local supply schedule in the national market to the right. As long as the country remains in an importing equilibrium, the local price and the local quantity demanded stay the same. The local quantity supplied rises and imports fall. •

Technological advance in this country’s bicycle-producing firms

Technological advance in this country’s bicycle-producing firms would shift the local supply schedule to the right, with similar effects to those of reducing the local wage. •

The imposition of a tariff on bicycle imports

The imposition of a tariff on bicycle imports would increase the transfer costs associated with importing and would increase the LIP. This would raise the local price, reduce the local quantity demanded, increase the local quantity supplied and reduce imports.

Problem 2: Consider a country endowed with K=100 units of capital, A=100 units of land and L=400 units of labor and that produces two goods, food and textiles. The textile production function is T=K0.5LT.0.5 and the food production function is F=A0.5LF.0.5, where LT indicates the units of labor allocated to the textile sector and LF indicates the units of labor allocated to the food sector. As in the Specific Factors Model, land and capital are fixed while labor is mobile across sectors. a. Derive an equation for this country’s PPF in a graph with units of food on the vertical axis and units of textiles on the horizontal axis. We want to derive an expression that associates each possible quantity of textiles T that might be produced with the maximum quantity of food F that could be produced simultaneously. The textile production function tells us that when T units of textiles are produced, the minimum quantity of labor employed in the textile sector is LT=T2/K. This means that L-T2/K units of labor are available for use in the food sector. The food production function tells us that when L-T2/K units of labor are combined with A units of land, the maximum quantity of food that can be produced is A0.5(L-T2/K)0.5. Plugging in the numbers, this becomes the function: F = (40,000-T2)0.5. b. Derive an equation for the slope of this PPF.

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We find the slope by taking the derivative with respect to T. We get -T/(40,000-T2)0.5. c. When the world prices of textiles and food are both 1 and there are no transfer costs, what quantities of food and textiles would this country produce? To find the quantities of food and textiles produced at these prices, we need to find the value of T for which the slope of the PPF equals -1. Setting the above expression for the slope equal to -1, we find T=100*20.5. Plugging this value into the equation for the PPF, we find that F also equals 100*20.5. d. Under these conditions, what would be the nominal wage? The per-unit return on land? On capital? To find the nominal wage, we must find the value of the marginal product of labor in either industry. The marginal produce of labor in food production (which is also the value of the marginal product of labor, because the price of output is 1) is the derivative of the production function with respect to LF or 0.5(A/LF)0.5. To find the value of the marginal product of labor under the given conditions, we must determine how much labor is employed in the sector, and plug this value and A=100 into the marginal product formula. Under the given conditions, the quantity of labor employed in food production is LF=400-T2/K=400-20,000/100=200. Plugging this into the marginal product function, we get 1/(2*20.5). Similar calculations indicate that the per-unit returns on land and capital are 0.5*20.5. e. If the world price of textiles rose to 2 while the price of food remained 1, what quantities of food and textiles would this country produce? Setting the slope of the PPF equal to -2, we find T==80*50.5 = and F=40*50.5. f. Under these conditions, what would be the values of the wage, and the per-unit returns to land and capital? Now LT=T2/K=160,000/5*100=320 and the value of the marginal product of labor in textiles (and the wage) = 2*5/(320)0.5. The per-unit return to capital is 200.5/5. The per-unit return to land is 200.5/10.

Chapter 12

Chapter 12: Institutions and Cooperation Discussion Question 1: Contrast the way the word institution is used here with the ways it is used in common parlance. In common parlance, the word “institution” often refers to an organization or group of people. Here the term institution refers to the set of rules, norms and related enforcement mechanisms that constrain people’s interactions with each other. Such an institution might be relevant to the interactions of people within an organization. Discussion Question 2: Describe the institutional rules or norms that might constrain peoples’ behavior in the following circumstances. What roles do you think communication, leadership, explicit punishment, repeated interaction and socially conditioned preferences play in catalyzing or sustaining compliance? a. Two people approach each other on a narrow path. How do they avoid collision or conflict? They avoid collision or conflict by each walking on the right (or left) side of the path. It doesn’t cost people anything to walk on the right rather than the left, and everyone has something to gain from avoiding collisions and conflict, so communication could be useful in determining this rule, and explicit or implicit punishments might not be required. b. Two drivers in the United States reach an intersection with four-way stop signs, one from the south and one from the east, and stop at the same time. Who proceeds first? The rules of the road indicate that the person to the right (the one coming from the east) has the right of way. Obeying this rule might cost people a little time when they are on the left. But they will also be on the right sometimes. Repeated interaction may be enough to get them to obey the rule when it is costly. We know, however, that governments often step in to make this a law attached to formal punishments, so perhaps repeated interaction isn’t enough. c. Residents of a remote rural community could try to steal grain from each other’s fields. Why don’t they? Formal community rules overseen by local leaders or informal norms might prohibit stealing, and infractions might result in formal or informal punishments. Repeated interaction may also contribute to enforcement. When they all obey the rules, they all benefit from more secure property rights. d. Residents of a U.S. suburb could try to steal each other’s belongings. Why don’t they? Formal rules protecting property rights are likely to play a larger role here, because people do not know each other as well and don’t expect to interact with particular partners very often. Informal norms probably also contribute, because many people do not steal even when they could get away with it. richard@qwconsultancy.com

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Discussion Question 3: Under what conditions may one individual or group successfully impose institutional rules on another group? What examples of this come to mind? Do you think the rules imposed are likely to create benefit or harm for the group on which they are imposed? One group can impose rules on another group when they have superior potential to use physical force, and thus greater ability to threaten punishment for non-compliance. This is not likely to bode well for those without power who must obey the rules. One example that comes to mind is the conquistadors in South America, who created rules that virtually enslaved the indigenous peoples. Discussion Question 4: Suppose you knew that the utility rewards that punishers derive from punishing “unfair” behavior play an important role in supporting community-level cooperation. Suppose further that you are asked to design an experimental institution-building program that would support community-level cooperation in some activity that is new to the community. Describe your design for this program. First, if possible, I’d try to set the activity up in a way that makes it desirable for people to participate when others participate. (That is, I’d try to set it up so that it is more like an assurance game than a prisoner’s dilemma.) If I could accomplish this, I’d try to get a local leader to coordinate everyone’s expectations around participating. If I cannot avoid a free rider problem, however, then I would try to understand what is considered fair and unfair behavior in the community, and work to create an understanding that it is fair to participate in the new activity and unfair not to participate. I would also work to make it easy to observe who is and is not participating and easy for people to punish those they catch shirking. Discussion Question 5: What general lessons do you take away from the discussion of CPR governance, informal insurance and land rights institutions regarding the importance of local institutions in shaping a policy’s impacts? If local institutions perform similar functions to those of the policy, the policy may just displace the local institutions, possibly with little net impact, and possibly making things worse for groups that are excluded by the formal policy but were included by local institutions. Local institutions might instead perform functions that are complementary to policies (as when strong local land rights institutions render farmers more prone to take advantage of improved infrastructure for transport to market or improved access to new technologies). Problem 1: Consider a small rural area inhabited by just two small farmers, Farmer A and Farmer B. The farmers must each choose whether or not to make investments that would allow them to produce a higher-value crop. If either farmer continues cultivating traditional crops, he earns a profit of 0. To switch to cultivating a higher-value crop, he must incur an investment cost of 10. Having made the investment he will obtain revenue of 20 if an urbanbased food processing company decides to set up a trucking route to collect produce in his area, but earns no revenue if the food processing company does not do this. Both farmers

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know that the food processor will set up local crop collection if and only if both farmers invest in producing the high-value crop. If only one farmer invests or if neither farmer invests, neither farmer will have an opportunity to sell his higher-value product to the processor. If both farmers invest, the processor will certainly collect their produce and pay them 20. a. Fill in the following table of payoffs to describe the game these two farmers are faced with, assuming their payoffs are equal to any revenue they receive from the food processor less any investment costs they undertake.

If Farmer A: Does not invest Invests

If Farmer B: Does not invest Invests 0,0 0,-10 -10,0 10,10

b. Does Farmer A have a dominant strategy? Explain. No. For farmer A to have a dominant strategy, it must be the case that no matter what Farmer B does, Farmer A’s best choice is always the same. Here, if Farmer B does not invest, Farmer A chooses not to invest, but if Farmer B invests, Farmer A invests, too. c. Is this game a prisoners’ dilemma, an assurance game or some other sort of game? Explain. This has the structure of an assurance game. If each expects the other to cooperate, he cooperates. If each expects the other to defect, he defects. d. What does the structure of this game imply about the kinds of activities an NGO might experiment with to encourage a shift to high-value crop production in this area? What is needed here is not a way of preventing free riding (as in the Prisoners’ Dilemma Game), but a way of coordinating expectations. The NGO might try getting the farmers together, helping them communicate. He might also try to get one farmer to serve as a leader, forcefully committing to making the investment. Problem 2: A village’s two villagers hold as common property a local forest from which they harvest nuts. If a villager exercises restraint, he exerts a quantity of labor equivalent to 5 in cost. If he does not exercise restraint, he exerts a quantity of labor equivalent to 10 in cost. If both exercise restraint, they each obtain a harvest worth 15. If neither exercises restraint they each obtain a harvest worth 18. If one exercises restraint and the other does not, the one who exercises restraint obtains revenue of 9, while the one who does not obtains revenue of 22. a. Fill in the following table to describe the payoffs in this game.

If Villager A is: Unrestrained

If Villager B is: Unrestrained Restrained 8,8 12,4

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Restrained

4,12

10,10

b. Suppose an external authority imposes a rule requiring each Villager to exercise restraint. Any villager caught harvesting in an unrestrained fashion must pay a fine F. F must be an integer. At least how high must F be to create the potential for a good equilibrium in which both exercise restraint (but not necessarily guarantee a good equilibrium)? At least how high must F be to make restrained use the dominant strategy for both players? For a good equilibrium to be possible (but not necessarily inevitable), it must be the case that if one villager exercises restraint, it is in the interest of the other to exercise restraint as well. If one exercises restraint, the other compares exercising restraint and earning 10 to not exercising restraint and earing 12-F. For cooperation to be possible, it must be that 10>12-F or F>2. For cooperation to be the dominant strategy, it must also be the case that when the other villager does not exercise restraint, it is still preferable to exercise restraint. This would require that 4>8-F, or F>4. c. Now suppose that the external authority is able to detect unrestrained use with probability of only 0.5. Suppose further that each villager maximizes expected profits. This means that the payoff he obtains when facing a probability p of paying a fine F is equal to R-L-pF, where R is his revenue and L is his labor cost. At least how high must F be to create the potential for a “good” equilibrium in which both exercise restraint? Now the condition rendering it in a villager’s interest to exercise restraint when he expects the other to exercise restraint is 10>12-.5*F or F>4. The punishment has to be twice as big now to render cooperation attractive. Problem 3: Suppose two villagers know that they are going to play the game of Table 12.2 two times (in two years). Consider the grim strategy “I will participate in the first year. In the second year I will participate if both of us participated in the first period, but will shirk if either of us shirked.” a. Is the outcome in which both players choose the grim strategy a possible equilibrium of the game? Why or why not? No, in the second period, the grim strategy would require both players to participate. But they could increase their current well-being by shirking, without incurring any future costs. b. More generally, is any outcome in which either player participates in the first year a possible equilibrium in this game? Why or why not? In the second year there is no motivation to participate, so the players will shirk in the second period. Knowing this, neither player has anything to gain from participating in the first period.

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Problem 4: Suppose that each year two villagers play a two-stage game. In the first stage they play the game of Table 12.2. In the second stage each Villager faces the opportunity to impose a punishment of P on the other, at a cost of c to himself, with P>L/2. a. If each Villager knew that the other player would punish him in the second period if he shirked in the first period and the other player cooperated, what first stage game would they face and what strategy would they choose? Under these circumstances, they would face the game:

If Villager 1: Shirks Participates

If Villager 2: Shirks Participates 0,0 R-P,R−L-c R−L-c, R-P R−L/2,R−L/2

Now if one player expected the other to shirk, he would shirk, too, because R-L-c<0. But if he expected the other to participate, he would participate, too, because R-L/2>R-P. This is an assurance game, so there are two possible equilibria, one in which both shirk and one in which they both participate. b. Now suppose that the Villagers expect to play this two-stage game once a year for an infinite number of years. If one Villager knew that by punishing the other Villager for shirking in the first year he could ensure that the other player would participate in road maintenance in all future years, and knew that by failing to punish shirking in the first year he would lose all opportunity for future cooperation, what benefits and costs would he perceive to punishing the other for shirking? Under what conditions (on the values of the game’s parameters) would he choose to punish in the first year? Let’s assume that the players discount the future, and that they seek to maximize C1+βC2+β2C3+…, where C1, C2, C3, and so on, indicate consumption in periods 1, 2, 3 and so forth. The cost of punishing is just c. The benefit of punishing is β(R-L/2)+β2(R-L/2)+β3(RL/2)+…. = [β/(1-β)](R-L/2). He would choose to punish if [β/(1-β)](R-L/2)>c. c. Suppose the conditions you just described are met. Consider the strategy: “I will participate in the first stage of the first year. In the second stage of the first year I will punish the other Villager if he shirked in the first period. In subsequent years I will participate in the first stage if both of us have always participated in the past, but I will shirk if either of us has shirked in the past, and I will punish in the second period if the other has shirked while I participated.” If one player credibly commits to play this strategy, would the other player have any reason to deviate from the same strategy? Why or why not? If each player knew the other player would play the strategy described in the question, then both would participate in every period and not punish in any period. Neither player could make himself better off by shirking, as long as P>L/2, and neither player would want to punish the other, because punishing is costly and gains nothing.

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Notice, though, that if both played the strategy described in the text, the threat of punishing shirking would not be credible, because punishing is costly and would not bring any benefits; once shirking has happened, there is no hope for future cooperation and thus no reward for punishing a shirker. The threats would be credible under a somewhat revised strategy, in which the part of the text highlighted above is replaced by “if neither of us has shirked and gone unpunished in the past, but I will shirk if either of us has shirked and gone unpunished in the past, and will punish if the other has shirked in that period.” Now punishing makes future cooperation possible, and the threat of punishment would be credible as long as the condition of part b holds. d. Compare the condition you derived in 4.b to the condition in equation 12.5 of the text. Discuss how the availability of the decentralized punishment technology employed here might expand the range of conditions under which cooperation is possible in the infinitely repeated road maintenance prisoners’ dilemma. The condition in 4.b compares [β/(1-β)](R-L/2) to c, while the condition in 12.5 compares it to L/2. If the cost of punishing the other person is smaller than doing one’s part in the collective activity (L/2), then the per-period gains from cooperation, R-L/2, could be smaller but still large enough to render cooperation in the present desirable. Problem 5: Consider a restricted version of an ultimatum game, in which the Proposer is given $10. In the first stage of the game the Proposer may choose to offer either $1 or $5 to the Responder. In the second stage the Responder may choose to accept or reject the Proposer’s offer from the first stage. If he accepts, the Proposer gives the offered amount and keeps the rest of the $10. If the Responder rejects the offer, neither receives anything. a. Describe the second stage of the game by recording payoffs to the Responder in the following table. What is the Responder’s best response to the Proposer’s offer of $5? Of $1? Explain.

If Responder: Rejects Accepts

If the Proposer offered: $1 $5 $0 $0 $1 $5

The responder’s best response to either proposal is to accept it, because something is better than nothing. b. Taking into account the Responder’s best responses in the second stage of the game, describe the first-stage game faced by the Proposer using the following table of payoffs to the Proposer. What strategy does the Proposer choose? Explain.

If Proposer offers: $1

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$5 $5 The proposer chooses to offer $1, because he knows the responder will accept the offer, and leaves the most for the proposer. c. Now suppose that the Responder has access to a punishment technology that would allow him to impose a fine of 6 on the Proposer at a cost of 1 to herself. She now faces three options in the second period: accept, reject and not punish, and reject and punish. Use a table similar to the one found in part a (but allowing for all three Responder choices) to describe the second stage of this game. What is the Responder’s best response to the Proposer’s offer of $5? $1? What does this imply about the first-stage game faced by the Proposer and the solution to the game? Explain.

If Responder: Rejects and doesn’t punish Rejects and punishes Accepts

If the Proposer offered: $1 $5 $0 $0 $-1 $-1 $1 $5

In both cases, the Responder’s best response is to accept the offer. So the game is the same from the Proposer’s perspective, and the Proposer still chooses to offer only $1. d. Now suppose that the Responder continues to have access to the punishment technology, but also has preferences that exhibit negative reciprocity in the following way. If (and only if) the Proposer offers anything other than a fair even split, the Responder enjoys a utility boost from punishing the Proposer that increases his payoff by 3. Use a table similar to the one in part a (but again allow for all three Responder choices) to describe the second stage of this game. What is the Responder’s best response to the Proposer’s offer of $5? Of $1? Taking into account the Responder’s best responses in the second stage, use a table similar to the one found in 5.b to describe the first-stage game faced by the Proposer. What strategy does the Proposer choose? Explain.

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If Responder: Rejects and doesn’t punish Rejects and punishes Accepts

If the Proposer offered: $1 $5 $0 $0 $2 $-1 $1 $5

Now the Responder’s best response to a proposal of $1 is to reject it, while the best response to a proposal of $5 is to accept it. Under these conditions, the game looks like this from the Proposer’s perspective:

If Proposer offers: $1 $5

$0 $5

Now the Proposer chooses to propose $5 and the Responder accepts it.

Chapter 13

Chapter 13: Policy, Governance and Political Economy Discussion Question 1: For each of the rationales for intervention in the text, discuss (a) whether and how we might expect it to inhibit economic growth, and (b) whether and why it may be a problem of particular relevance to the poor. The main point here is that many of the market and institutional failures could constitute barriers to investment, and thus slow growth. Some of the potential failures would be especially important for the poor, including financial constraints (for reasons discussed in Chapter 10) and public goods problems surrounding rural road infrastructure (because the rural communities that remain unconnected by roads to market tend to be quite poor). Discussion Question 2: What are some of the reasons why a government bureaucrat responsible for issuing business registration papers may perform her responsibilities very slowly? What sorts of governance reform might be effective in increasing the speed at which she processes licenses? Describe the logic of how the reforms might increase her speed. What other benefits or costs might follow from such reforms? The point here is to think through how the bureaucrat’s performance might be inhibited by inadequate motivation, resources, capacity or coordinating oversight, and then to consider how the various types of governance reform might succeed in increasing the input that was lacking and how the reform might also reduce other inputs. Discussion Question 3: What are some of the reasons why a primary school teacher may have little impact on his students’ human capital? What sorts of governance reform might be effective in increasing the quality of education he provides? Describe the logic of how the reforms might increase his impact. What other benefits and costs might follow from such reforms? The point here is to think through how the teacher’s performance might be inhibited by inadequate motivation, resources, capacity or coordinating oversight, and then to consider how the various types of governance reform might succeed in increasing the input that was lacking and how the reform might also reduce other inputs. Problem 1: A small NGO sets up a project in a remote community in Cameroon, intending to provide local women with a sustainable source of cash income: the processing and sale of shea butter (which is used in cosmetics and chocolate production). The shea tree grows in this community, and local families consume its fruit, but they have never before dried, ground and processed the nuts inside the fruits to make shea butter. The project provides the women (free of charge) with a single motorized crusher that they may all take turns using to process the nuts, and trains them in processing techniques. The project plans, for the first two years, to send trucks to help the women with transporting their shea butter to a regional capital city, where they may sell it to an exporter. After two years the NGO plans to exit the community, and expects to leave behind a self-sustaining shea processing business.

richard@qwconsultancy.com

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a. What diagnoses as to why local women would not make the shea butter processing investments without intervention seem to underlie this project? (You might want to differentiate the diagnosis of underlying problems – or lack thereof – between the introductory two-year period and the subsequent period.) The project designers seem to assume that the women lack knowledge about how to pursue this investment opportunity. They also seem to assume that even if the women were given assistance in organizing for collective action (i.e. purchasing a shared crusher), and even if they had financing (through a loan), there would still be a need for additional subsidy (in the form of giving them the crusher free of charge). A first possibility is that they believe the future profits are not enough to merit the full cost of the investment, but that transferring the asset would reduce poverty in a sustained way. A second possibility is that they believe the investment would be attractive if financial markets worked well, but that the women are severely liquidity constrained, together with the belief that it is cheaper to give the crushers for free than the provide loans with which to purchase the crushers and administer the loan program. The project designers seem to think that a subsidy even greater than the full value of the crusher is required, because they also subsidize the transport for the first two years. They seem to believe, however, that the returns from export sales will be enough to cover the costs of transport and operating and maintaining the crusher, etc., after the first two years are up. In terms of “rationales for intervention,” their design seems to reflect the belief that these concerns are present: lack of knowledge potential for poverty reduction (hence willingness to subsidize) or financial constraints It also suggests they assume these concerns are not present: need for on-going subsidization (for poverty reduction) difficulties in collective action regarding operation and maintenance of the grinder on-going info problems related to grinder or market b. Describe one or more alternative diagnoses under which this project design would be ineffective in stimulating sustainable new income generation. Their assumption that the export sales will pay for transport and other costs in later years (and thus that no on-going subsidy will be required) may be wrong. The women may not be able to cover costs, and may choose to go out of business rather than lose money. The assumptions that they will not need any expert help with maintenance, and that they will have no problem cooperating, might also be wrong. c. Describe another alternative diagnosis under which this program would succeed in stimulating sustainable income generation but might cost more to the NGO initiating the project than absolutely required to make the investment happen. It may be that after needs for information and assistance with collective action have been met, either no additional assistance is required, or only financial assistance in the form of a loan is

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required (because of liquidity constraints). Maybe the NGO could recoup much of the cost by asking for repayment once the profits start to roll in. Problem 2: A city’s domestic water market is a natural monopoly. The city’s government initially owns and operates the city’s water utility, which supplies the whole market with water services. The utility charges a low base per-gallon fee for the first gallons of water consumed by any household each month, and then charges a higher per-gallon fee for water consumed over the base level. This allows poor households to pay low rates for small quantities, while non-poor households pay higher average rates for larger quantities. The utility is inefficiently run and provides poor service. It also operates at a loss, receiving subsidies to cover its losses out of general government revenue. In a major reform, the government auctions off the right to run the water utility to a private firm. At the same time the government ceases to provide any subsidy to the firm out of general government revenue. a. Which of the “governance structure design choices” discussed in the chapter are altered by this reform? (Base your answer only on what you have been told about the reform.) Decisions regarding day to day operations of the utility have been shifted from government bureaucrats to a private sector firm that must compete to get the concession. Presumably decisions about fees are also shifted to the firm. Subsidization for the provision of services is reduced to zero. The private sector operator must compete for the concession. To win the concessions the firm must bid the most, which means it must expect to experience relatively low costs and still make a profit. Competition and profit-maximization should thus hold the firm accountable for operating efficiently. b. How would you expect each of these changes in a governance structure design choice to alter the motivation, local information, resources, capacity, or coordinating oversight brought to bear on the decision regarding the level of the base fee charged by the utility? Which of these changes in input would tend to raise the level of the base fee and which would tend to lower it? The shift of decision-making authority from bureaucrats to the private sector might increase motivation and capacity for efficient operation. If this lowers costs enough that the initial low fees exceed costs, then it might even encourage a reduction in fees, in the hope of drawing in more low-income consumers. As long as the low fee continues to be too low to cover costs, however, the shift from government to private sector might tend to reduce the motivation of the decision-makers to reduce poverty, tending to increase the fee. The reduction in subsidization would tend to reduce the resources brought to the decision in a way that would tend to increase the fee.

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The shift to profit-maximizing decision-makers would tend to alter motivation in the direction of raising fees.

Chapter 15

Chapter 15: Targeted Transfer Programs Discussion Question 5: In some countries affected by HIV/AIDS, as many as 20 percent of children under 15 years of age are orphans. They may be maternal orphans (who have lost their mother), paternal orphans (who have lost their father) or double orphans (who have lost both parents). Some orphans live with a surviving parent, some live in child-headed households and some are cared for by adults under informal “fostering” arrangements. Foster parents may be grandparents, other relatives or unrelated adults in the children’s communities. Many orphans and other members of the households in which they live are poor, and many orphans are vulnerable to exploitation or ill treatment, having no adults to look out for their interests. While most foster families care as best they can for foster children, some foster children are taken in by foster parents who treat them more like unpaid servants than like children. a. Suppose you are asked to design a targeted transfer program that will help orphans or foster families in some way. What are some possible objectives that might guide your program design? Please state each possible objective specifically, identifying target group and primary dimensions of well-being or behavior the program might aim to improve. Possible objectives include: • To increase the consumption or schooling of orphans • To encourage more families to take in orphans so the orphans can have homes and protection • To make sure foster families treat orphans well • To raise the income of foster families to help defray the cost of taking in orphans • To reduce poverty among orphans or foster families Notice that different objectives would lead to programs with different key design features. b. Suppose you are asked to create a program that pays foster parents of orphans to help defray the costs of fostering and to encourage more fostering. What practical questions would you have to answer when defining eligibility rules and eligibility assessment procedures? The program wishes to make payments to foster parents of orphans. It is important first to define the terms, and then to consider practical ways of operationalizing and enforcing the requirements. We would have to answer such questions as: •

What is a “foster parent”? Must this person be an adult? If so, at what age does one become an adult? Must the person be a household head? If so, what does it mean to be a household head? o What proof must be offered regarding the individual’s age and household status?

richard@qwconsultancy.com

0|Pa ge

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•

What is an orphan? Is the program intended for only double orphans, or also single orphans, or perhaps single orphans whose remaining parent is ill? How old may someone be and still be considered an orphan in need of fostering? o What proof must be offered of the death of one or both of the child’s parents? o What proof must be offered regarding the child’s age? What does it mean to be providing foster care? o What proof must be offered that the child indeed lives with the person claiming to be the foster parent? What proof must be offered that adequate care is being provided within that home?

c. Discuss the potential benefits and costs of a program that provides monthly transfers of a fixed per-orphan amount to any adult household head who provides foster care for one or more child orphans in his/her home. To answer this question, first use the questions in Box 15.3 to brainstorm about the program’s potential direct and indirect impacts. When brainstorming answers to the questions listed under questions 4 and 5 in the box, notice that different groups of households might be affected in different ways. For example, households that were already fostering orphans are affected differently than households that take in foster children in response to the program. Notice also that different groups of households (e.g. those headed by well-intentioned parents and those headed by exploitative parents) enter into policy analysis in different ways. Let’s consider the ideas and questions raised by each of the 7 questions: Question 1 (Objectives): The program design suggests that the program designers’ objectives are to encourage foster parenting and/or to help defray the costs of foster parenting. Question 2 (Design): This question would lead us to raise the sorts of questions indicated in part b. It would also raise questions about how generous we want to make the transfers and how we would distribute the funds. Question 3 (Implementation): This question leads us to question how well we would be able to identify members of the target group and get transfers to them. Question 4 (Directly affected): This question requires us to identify the different groups that might be directly affected by the program (in the sense that they receive benefits) and also the groups in the target population that would be left out. It is useful to recognize that the directly affected groups might include families that were already fostering children and families that start to foster children as the result of the program. It would fail to reach orphans in child headed households, and might also fail to reach foster families for various reasons related to the difficulties of participating. Among the families that participate (whether families that were already fostering or families that are newly fostering), some families are well-intentioned families taking good care of the orphans, while others may be less well-intentioned and more exploitative. Furthermore, among any of these groups, some households may be poor while other are non-poor. All of these distinctions are of interest to policymakers, who are probably especially interested in directing benefits to well-intentioned and poor families and who would not want to encourage exploitative parents to take more children in for the money.

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Question 5 (Direct effects): This question requires us to consider the possible effects of participation on well-being and behavior for diverse members within diverse types of households. For families who were already fostering, the program raises per capita household income, and we’d be interested to know how the households use this to improve the consumption and schooling of orphans, other children and other family members. For families who were not fostering and now are, the program provides a home for an orphan, and we would be interested to know what improvements in protection are associated with this change. The answer probably differs across new foster parents who are exploitative and well intentioned. The families who newly take children in do not experience as much of an increase in per capita income, and may even experience a decline in per capita income, if the transfer is enough to encourage them to take a child in, but not enough to maintain the level of income per person. In general, these questions might get us brainstorming about how to design the program in a way that discourage exploitative families from taking children in for the money, and perhaps also provides discipline that improves the way exploitative foster families treat orphans. We might be wary of offering benefits that are too generous. Question 6 (Spillover and feedback effects): The most likely spillover effects probably have to do with community institutions related to the support of orphans. Many communities have their own informal arrangements for helping families that take in orphans. It is possible that the program will simply crowd out this help. The public program might reach some people the informal programs don’t, but also might fail to reach some families that informal programs do. Question 7 (Budgetary costs): This question gets us asking questions about how many families are likely to participate, how costly it will be to administer the program, and what the total price tag will be. d. Now discuss the potential benefits and costs of replacing the program described in part c by a program that is in every way identical except for the addition of the behavioral conditions that (1) the orphans attend school at least 85 percent of the time and (2) the orphans are receiving adequate care, as evidenced by the results of un-announced home visits by program staff. To answer this question, take the approach described in Section 15.4A. Let’s again walk through the 7 questions, this time asking how the answer to each question might change with the addition of the two behavioral conditions. Question 1 (Objectives) What would be the reason for making this change? The objectives of the design change would probably be to prevent participation by some exploitative parents and also to improve the treatment of orphans in families that would participate under either design. Question 2 (Design) What, exactly, would be involved in operationalizing and enforcing these behavioral conditions? Who would monitor and document school attendance? What assessment would be used to determine whether care is adequate?

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Question 3 (Implementation) Would the agents responsible for monitoring and reporting on school attendance have the information, capacity and motivation to monitor effectively? Would the agents hired to do the home visits have the information, motivation, resources and capacity to do a good job? Under what conditions might they miss poor treatment? Under what conditions might they render a judgment of poor treatment erroneously? Question 4 (Directly affected) What would happen to the numbers and nature of families in each of the groups we identified before? More specifically, might some well-intentioned families who were already fostering before the program and would have participated in the unconditional program decide not to participate, because the home visits are too intrusive? Or might they even be kicked out of the program incorrectly because of erroneous tests? How many of the exploitative parents would drop out? What would happen to the numbers of wellintentioned and exploitative families that take children in? Question 5 (Direct effects) What would happen to the effects of participation on households? In general, the imposition of conditions, if it changes behavior, will also reduce well-being for at least someone within the household. We’d be interested in knowing what the imposition of the restrictions does for the actual schooling and care of the orphans within participating households. We’d also like to know what the restrictions imply for the schooling and consumption of other members of the household, including other children. Question 6 (Spillover and feedback effects) How would the additional rules alter the effect of the program on community institutions? Might it have some kind of demonstration effect that improve the care even of orphans who are not in participating households? If it raises the number of children attending school, would this result in a deterioration in school quality that spills over to other children in the community? Question 7 (Budgetary costs) How much would the enforcement of the behavioral conditions increase the per-beneficiary household administrative cost? How much would the conditions reduce the total volume of benefits distributed by causing some people to drop out of the program? Stepping back, it seems that the main potential benefits of the design change are the reduction in the distribution of benefits to exploitative families, a reduction in the extent to which the program encourages exploitative parents to take children in, and improvements in the schooling and care of orphans in the program more generally. The main costs include the increased administrative cost, the discouragement of well-intentioned families from receiving benefits, a reduction in the number of orphans who are drawn into good families, and any costs borne by other household members (or even the orphans themselves) when compliance (e.g. sending children to school) reduces household disposable income. Discussion Question 6: Suppose a sample survey reveals that 30 percent of the truly poor fail to participate in a cash transfer program. You are hired to prepare a report in which you list potential program changes that might reduce this non-participation rate, discussing the costs

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and benefits of each potential change. Which program design features would you consider changing? What costs and benefits would be associated with each? Potential changes might include alterations in the eligibility requirements that reduce the barriers to participation among the poor, alterations in the procedures for application and distribution of benefits, that make it easier and cheaper for the poor to participate, relaxation of behavioral conditions that may constitute barriers to participation, or complementary efforts to render it easier for families to comply with behavior conditions (e.g. building more schools so that school enrollment conditions don’t prevent as many families from participating). In each case there are costs as well as benefits. The costs might involve increases in leakage (because when you make it easier for the poor to participate, you often also make it easier for the non-poor to participate), increases in administrative costs, reductions in desired behavioral changes associated with behavioral conditions, or increases in costs of complementary efforts. Discussion Question 7: Suppose a sample survey reveals that 50 percent of participants in a cash transfer program are, in fact, not poor. You are hired to prepare a report in which you list potential program changes that would reduce this leakage rate, discussing the costs and benefits of each potential change. Which program design features would you consider changing? What costs and benefits would be associated with each change? I might consider the opposites of the changes listed in the answer to Discussion Question 7, and perhaps also increased efforts to use advertising and moral suasion to make the non-poor less likely to try to participate, even if they are eligible. Again, each possible design change comes with corresponding potential costs as well as potential benefits. Problem 1: You are asked to evaluate two very simple alternative transfer programs that provide transfers of $100 to all eligible households in a particular region. In both programs targeting is based solely on a single categorical restriction. Policy A limits eligibility to households with illiterate household heads. Policy B limits eligibility to households with disabled household heads. The following table describes the population in the program region. Poor Households Total number of 1,000 households Percent of household 80 heads that are illiterate Percent of household 20 heads that are disabled

Non-Poor Households 2,000

All Households

27.3

3,000

a. Assume for this part that program staff are able to identify accurately whether a household head is illiterate or disabled (or both), and that they indeed provide transfers to all eligible households and withhold transfers from all ineligible households. Fill in the following table.

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Percentage of poor households covered by the program Total dollars transferred to poor households Total dollars transferred to non-poor households Total dollars transferred to all households

Policy A

Policy B

80 percent $80,000 $2,000 $82,000

20 percent $20,000 $10,000 $30,000

b. Now abandon the assumption that program staff can identify illiterate and disabled household heads perfectly and think practically about the challenges of implementing categorical restrictions tied to illiteracy and disability in a real world program. First for Policy A and then for Policy B discuss: •

What practical rules and procedures might be involved in testing for eligibility?

For the illiteracy program, program designers would have to set up some kind of literacy test to identify the eligible. When you think about what the eligibility assessment might look like in practice, you immediately realize this is going to be very difficult, since people have an incentive to flunk the test. For the disability program, program designers would have to set up some kind of disability evaluation to identify eligible. When you think about what this might look like in practice, you start to see that it might be difficult to define “disability” and it might be costly to implement an objective assessment, which might involve some kind of clinical assessment. •

For what reasons might the actual coverage of the poor be lower or higher than the coverage rate you calculated in part a?

For both programs, actual coverage may be lower than the estimates of part a as a result of people’s failure to hear of the program (perhaps worse for reaching illiterate heads), daunting procedures to verify eligibility or collect benefits (perhaps worse for disabled heads), poor treatment by program staff, etc. Actual coverage might also be higher than the estimates of part A because some of the nonqualifying poor may successfully represent themselves as eligible (even though they aren’t). (This suggests that slippage in enforcing the categorical restrictions is not always entirely bad.) •

For what reasons might the volume of funds leaked to the non-poor be lower or higher than you calculated in part a?

For both programs, leakage might be less than estimated in part a, because stigma, social considerations and inconvenience may keep the non-poor from applying. Leakage may be higher than in part a, however, because people have an incentive to misrepresent themselves as illiterate or disabled, even if they are not, and it may be difficult to fashion tests that do a good job of weeding out the fakers (esp. for literacy).

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c. For which of the two programs do you expect the practical difficulties of part b to lead to larger increases in leakage rates relative to the (unrealistic) calculations of part a? I would expect the practical difficulties of preventing leakage to be greater with the illiteracy program, because I suspect it is easier for people to pretend to be illiterate than to pretend to be disabled. d. How might the two programs differ in their ability to target funds to the poorest and most vulnerable among the poor? I would guess that the disabled among the poor tend to be poorer on average than those who are illiterate but not disabled. Thus the disability-based program might be a better tool for targeting the poorest. e. How might the two programs differ in the way they modify the incentives of potential program participants? The illiteracy program may stifle incentives to become literate or make use of literacy in public. This is not the kind of incentive one wants to create. The disability-based program seems less likely to induce undesirable choices, because I would guess that people are less likely to disable themselves to receive money than they are to stay out of school in order to get money. While both would tend to discourage work effort, this is less likely to be an issue for the disabled, who are less likely to be working in the first place. f. Write up a succinct, clear paragraph summarizing your analysis of the relative merits of Policies A and B, drawing on everything you learned in parts a through e. That is, write up a summary discussion of the likely benefits and costs of choosing Policy A relative to Policy B (or vice versa). Note: This question is not asking students to decide which policy is better. It is asking them to write an objective discussion of how one policy is better than the other along some dimensions and worse along other dimensions. Here’s an example paragraph.

At first glance, the program that targets transfers to households with illiterate heads (henceforth the “illiteracy program”) appears likely to be more effective at reaching the poor and limiting leakage to the non-poor than the program that targets transfers to households with disabled heads (henceforth the “disability program”), but deeper thought suggests that in practice the disability program may do a better job of limiting leakage and containing program cost, may be more effective in reaching the poorest of the poor, and may produce fewer undesirable incentive effects. If identification of the truly illiterate or disabled could be done cheaply and effectively, then the illiteracy program would reach 80 percent of the poor and leak only about 2 percent of total funds to the non-poor. This appears more attractive than the disability program, which would reach only 20 percent of the poor and leak a third of total funds to the non-poor. The higher coverage of the poor under the illiteracy program would, of course, come with a much larger price tag (roughly $82,000 versus $30,000). Unfortunately, it is difficult to imagine a reliable way of identifying the illiterate, in the face of strong incentives for individuals to represent themselves as illiterate to obtain program benefits.

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Thus the illiteracy program is likely to suffer much higher leakage rates and total program costs than the above numbers suggest. Misrepresentation would be more difficult under the disability program than under the illiteracy program, assuming that the definition of disability is sufficiently serious and objective. In practice, then, the disability program is likely to do a better job of limiting leakage to the non-poor and containing total program cost. While it reaches a smaller share of the poor, it targets a group among the poor who are likely to be especially disadvantaged. It is also somewhat less likely to create perverse incentives, because people are less likely to disable themselves than to avoid school in order to qualify for program benefits. Problem 2: Mexico’s PROCAMPO program was introduced to compensate farmers for crop price reductions associated with the North American Free Trade Agreement (NAFTA), and to support farmers as they transitioned away from producing the affected crops into new economic activities. Farmers were eligible if they cultivated one of nine qualifying crops in the three years just prior to NAFTA. Farmers received payments equal to about $70 per hectare of qualifying land (i.e. land on which qualifying crops had been grown in 1991-1993). The program was implemented by program staff located in government offices in major market towns and was publicized on radio and TV. At the beginning of each planting season eligible farmers could claim payments at program offices, as long as they continued to cultivate any crops (not just the crops affected by NAFTA) on their qualifying land. To put this another way, farmers could not continue to collect benefits if their qualifying land was idle, and no one could collect benefits if the land had been sold or given to new owners. The program was originally designed to make these payments at the initial levels for 10 years, and then to reduce the per-hectare payments down to zero over a five year phase-out period. a. What are PROCAMPO’s eligibility requirements? What are PROCAMPO’s behavioral conditions? Why do you think eligibility is tied to historical cultivation of NAFTA crops rather than to current cultivation of those crops? Farmers are eligible to receive payments under PROCAMPO if they cultivated one of the nine major crops (whose prices fell after NAFTA) at least once during the 1991-1993 period. The behavioral condition that they must comply with to continue to receive payments under the program is that they must continue to cultivate their “qualifying land”, which is the land that they had used during the 1991-1993 period to cultivate one of the nine crops affected by NAFTA. They can cultivate any crop on that land, but cannot leave it idle or sell or give it to someone else. Eligibility is tied to historical cultivation of NAFTA crops rather than current cultivation of those crops, because the program designers did not want to create an incentive for farmers to continue in production activities that had been made less profitable (and less valuable for the economy as a whole) as a result of NAFTA. They wanted farmers to transition into new activities. b. Given what you know about the program’s design, what concerns do you have about potential targeting failures?

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I would worry about failures in the coverage of the poor and leakage to the non-poor. My main concern related to leakage arises out of the observation that payments are made to anyone who cultivated some land in one of the nine eligible crops in the 1991-1993 period, and payments are proportional to the amount of land used for those crops. The non-poor may well cultivate those crops, and probably have larger farms and will receive larger payments. My main concerns regarding noncoverage of the poor are that some of the poor in affected regions may be ineligible because they do not have farms (and may even be disabled and unable to work on farms), or because they have farms but cultivate other crops. Even among the poor who are eligible, some may lose access to the benefits because they cannot comply with the behavioral conditions. For example, they may find their situation so depressed that they decide to leave (or sell) their land and go elsewhere in search of work. Others among the eligible poor may be put off from participation by the procedures for collecting benefits, which require traveling to program centers in major market towns. They also have to document what they produced in 1991-1993 and what they are doing with their land now. This may be difficult for some, especially the subsistence farmers who produce but do not sell, and the illiterate. It is also possible that some, especially among the poor, do not know about the program and will not come to claim benefits, because they do not have radio or TV and live in remote areas. Addition comment: An interesting feature of this program is that farmers had to cultivate one of the nine crops but did not have to sell one of the nine crops, to be eligible. This means that even subsistence farmers could (and did) receive the subsidy. Problem 3: Discuss the potential benefits and costs of replacing a means tested cash transfer program implemented in every one of a country’s communities by a program that first employs geographic targeting to identify program communities and then implements the same means test to assess eligibility within communities. Use the approach described in Section 15.4A to develop a list as comprehensive and specific as possible of the potential benefits and costs. Be sure to identify the groups most likely to experience the various benefits and costs. It is useful to begin by working through the “seven questions to guide policy analysis,” identifying how answers to them would differ across the original and new policies. The answers to Question 1 (Objectives) are probably much the same, and the intention of the reform is largely to retain costs without reducing too much the program’s impact on poverty. Differences in answers to Question 2 highlight that the new program would function in fewer communities, presumably reducing the number of communities in which the program needs to have offices and staff. Question 3 (Implementation) raises questions about how, exactly the geographic selection would be done, and which communities would no longer receive any benefits after the changes. Question 4 (Directly affected) points to the importance of identifying groups among the poor and non-poor who might lose or gain access to the program as a result of the change. In this case, poor households who participated in the original

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program but live in communities that are not included in the new program would lose coverage. At the same time, non-poor households in those same communities would also lose coverage. It is not obvious that targeting outcomes would change within communities that continue to be included in the program, though it is possible that by reducing the number of communities that must be overseen by central staff, the execution of means tests within the remaining communities might improve, potentially reducing leakage and increasing coverage of the poor within those communities. The answers to Question 5 (Direct effects) might not change much, because the level of benefits is the same and the change involves no change in behavioral conditions. It might, however, introduce some incentive for families to move into the program communities in order to obtain benefits. Question 6 (Spillover effects) reminds us that when the direct effects are concentrated in a smaller number of communities (meaning that other communities lose out), the spillover effects are likely to be concentrate there as well. Finally, answers to Question 7 (Budgetary costs) reminds us that the total benefits paid out will fall, as benefits going to non-program communities are eliminated. Total administrative costs would fall, too. They may even fall on a per-beneficiary basis, because in poor communities, where smaller numbers of residents are non-poor, program personnel may find themselves undertaking fewer means tests for households who ultimately fail the test. Summing up, it appears the main benefits are the reductions in leakage to the non-poor living in the less poor communities that no longer participate in the program, the reduction in administrative costs and the reduction in total budgetary cost. The potential costs include the loss of coverage for the poor in communities that are not included in the program, and possible encouragement of migration into communities where incomes are already especially low. Problem 4: Consider two quite different food-based transfer programs that might be used to encourage school attendance. A food-for-education program offers monthly distributions of bulk, uncooked food for households whose children attend school on the days food is distributed. A school feeding program provides a prepared meal to children daily at school. Discuss the potential benefits and costs of shifting from the food-for-education bulk distribution program to the school feeding program, while leaving the total caloric content of the benefits roughly the same per month per household. Question 1 (Objectives) causes us to ask what motivates this reform. Let’s press on to see what answer suggests itself. Question 2 (Design) requires us to think through what all would be involved in making this change. Given what we are told, similar quantities of food would be distributed, but now the food is distributed in much smaller bundles much more frequently, and it is also now cooked before distribution. This seems likely to increase the cost of the program on a per-child basis steeply. It might also place burdens on teachers and school facilities. Question 3 (Implementation) raises the question of how governance problems might change with the reform. It seems likely that central government monitoring of the distribution would be more feasible in the case of monthly distributions than daily distributions, and the daily distribution of cooked meals also requires more skill, thus we might worry that losses to corruption and food spoilage might rise, and we might worry about the quality of the food provided to recipients. Question 4 (Directly affected) raises the question of how the distribution might affect who participates. For a household to participate in the food-for-

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education program, it was necessary only that a child from the household attend school on one day per month. Under the new program the child must attend every day to obtain the full benefit. This increases the time cost of participating, and may cause some to drop out, especially among those who do not value schooling highly and especially among those for which the opportunity cost of the child’s time is high. Question 5 (Direct effects) For households that participate under either version of the program, the change might require them to send the child to school more frequently, and the child would eat the distributed food at school each day, rather than bringing it home. If the household pools income as in the unitary household model, then this might not much affect the way the household allocates the additional resources. Under either program, all household members might consume more as the result o the benefits. Under the school feeding program, the sharing would be implicit, which school children receiving less food at home, and the food freed up in this way being shared with other household members. If household decision making is not so simple, however, the food given to the child at school might “stick” to the child, to a greater extent than did the food sent home in bulk. The aim of the program reform might well be to try to increase the share of the benefit enjoyed by the children within households. It might also aim to move the time at which children eat an important meal into the middle of the school day, with the aim of improving their concentration during school. Question 6 (Spillover and feedback effects) requires us to question how the program’s spillover effects might change. The total value of benefits distributed in a community probably rises, because the total value of food distributed (which is now processed) rises, though it could fall if the more stringent attendance requirement causes many families to drop out. If the value of benefits rises, the stimulus to local economies would rise, too. If the program takes up teacher time and school space, it may also crowd out some education activities, reducing the value of schooling for all who attend those schools. Question 7 (Budgetary cost) lead us to notice that total program costs might rise, because the cost per participating child rises, but might also fall, if the more stringent attendance requirement cases some households to drop out. Summing up, the main potential benefits of shifting from the food-for-education program to the school feeding programs are increases in school attendance and increases in children’s concentration during school (and the long-run benefits they derive from education). Program officials may also consider it a benefit if the change discourages participation by families who send their children to school only a few days per month to obtain the benefits. The main potential costs are the increases in the cost per child for preparing and distributing the food, and any reductions in school quality arising out of the increased pressure on teachers’ time and school space.

Chapter 16

Chapter 16: Workfare Discussion Question 2: Why might some analysts conclude that public employment schemes are unlikely to reach the “poorest of the poor”? Some of the poorest of the poor would have difficulty participating in a workfare program, because they are ill or disabled, or because they are elderly grandparents or single mothers raising young children. Discussion Question 3: Draw a graph with budget constraints similar to those in Figure 16.1a but that depicts a worker who (a) chooses not to work in the absence of the program, (b) chooses to participate when the workfare program is introduced, but (c) is not made much better off by the program (despite earning the full program wage). C

M+wp(T-H)

M+wa1(T-H)

Discussion Question 4: Discuss the possible channels through which workfare program participation might affect children’s school attendance, even when the program does not allow children under 18 years of age to participate and this restriction is well enforced. If the workfare program attracts participation by a child’s mother or older sibling, the household may choose to take the child out of school to care for younger siblings or perform household chores that the workfare participant can no longer perform. Discussion Question 5: Drawing on the discussion of workfare program impacts on labor markets, discuss the conditions under which major employers in a small rural community would be most likely to oppose the creation of a workfare project in or near their community. When local labor markets are in autarky, and when they are in equilibrium with supply equal to demand, the introduction of a workfare program would increase local wages for low-skill labor by increasing the demand for this labor. Local employers might oppose the workfare program because it would drive up their costs of production. richard@qwconsultancy.com

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Chapter 16

Discussion Question 7: Discuss the potential benefits and costs of replacing a means-tested cash transfer program by a workfare program. Careful thought about the seven questions reveals that the main potential benefit of replacing a means-tested cash transfer program by a workfare program are the reduction in administrative costs if the workfare program is self-targeting and therefore requires no assessment of eligibility requirements, a possible reduction in leakage to well-off people who managed to obtain cash transfer benefits but would not wish to participate in a workfare program, and possibly the creation of infrastructure by workfare participants. The potential costs include an increase in leakage to members of non-poor families who are allowed to participate in the workfare program, the loss of coverage for the incapacitated poor who would participate in the cash transfer program but are physically incapable of participating in a workfare program, a reduction in the program’s impact on participant’s well-being associated with their need to fulfill the work requirements, and the addition of costs for non-labor inputs for workfare construction projects. Discussion Question 8: Discuss the possible rationale for combining a large workfare program with a small, explicitly-targeted cash transfer program when designing a strategy for poverty reduction in some regions. What approach to targeting of the cash transfers would render the cash transfer program most complementary to the workfare program? Because workfare programs may not deliver benefits to some very poor and vulnerable households, in which there are no adults capable of performing workfare work, it may be useful to pair workfare programs with cash transfer programs targeted at the incapacitated poor. Problem 1: Consider a workfare program that employs no means testing or categorical restrictions. That is, it is a program that provides jobs to any workers who come forward to accept program jobs at the program wage. a. List some details of program design that could be modified to reduce leakage to the non-poor. b. State the direction in which those design details should be modified to reduce leakage, and explain how such a change might reduce leakage. c. Discuss the potential costs associated with modifying the program in the indicated directions. To reduce leakages as a percent of total cost program designers could: • Reduce the wage. But this would bring costs of: (1) a smaller income boost to those who participate and (2) perhaps less participation of the truly poor facing the highest fixed costs of participation (because, e.g., they are further from the program). It might also (3) reduce the extent to which the program achieves notions of fairness, standard setting, etc. (Notice how “question 4” gets us to recognize how the change might cause some poor to drop out, “question 5” gets us to recognize that the well-being impact on those who

Chapter 16

participate would fall, and “question 6” might get us to think about impacts on norms of fair pay, etc.) Choose a less desirable or more strenuous kind of work. But this might bring costs of (1) discouraging some of the poor from participating. And (2) the less desirable work may have adverse health consequences for participants. Choose project locations where populations are more uniformly poor, so that a smaller share of the population with access to the program is non-poor. But (1) you would eliminate the potential to help the poor who live in communities with more non-poor people. You may also (2) reduce the value of the projects undertaken and/or increase the cost of carrying the projects out (if the more uniformly poor places are more remote locations or are places where infrastructure investments are less valuable for other reasons). Switching from cash to food payments (more specifically, for the purposes of thinking carefully about costs, replacing the cash payment by a quantity of food for which the cost at initial local market prices is the same as the value of the cash transfer). If the food is not much consumed locally, so that households do not want to consume more than the quantity distributed (and would prefer to consume less at the same total income), then the switch might reduce the interest of the non-poor in the program. But it (1) may also reduce the interest of the poor in the program, and (2) will reduce the value to beneficiaries of participation in the program. It may (3) lead to depressing effects on the local economy, and may (4) increase the cost per unit of the additional food participants ultimately receive (if the cost to the NGO/government of transporting and distributing is higher than the cost to the private sector of these activities).

•

Problem 2: The following table describes some features of income distribution and workfare program participation in Village X. The program provides employment to anyone who wishes it at the program wage. “Quintile 1” refers to the poorest 20 percent of the population. In this village there are 1,000 households. Thus “Quintile 1” refers to the poorest 200 households, “Quintile 2” refers to the 200 households with the next lowest incomes, and so forth. The poverty line is such that only households in Quintile 1 are considered poor. Total income for each household is the sum of program income (the wages received for work in the program) and non-program income (income from any other source, including labor income and receipt of private transfers).

Quintiles based on non-program inome

1 2 3

Average nonprogram income per household

100 200 300

Average total income (including both program and non-program income) 200 210 302

Percent of households participating in the program 70 10 2

Chapter 16

4 5

500 1000

0 0

a. Do leakages to the non-poor appear to be large or small relative to total transfers to the poor? Explain. 200*100=20,000 goes to poor, while 200*10 + 200*2=2400 goes to non-poor. Leakages are a fairly small share of total program transfers. b. What do you learn about noncoverage of the poor from this table? What more might you guess about the groups among the poor that are excluded from benefits? We know that 30 percent of the poor do not participate. They are likely to be especially poor households, who do not have able-bodied workers or who live in more remote locations. c. Explain how the numbers in the table can be used to derive the conclusion that among poor program participants, total income (including program income) is more than double their non-program incomes. Average income received from the program (averaged over all the poor households, whether they participate or not) is 100. That overall average can be thought of as the weighted average of two sub-group averages: the average among those who participated and those who did not. We know that average program income among those who did not participate is zero. The only way the overall average can be 100, when the sub-group average for non-participants is zero, is for the average program income among participants to be more than 100. [This question emphasizes the importance of making sure you understand what groups are included or excluded in the calculations of “averages.”] d. Do the figures in the table justify the conclusion that the program impact on the income of participating poor households is to more than double it? Why or why not? Part c explained the justification for the descriptive statement that “total income is more than double non-program income.” This part examines the cause-effect statement that “the program has doubled total income,” which is not justified by the figures in the table. Program income is more than half of total income in the presence of the program, but the program may nonetheless have had very little impact on total income, if the program income crowded out a great deal of other labor income or private transfers. It is important to recognize here that the data are “after-the-fact” – that is, they were collected after the program was already in place. Any reactions to the program have already taken place. They do not tell us the counterfactual, of what income from other sources would have looked like in the absence of the program. Problem 3: Draw three graphs in which the horizontal axis measures home time H and the vertical axis measures consumption expenditure C, as in Figure 16.1a. a. In the first graph draw in and label the alternative activity budget constraint and the workfare program budget constraint for a situation in which the market wage for low-

Chapter 16

skill labor is greater than the program wage, but the individual in question is unemployed, unable to find any private sector work at the market wage. You may treat this as a situation in which the individual effectively faces a wage of zero; for each additional day she attempts to work, she reduced home time by one day and increases consumption expenditure by zero. b. In the second graph, draw in and label the alternative activity budget constraint and the workfare program budget constraint for a situation in which the market wage for low-skill labor is greater than the program wage, and in which the individual in question is under-employed, in the sense that she can find only a small, fixed number of days of work per month at the market wage. (After exhausting those days, any additional days of work she might devote to alternative activities would generate no increases in labor earnings.) Draw in indifference curves to demonstrate that a worker might choose to participate in the workfare program under these conditions. c. In the third graph, first replicate what you have drawn for part b. Now add in a third budget constraint that depicts the possibility of first working the limited number of hours at the market wage and then allocating additional work hours to the workfare program.

(a)

(b)

Program b.c.

Alternative activity b.c.

Budget constraint associated with first exhausting hours at higher non-program wage and then working at the program wage.

(c)

Problem 4: Draw a diagram depicting the local market for low-skill labor in competitive equilibrium. Describe (in the graph and in words) the impact on the market wage of introducing a workfare program that offers a wage higher than the initial equilibrium wage and that truly guarantees employment for anyone who wishes it at the program wage. You may assume that there are no fixed costs of participation and that work in the program and work in alternative activities are equally attractive. What happens to the competitive wage paid by private sector employers?

Chapter 16 Wage Program employment

Program wage = Market wage

LD Low-skill Labor

If the program truly guarantees employment at the higher program wage, then employers must match that wage if they wish to attract any workers. All workers in the market will receive that higher wage, whether in the program or from private employers. We identify the quantity of workers demanded and employed by the private sector by identifying where the line at the height of the program wage crosses the local supply schedule. We identify the total quantity of labor supplied at that wage where the program wage line crosses the labor supply schedule. The difference is the quantity of labor the program must employ to truly guarantee employment at that wage. Problem 5: By some estimates, over 3,000 farmers in the Indian state of Karnataka committed suicide between 2000 and 2006. (Though large enough to be troubling, 3,000 is a small number relative to the total number of farmers in the state.) In many cases the farmers had been hit by shocks—such as poor rainfall, irrigation system failures or pest attacks— which rendered it difficult for them to feed their families and repay debts. The state government implemented a cash transfer program which can be thought of as a suicide compensation program, in which the families of farmers who commit suicide are compensated for the loss of their main breadwinner with a sum of money equivalent to about U.S. $2,000 (a very large sum of money relative to local incomes and debt burdens). Consider replacing this suicide compensation program by a workfare program that truly guarantees employment and that puts participants to work building infrastructure. The program would pay a daily wage below the wage typically paid to low-skill manual labor in this region, and below the typical daily returns to farmers cultivating farms that have not been hit by shocks, but high enough to provide workers and their families with at least enough food to subsist. List the main potential benefits and costs associated with replacing the suicide compensation program by the workfare program, and provide a brief explanation as to why each benefit or cost might emerge. It is useful to work through the seven questions side by side for the two programs, and then to re-organize the differences in impact discovered through that process in a way something like what follows here. Potential benefits of the shift from the suicide compensation program to the workfare program:

Chapter 16

• • • • •

Workfare directs benefits to a much larger group of poor households (including all distressed farmers, not just those in which someone has committed suicide, plus some landless households) than did the suicide compensation program. Workfare has the potential to prevent suicide rather than encourage it, thus the change might reduce suicides. If participants in the workfare program build valuable infrastructure, replacing the suicide comp by the workfare program will also produce the benefits associated with those assets. Workfare provides insurance even to those who do not participate (unlike suicide prevention). If the program truly guarantees employment, then it raises the wage for everyone in the region, not just the workers in the program, causing an even greater expansion in the coverage of the poor (relative to the suicide compensation program)

Potential costs of the shift from suicide compensation to workfare: • Families of those who still commit suicide (which we hope is a smaller number) will no longer get compensation, and probably won’t even get any money, because they won’t have able-bodied workers. • The total cost of benefits distributed (and the total program cost) is likely to be much larger, because the population taking advantage of the workfare program is probably much larger than the population taking advantage of the suicide compensation program (though the benefit amount per recipient in the first year, say, has gone down, tending to reduce total cost of benefits). The workfare program also provides on-going rather than one-time benefits. Dimensions of program performance that might improve or deteriorate (and thus might be design change benefits or costs): • Total costs per dollar of cash distributed to the poor may rise or fall. On the one hand, such costs may go down, because the workfare program sounds like it should be selftargeting while the suicide compensation program required assessment of eligibility. On the other hand, however, the workfare program might include substantial costs for non-labor inputs to the construction of infrastructure. • The magnitude of help received by any one beneficiary household. In the short run the benefit per family is probably smaller under the workfare program, because workfare benefits are low relative to the size of the suicide compensation transfer. Over the longer run, however, a household might benefit more from the workfare program, because the suicide compensation is one time, while the workfare is on-going.

Chapter 17

Chapter 17: Agricultural Market Interventions and Reforms Discussion Question 1: Draw two figures similar to Figure 17.1, except that in one of the figures the local supply of the export crop is highly inelastic and in the other the supply is highly elastic. Draw the LEP and LEP* lines at the same height, so that in both figures you examine the impact of imposing an export tax of the same size. a. In which case is the new tax more effective at raising tax revenue? b. Demonstrate in each figure what happens to tax revenue collection when the tax rate increases (by the same amount in each figure)? Discuss the conditions under which an increase in the export tax rate might reduce tax revenue. For graphs, see the accompanying PowerPoint presentation for chapter 17. Discussion Question 2: Draw a market diagram describing a national crop market in importing equilibrium. How would you illustrate the imposition of an import tariff in this diagram? What does the diagram have to say about the potential impacts of imposing an import tariff? Here is a diagram illustrating a market in importing equilibrium. Price of import (Dollars per ton) LS

LIP LEP

Imported good (Tons)

Initial imports

The imposition of a tariff increases the transfer costs associated with importing and raises the LIP. Here is the market after the imposition of the import tariff.

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Chapter 17 Price of import (Dollars per ton) LS

Imports after tariff is introduced T LIP LEP

Import good (Tons)

Initial imports

The imposition of the tariff raises the local price, reduces the local quantity demanded, increases the local quantity supplied, reduces imports, raises revenue for the government, reduces the real income of local net buyers and increases the real income of local net sellers. Discussion Question 3: Use Figure 17.2 to describe and explain what happens when a government imposes a quantitative restriction on a crop’s export. If the market price remained at the pre-restriction level, the market would be in disequilibrium. Which kinds of actors would find it impossible to achieve the purchases or sales they wish to make at the going price? How might their reaction to this situation help move the market toward the new equilibrium? If the market price remained at the initial price (which is the LEP), some local producers who wished to sell at the going price would be unable to, because the quantity they can sell in the international market is limited by policy, while the quantity they can sell locally is limited by what demanders are willing to demand at the current price. Some producers who are unable to sell at that price would offer to local consumers to sell to them for less, seeking to bid their business away from their current suppliers. This process would continue until supply equals demand and the market re-achieves equilibrium at the lower price DP indicated in the diagram. Discussion Question 4: Use a graph like Figure 17.3 to describe an export crop market in which a marketing board taxes farmers and subsidizes local consumers. a) How would you illustrate the effects of a policy reform that raises the price paid to farmers while holding the price charged of domestic consumers unchanged? What would happen to domestic sales, domestic purchases, exports and total export tax revenue? A policy that raises the price paid to farmers while holding the price charged of domestic consumers constant would raise the producer price line while holding the consumer price line in the initial position. The local quantity supplied, and exports would rise, while the local quantity demanded would remain the same. The implicit tax revenue collected by the marketing board might rise or fall, depending on how inelastic or elastic the supply schedule is.

Chapter 17

Discussion Question 5: Use a pair of graphs like those in Figure 17.5 to describe the impact of a marketing board that engages in pan-territorial pricing. Suppose that Near Village is very close to the central market and that the transfer costs of exporting produce from Near Village to the country’s central market is zero. Suppose further than the transfer cost of shipping produce from Far Village to the central market (or Near Village) is equal to the vertical distance between the LEP1 and LEP2 lines. a. At what level of administered pan-territorial price would the marketing board neither collect tax revenue from Near Village nor distribute subsidy to Near Village? LEP1 b. Illustrate the impacts in both villages of a policy change that sets the pan-territorial administered producer price to the level you just identified. This would introduce a producer price line at the height of LEP1 in Far Village, raising the local price and local quantities supplied more, and reducing local quantity demanded more, than the policy illustrated in Figure 17.5. c. Assume that, in addition to making the policy change of part b, policymakers wish to eliminate subsidies for farmers in Far Village. What per-unit fee could they charge Far Village farmers that would just compensate for the subsidy implicit in the high pan-territorial price? How would this fee compare to the cost of transporting goods from Far Village to the central market? They could charge LEP1-LEP2, which is just equal to the cost of transporting goods from Far Village to the central market. d. Suppose policy makers always set administered prices in Near Village and Far Village to the local export price relevant to those villages. (This means that when the local export price in a village rises, the administered price also rises.) Illustrate the effect of an institutional change that reduces transfer costs (both the costs of exporting from the central market to world markets and the cost of exporting from Far Village to the central market). A reduction in the transfer cost associated with international exports would raise the LEP1 and LEP2 lines by the same amount. The reduction in the costs of domestic transport would raise the LEP2 line further. The expectation that the privatization of marketing activities would reduce transfer costs in this way is what fueled hopes that liberalizing reforms would leave remote farmers better off, even if they had been subsidized by the marketing boards. Discussion Question 6: Read Alderman and Lindert (1998). What does it mean for a general consumer food subsidy to be self-targeting? What empirical evidence suggests that when choosing the foods to use as vehicles for general consumer subsides, policymakers may have

Chapter 17

to trade off greater effectiveness at directing a large fraction of subsidies to the poor against reduced absolute improvements in well-being for the poor? A general consumer food subsidy is self-targeting when demand for the food involved declines relatively steeply (compared to other foods that could have been subsidized) as household income level rises. For such a food the share of total subsidy (i.e. per-unit subsidy multiplied by the quantity purchased at that price) going to non-poor households is relatively low. In the cases the authors study, the foods for which demands decline most strongly with household income level are also foods that constitute only low shares of consumption expenditure, even among poor households. This means that even large general subsidies on these items would raise poor households’ real income levels only a little. Discussion Question 7: Suppose you are asked to make predictions regarding the distribution of the direct real income effects associated with an increase in the price of rice in a particular rural region. a. What information would you like to collect and why? Think first about how you might break down the entire population of interest into groups that might be affected by the price increase in different ways and to different degrees. Then indicate what you would like to know about each group, as well as about the policy and the nature of the region’s economy. At the very least, we’d like data on net purchases and sales of rice as percentages of total household consumption expenditure for households at different levels of per capita income or consumption expenditure. This would allow us to estimate the real income impacts of the rice price increase for groups at different income levels. We might further like to differentiate households earning income entirely from low-skill labor, farm households that are poor, larger farm households that are not poor, households running non-farm businesses, and households earning income from higher-skill wage labor. If the region is large and some areas are more remote from markets than others, I would want to measure how large the price increases are in different places, and take that into account in my estimates. b. Describe some conditions under which a large fraction of the direct benefits accrue to the households with the highest incomes, but a large fraction of the ultimate benefits (including both direct and indirect benefits) accrue to low-income households. Large fractions of the direct benefits could accrue to high-income households running large farms on which they employ wage labor. Large fractions of indirect and total benefits could nonetheless accrue to low-income low-skill labor households who do not own land, if the price increase significantly increases the demand for labor by the directly affected large farmers. Discussion Question 9: Through what logical channels, and under what conditions, might an increase in the world price of coffee lead to an increase in school enrollment rates among girls in a rural area of a developing country?

Chapter 17

An increase in the world price of coffee would raise the local price of coffee, unless the local market was insulated from world price fluctuations by a marketing board. The increase in the local price of coffee might raise incomes for net coffee selling farm households, and this increase in income might lead to increased expenditure on school fees for girls, because it relaxes liquidity constraints. Problem 1: This question examines the effects of a quantitative restriction on fertilizer imports. a. Draw a diagram illustrating a fertilizer market in initial importing equilibrium. Introduce into the graph any additional features necessary for examining the effects of a quantitative import restriction. What are the effects of this restriction on price, purchases, sales, imports and import tax revenue? When the government restricts imports to the total quantity Q, consumers no longer face an infinite supply of goods at the LIP. Instead, it is now as if they face an upward-sloping supply schedule, which lies to the right of the local supply schedule by the quantity Q. The restriction in supply to the local markets leads to price increases, which continue until the quantity equals the new total quantity supplied at the price DP. Fertilizer price (dollars per ton) LS

Q LIP LEP

Tons of Fertilizer

Initial imports

b. Now draw a graph like Figure 17.1 to describe an export crop market in equilibrium after the introduction of an export tax. Use the graph to describe and explain the impact on this market of the imposition of a quantitative restriction on imports of the fertilizer that is used in export crop production. Suppose the export crop is rice. Here is a graph of the rice market after the imposition of an export tax, assuming that the LEP already reflects the subtraction of the per-unit export tax. When the quantitative restriction raises the price of fertilizer, this increase in an input price shifts the local supply schedule for rice to the left. The local price and local quantity demanded stay constant, while the local quantity supplied and exports fall. Export tax receipts fall.

Chapter 17 LS’

Rice price (dollars per ton)

LIP

LEP

LD Tons of Rice

Initial exports

c. Now draw a graph like Figure 17.2 to describe an export crop market in equilibrium after the introduction of a quantitative export restriction. Use the graph to describe and explain the impact on this market of the imposition of the quantitative restriction on imports of the fertilizer that is used in export crop production. In the presence of the export restriction, it is as if the total demand in the local market is equal to the quantity demanded locally plus the fixed quantity of exports. Thus it is as if the total demand in this market lies Q to the right of the local demand schedule. The local price is DP. When the import restriction shifts the supply schedule to the left, the local price rises. Rice price (dollars per ton)

LIP

Q LEP DP

TD LD Tons of Rice

Problem 2: Here are some statistics for two countries. In which country does an export tax on rice seem likely to be the most progressive, in the sense that on average it taxes higherincome groups at a higher rate (or subsidizes them at a lower rate) than lower-income groups. Explain, making explicit reference to the information provided in the table.

Number of people Average expenditure on rice

Country 1 Poor 100,000

Non-poor

Country 2 Poor

Non-poor

200,000

100,000

200,000

Chapter 17

as share of average total 60 % consumption expenditure Average value of production of rice as a share of average 70 % total consumption expenditure

20 %

50 %

40 %

10 %

40 %

50 %

An export tax on rice reduces the price of rice. This will raise the real income of net rice buyers and reduce the real income of net rice sellers. In Country 1, the poor are (on average) net rice sellers, while the non-poor are net rice buyers; so in Country 1 the rice price reduction hurts the poor and helps the non-poor. In Country 2, the poor are net buyers while the nonpoor are net sellers; so in Country 2 the poor benefit from the price reduction while the nonpoor lose real income. The export tax is, therefore, more progressive in Country 2. Problem 3: Consider a country that exports corn, and assume that: • Corn is cultivated using highly labor intensive methods. • The primary way in which corn production can be expanded here is by expanding cultivation onto previously fallow land,. • There is no migration or commuting between rural and urban areas. • Markets for the output of the rural non-farm sector are in autarky. a. Describe the likely effects of an increase in the price of corn on the well-being of each of the following groups, being careful to describe all relevant channels through which the price increase might affect the group’s well-being, and the likely direction of the effect. • Small commercial corn farmers who sell corn, but do not buy or sell labor • Rural poor households who run small nonfarm businesses using only family labor • Rural poor wage laborers • Urban poor wage laborers The increase in the price of corn would directly raise the well-being of net corn sellers and reduce the real income of net corn buyers. The price increases encourages an expansion of corn production, which is possible only by expanding labor-intensive cultivation onto new land; thus the price increase will tend to increase the demand for labor and raise local wages (because the labor market is in autarky equilibrium). The increased farm profits and wages may also increase the demand for the goods produced by the non-farm sector, tending to raise prices and encourage an expansion of production and perhaps employment in that sector. The small commercial corn farmers who sell corn, but do not buy or sell labor, would enjoy the real income increase associated with the increase in corn price. Rural poor households who run small nonfarm businesses using only family labor would tend to benefit from the increased price of nonfarm goods, but would also be hurt by the increased price of corn, if they are corn consumers.

Chapter 17

Rural poor wage laborers would tend to be hurt by the corn price increase (if they are corn consumers), but would be helped by rising wages (driven by expanded demands for labor in agriculture and non-agriculture). The urban poor wage laborers might suffer reduced real income from the increased corn price, if they are corn consumers. Because we are told that there is no commuting or migration between rural and urban areas, we know that rural and urban labor markets are not integrated, so the urban laborers do not benefit from the increases demand for labor in rural areas. b. The table below shows some statistics describing the corn-exporting country’s population. If this country reduced its import tariff on corn, would you expect the number of poor who benefit from the change to be greater or smaller than the number of poor who are hurt by the change? Explain. Please assume that this country is a small importer in world corn markets. Among All Households: Percent Urban Percent Rural Among All Urban Households: Percent Poor Percent Non-poor Among All Rural Households: Percent Poor Percent Non-Poor Among Poor Rural Households: Percent Small Commercial Corn Farmers Percent Non-Farm Self Employed Percent Wage Laborers

20 80 20 80 60 40 70 15 15

The reduction in the import tariff would reduce the local price of corn. Net corn buyers would benefit while net corn sellers would be hurt. Only 20 percent of the country’s population is urban, and of them only 20 percent are poor, so a small fraction of the population is made up of households that are net corn buyers, who would benefit from the corn price reduction. On the other hand, 80 percent of the country’s population is rural and 60 percent of them are poor. Of the rural poor, 70 percent are small commercial farmers who would be hurt by the corn price reduction. As they reduce their production, their reduced demands for labor and the products of the non-farm sector might reduce earnings for the two other rural groups mentioned in the table. Thus it seems likely that the number of poor who would be hurt by the corn price reduction would be much bigger than the number of poor who would be helped by it.

Chapter 18

Chapter 18: Infrastructure Policies and Programs Discussion Question 1: Suppose you work for an NGO that has built wells for drinking water in several villages. Reports indicate that the wells are not used much. You are asked to brainstorm about the kinds of program design change that might improve usage. a. What basic facts about the program and context would you want to ask as you begin your investigation? Recognizing the importance of people’s decisions regarding whether or not to use the new drinking water source, I would want to understand all the ways in which use of the new source differs from use of the old source. I would, therefore, want to learn all the details regarding the type of infrastructure built, the fees, and the quality, reliability and convenience of the water provided by the program, as well as the cost, quality, convenience, and other characteristics of the alternative source of water for this population. b. What kinds of design change might merit consideration? It might make sense to consider reducing fees, running information campaigns about the benefits of clean water, providing on-going technical or financial support for operation and maintenance (in the hope that higher quality or more reliable water would attract more users), or altering the physical infrastructure in some way (such as adding pipes to people’s homes) that increases the convenience of using the water. Discussion Question 3: How might choices made during the selection, design, and construction of an infrastructure asset affect its likely longevity? Longevity may be increased, all else equal, by selecting types of infrastructure that are easier to maintain and less subject to breakdown, designing them for resilience in the face of local stresses, and constructing them with good skills and good materials. This suggests that low quality implementation choices at many stages might contribute to problems of infrastructure that quickly falls into disrepair. Discussion Question 4: For which kinds of infrastructure would you expect the study of spillover effects to be the most important for understanding the size and distribution of overall impacts? Spillover effects are most important for infrastructure services that are primarily inputs to production, including irrigation and commercial electricity, as well as transportation and communication services, which generate many of their effects by encouraging the development of markets. Discussion Question 5: What complementary policies might increase the extent to which a rural electrification program increases rural non-farm employment?

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Chapter 18

Lack of access to cheap and reliable power may be just one of many barriers to the development of a rural non-farm sector. In addition to making electricity available, it may be useful to provide credit, to help potential entrepreneurs overcome liquidity constraints, as well as training and better transport and communication infrastructure. Discussion Question 6: Why and how might the rationales for government intervention differ between road investments and railroad investments? On many roads it would be difficult to charge tolls, because people could drive around the tolls booths. Thus government intervention in roads may be motivated by the public goods problem. With railroads it is much more feasible to charge fees, because people cannot easily get onto the tracks surreptitiously and use them without paying. With railroads the rationales for intervention are more likely to be related to liquidity and insurance constraints, weak property rights, or externalities (knowing that the existence of a railroad is likely to encourage a variety of complementary private investments). Discussion Question 7: Why might private investors fail to invest in the provision of socially beneficial latrine services? Would you guess that for-profit provision of latrine services is more likely to arise (in the absence of intervention) in urban or rural areas? Explain. Private investors might fail to invest in the provision of socially beneficial latrine services because potential users are not willing to pay fees that cover the cost of provision. Users may be unwilling to pay fees commensurate with the social benefit, because many of the social benefits may arise through externalities, which private individuals do not take into account. They may be especially unwilling to pay when there are relatively easy and attractive alternatives to using the latrines that do not require payment of fees. I would guess that forprofit latrine services are more likely to arise in urban areas than in rural areas, because there are fewer free and convenient alternatives in urban areas. Problem 1: An NGO brings electricity to remote communities by setting up small dieselpowered generators, together with electric grain mills large enough to meet the grain-milling needs of the community. Prior to the intervention, women spend hours each day grinding grain into meal using mortar and pestle. The NGO organizes the communities’ women into groups, and then sells the generators and mills to the groups at a price that covers cost, while also providing them with loans, so that they may pay off the purchase in installments. Except for collecting loan repayments, the NGO has no further interaction with the communities after installing the machines and training designated operators for operation and maintenance. In addition to running the grain mill, the generator may be used for charging batteries or running equipment directly connected to the generator. The women are free to give or sell the electricity or mill services as they see fit. a. Are the services of these diesel-powered generators public goods? Why or why not? No, the services provided by these generators are not public goods, because the people operating the assets may deny access to the services and may, therefore, charge for the

Chapter 18

services. That is, these services are “excludable,” and public goods are goods that are nonrival and nonexcludable. b. What market and institutional failures might have prevented local investment in such generators? Locals may not have undertaken this investment in the absence of intervention because they lacked information or because they faced liquidity constraints; and these barriers might have prevented the investment even if the investment would have been profitable if financial markets worked well (allowing them to finance the investment at a reasonable interest rate). Alternatively, locals might not have undertaken this investment because it simply would not be profitable, even if it could be financed at the interest rate that would be relevant if financial markets worked well. Policymakers might nonetheless consider the investment socially beneficial if it successfully reduces poverty along some dimensions. In this case the rationale for intervention is not a market failure but the desire to reduce poverty. c. What features of program design give you reason to worry that some poor households might fail to benefit from this program? Explain. My greatest concern is that the program eventually requires the community to pay for the cost of the generators and mills, including interest payments on the loans used to finance the investment. This means that they will have to charge fees or levy contributions of at least some members of the community. Fees may prevent poor households from participating. Second, it seems likely that the grain milling benefits will accrue only to households that include women who are members of the new groups formed by the program. Some households might be excluded because they are not welcome in the groups or find the groups too burdensome. Finally, most poor in the community might fail to benefit much from this program if the generators and mills quickly fall into disrepair. This might happen because communities might need on-going technical expertise for repairs, on-going help with maintaining cooperation, or on-going financing. d. What direct and indirect impacts would you want to measure within participating communities? To identify the direct impacts of most interest, I think about how using the services of the infrastructure assets might change people’s lives. If women use the services of the grain mill, this will free up some of their time for other uses. If they take over some responsibilities of other household members, then other members, too, would have freed up time that they could use in diverse ways. The ability to charge batteries and use small quantities of electricity for running other appliances, such as light bulbs, could also alter life in diverse ways, changing the way people light their homes and cook. I would, therefore, be interested in these direct effects:

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• • • • •

total income from all sources food consumption time in wage labor, self employment, school, childcare, and leisure, separately for males and females, adults and children use of electricity for other things impacts on health

To identify indirect impacts, I consider how the changes in behavior associated with the direct impacts might alter markets, institutions or the environment, and how these changes might affect the households within the community that do not participate directly. Indirect effects might be worked out through markets for grain, grain milling services or labor markets, in schools (if, for example, time savings or additional lighting allow more children to attend school), or through changes in the health environment. e. Why might some communities fail to take advantage of the NGO’s offer? High poverty rates might imply a low willingness to pay for the services of the grain mills and generators, and communities might recognize that this will make it impossible for them ever to repay the loans. In other communities, households might be willing to pay high enough fees for the services that the community could pay for adequate operation and maintenance and also repay the original loan, but they recognize that they will not have the technical expertise required to keep the mills and generators running, or they will not have the administrative capacity to collect fees or oversee maintenance. Problem 2: A government program has just constructed a new road connecting a set of small villages to a larger market town. For residents too poor to own their own motorized vehicles, the new road provides them with cheaper and faster transport services only if it leads a private entrepreneur to set up a business that sells minibus services between the villages and the market town. Only one local resident has sufficient access to capital to start up a minibus service, and nonresident entrepreneurs choose not to start up such a business, because they will not be able to keep close enough watch on the employees they hire to drive their buses. The following table describes local demand for minibus round trips (in average trips demanded per day) within three income groups and for three fare levels.

Fare=$3 Fare=$4 Fare=$6

Poor Percent who ever ride 40 0 0

Avg. daily no. of round trips 3 0 0

Near Poor Percent who ever ride 50 40 0

Avg. daily no. of round trips 3 2 0

Non-poor Percent who ever ride 30 30 30

Avg. daily no. of round trips 8 8 8

a. Suppose the cost of running a minibus for a day is $28 (a fixed cost) plus $2 per rider (a marginal cost). The minibus can seat up to 16 passengers. Fill in the first five columns of the following table, using the minibus service demand information presented in the table above, as well as the cost information.

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Round trips (Average daily number) Fare=$3 Fare=$4 Fare=$6

14 10 8

Average daily revenue (Fare× Round Trips) 42 40 48

Daily fixed cost

28 28 28

Average daily variable cost (2×Round Trips) 28 20 16

Average daily profita

Average daily profit after subsidy

-14 -8 4

6 -8 4

Average daily profit=Average daily revenue – daily fixed cost – average daily variable cost. (Negative indicates loss.) a

b. The potential minibus entrepreneur seeks to maximize profits and sets up the new minibus service only if he can derive a positive profit on an average daily basis. The entrepreneur faces no competition and expects to supply all the services demanded at any fare he charges. Will he choose to set up business? If so, which of the three prices in the table would he prefer to charge? Why? Yes, he will set up because he can make positive profits, and he will charge $6 because this maximizes profits. c. The government creates a minibus service subsidy policy that would pay the entrepreneur $20 per day, but only if he charges a fare of $3 or less. Use the final column in the table to indicate the average daily profits associated with charging each fare after accounting for the subsidy (which provides revenue of $20 if the fare is $3 or less). See above. d. In the presence of the subsidy, will the entrepreneur set up business? If so, which of the three prices in the table would he prefer to charge? Why? (Please assume that the fare limit is well enforced.) Yes, he will set up because he can earn positive profits, and he will charge $3, because this maximizes profits. e. Discuss the benefits and costs of introducing the minibus service subsidy, including both benefits and costs that you learn about in the table and any other benefits and costs that you would like to measure. The potential benefits and costs we are interested in here are “design change benefits and costs,” or improvements or deteriorations in program performance. The potential benefits of introducing the minimum service subsidy include expansion of outreach (i.e. providing valuable services to more households and poorer households within the community), increases in real income for the few households who would have ridden even in the absence of the subsidy, more profits for the minibus owner, spillover benefits for other members of the

Chapter 18

community as the transfer costs associated with exporting to or importing from the external market fall (assuming that the people who ride the minibus can use it to carry some kinds of goods back and forth between the local community and the external market). The potential costs include the budgetary cost of the subsidy itself, potential reductions in income for people who were providing alternative forms of transportation and for households in the community that are net sellers of any goods whose prices fall as the result of the reduction in transfer costs. Problem 3: Consider the Swajal Project as described in Box 18.1. Discuss the potential benefits and costs of imposing the restriction that communities can receive funding for piped domestic water systems only if they also include in their system design a community tap at which people may collect water without charge. You may assume that the program operates in villages where community members have easy access to untreated river water. We would expect this restriction to affect primarily communities that would have chosen to build piped water systems without free community taps in the absence of the restriction. So let’s start by thinking about what these communities are like and what the restriction would do if these communities continued to participate. These are probably communities in which the committees largely represent the interests of households that are well enough off to be able to pay fees for piped water. The committees may only represent the interests of the top elite, who use the funds to construct infrastructure mostly for the private benefit of a few (we’d like to discourage this fraudulent use of government funds), or may represent a larger share of the population, including many poor and near poor households for whom this water is important to their health (we’d probably like to encourage much of this use of government funds). The requirement that these community committees add a free community tap into their plan might increase the cost of construction (shared between government and committee) a little (probably not a very large percentage increase) but might increase the cost of operation and maintenance (borne by committee) a lot (if there are many poor households that would choose to use the free tap). This increase in cost must be covered by increased collection of fees (charged only to households receiving water piped to their homes) or other community contributions (presumably mostly from better-off households). With free clean water at the community tap now available, and the fees for piped water higher, households that would have paid for piped connections may now decide to use free community tap water instead. This may raise or lower the well-being of these “switching” households, but it certainly reduces the number of households paying fees for piped water. This means that use charges would have to rise even higher to cover the costs of operating and maintaining the whole system. This would cause even fewer households to pay for piped connections. It may become impossible to charge fees for piped services that cover the cost of the whole system. If the community goes ahead and builds a system anyway, they may charge fees too low, leading to poor operation and maintenance, low quality water and/or quick deterioration of the system. They might instead choose not to participate in the program at all. This suggests that the new requirement could have several effects (on communities that would have chosen piped water systems without community taps in the absence of the restriction).

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Some of these communities may continue to build their water systems, but would add the community tap. This would increase the program’s outreach among the poor households who would not have purchased piped access, improving their health. It would reduce the wellbeing of the piped users, who now pay higher rates, and would have uncertain impact on the well-being of those who shift from piped water to free community tap water. It might also lead to quicker deterioration of the system and poorer water quality. Some of these communities may decide not to participate in the program anymore. Of these, some are communities where a few elite were going to use the program fraudulently; causing them to leave the program is probably a benefit. Others of the communities that drop out, however, may be communities where the program would have done a lot of good for many households (though perhaps not for the poorest). Losing these communities is probably a cost. Digging a bit more deeply into the incentives toward operation and maintenance, we realize that in these communities that would not have included a free public tap, the committees will feel little desire to maintain the free community tap portion of the system. Unless the government provides very serious monitoring and punishment, they could just “let” the community taps stop working, or put them in places where poor households would not want to use them. They might thus effectively prevent the restriction from changing program impacts very much. Pulling all this together, we could come up with the following lists of potential benefits and costs, but would recognize that in practice communities may be able to satisfying the letter of the restriction without experiencing much real change (in which case all these benefits and costs may be quite small in practice). Potential benefits: • eliminate participation by fraudulent community committees that only represent the interest of a few elite • within communities that continue to participate, and that would have built only piped water systems without free community taps in the absence of the restriction, improve participation (and health) among poor households who would not have purchased piped connections (instead using unclean water from river) Potential costs: • eliminate participation by communities in which many households could have benefitted from a piped water system under the original program, but in which financing of the system becomes impossible under the restriction • within communities that continue to participate and that would have built only piped water system without free community taps in the absence of the regulation, either o increase payment burdens on the households that continue to pay for piped connections or o deterioration in operation and maintenance, quality and duration Effects that could go either way:

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•

budgetary costs to government - some communities may choose not to participate, tending to reduce total costs; in communities that continue to participate, construction costs may rise (from adding free tap) or fall (from fewer households wanting piped connections) well-being of the households who shift from paying for piped connections to using free water from community tap – their health may not be affected (all this water is treated); they may be made better off by the opening of the free water option, but may be made worse off if they would have preferred piped water over free water at the initial fee for piped water, but decide to shift into use of free water only because of fee increases.

Chapter 19

Chapter 19: Education Discussion Question 1: Many children complete primary school but do not complete secondary school. Within the simple model of school enrollment decisions presented in Part 19.2A, what might explain why their parents choose to send them to school for all primary school years but not for all secondary school years? What kinds of policies might be useful for increasing secondary school completion rates among children who complete primary school? After children complete primary school, parents consider the benefits and costs of sending a child to the first year of secondary school. They may decide not to send the child to secondary school because the perceived benefits of that year of schooling are lower than the perceived benefits of previous years or because the perceived costs are higher than for previous years of schooling. The perceived benefits might fall if parents think secondary school is irrelevant for the kinds of work their children will do (even while they believe that becoming literature during primary school is useful) or because the secondary school is lower quality than the primary school. The perceived costs might rise because the secondary school is further away, because secondary school fees are higher, or because the opportunity cost of children’s time is higher. This points to many kinds of policies that might be useful: improving secondary school quality and relevance, reducing fees, building secondary schools in more locations or providing bus services, and possibly offering scholarships or conditional cash transfers. Adjusting school schedules to allow students to work while also attending school might also increase secondary enrollment. Discussion Question 2: Consider the impacts of an education policy reform that increases the years of schooling an individual must have to obtain a position as a primary school teacher. Through what channels might this reform affect school quality and learning outcomes? How might the impact on learning differ depending on whether teachers are hired by schools receiving capitation grants from the central government (which do not change) or are allocated to schools by the central government (which pays their salaries)? Increasing the years of schooling required for teachers will probably increase the typical wage paid to teachers, increasing budgetary costs. If the government gives local schools capitation grants that do not change, the requirement that local schools hire more expensive teachers will require them to either reduce the use of non-teacher inputs or raise fees. If the central government provides the teachers and pays their salaries, then the total central government budget for education might rise, or policymakers might try to hold the education budget constant by making compensating cuts, such as reducing the number of teacher, reducing grants to schools for non-teacher inputs. They might also decide to raise fees. All this suggests that the quality of teaching and learning may be affected through several possible channels: increased skills of teachers, reduced non-teaching inputs, reduced numbers of students per teacher (if increased fees cause some students to drop out) or increased numbers of students per teacher (if the government hired fewer teachers).

richard@qwconsultancy.com

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Discussion Question 4: Consider a country where national-level policymakers have long dictated that a single language be employed for instruction in all schools throughout the country, and where this single language is the second or third language for many children. Discuss the potential benefits and costs of a reform that allows individual schools to select their own primary language of instruction. Potential benefits: • Increased enrollment of children who gain opportunity to learn in a language that they know better and that their parents consider more appropriate • Improved learning by children who were already in school and now learn better because they understand the language better • Preservation of a language and culture Potential costs: • Transition costs of creating curriculum in new languages and training up teachers to teach in the new languages • On-going costs of providing services to larger numbers of school children • Possible loss of enrollment or deterioration in learning among children who preferred to learn in the previously required language and whose schools now switch to other languages • Possible loss in the extent to which the education system assists nation-building (by teaching everyone a common language and culture) Discussion Question 5: Consider an education reform that is financed by additional international funding and that increases the ratio of textbooks to students throughout the school system. Discuss as comprehensively as possible the potential benefits and costs of this reform. Potential benefits: • Improved quality of teaching and learning for children already in the school system • Improved enrollment among children whose parents now perceive the school to provide better services Potential costs: • Increased budgetary costs from the additional books per child, and the additional books required even to maintain the book/student ratio when additional students entre the schools. Discussion Question 6: Consider an education policy reform that shifts authority over many school management decisions from central-level government bureaucrats to school principals, while holding constant the level of per-student funding. What hopes and worries would you have regarding the effect of the reform on the five ingredients – local information, motivation, resources, capacity and central oversight – brought to the affected school management decisions? What effects might the reform have on school policy and management choices, and thereby on implementation outcomes?

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Presumably the shift of decision-making from the center to school principals would increase the access of the decision-makers to necessary local information (e.g. regarding day to day behavior of school staff). Principals might have better or worse motivation to make good and honest decisions relative to the central decision-makers. On the one hand, they may be innately more concerned about supplying good education services or may be easier for community members to reward and punish, and may therefore exhibit better motivation. On the other hand, they may be harder to monitor than centralized bureaucrats, and may take advantage of the situation to divert resources for personal or political gain. Their capacity may be greater or less than that of the central decision-makers. They may have less education and exposure to professional journals, and it is possible that the lack of these experiences diminishes their capacity to make good choices. The decentralization of decision-making inherently diminishes the ability of central policymakers to impose uniformity on school-level implementation outcomes. The hope would be that the principals would respond better to local needs in their choices regarding fees, schedules and outreach efforts, do a better job of ensuring good teaching by teachers, and perhaps raise additional financing locally. Unfortunately, the principals may lack better motivation for various reasons (including low salaries and being posted to communities in which they have no ties), and may also have lower capacity. Problem 1: In some regions girls receive less education on average than boys. a. State at least two reasons why parents might perceive the benefits of educating their daughters to be lower than the benefits of educating their sons, and at least two reasons why they might perceive that the costs of educating their daughters are higher than the costs of educating their sons. Parents might perceive that the benefits of educating their daughters are lower than the benefits of educating their sons because the girls are less likely to become involved in jobs or other activities in which the skills learned in school are valuable, or because the intrinsic value they place on providing good things for their daughters is lower than the intrinsic value they place on providing good things for their sons. Parents might perceive that the costs of sending girls to school is higher because they perceive greater dangers for girls than for boys in getting to school and being at school during the day, because they face greater disapproval by neighbors and family when they send girls to school than when they send boys to school, or because they consider it important to prepare their children for acceptance by other members of their culture group, and acceptance requires that girls marry and begin having children young. b. What sorts of policies might be useful for raising girls’ enrollment rates relative to boys’? It may be possible to raise girls’ enrollment rates relative to boys’ simply by raising household incomes (with unconditional cash transfers or through development efforts that raise incomes in regular economic activities) or reducing school fees for all children (because the demands for girls’ education may be more income and price elastic than the demands for boys’ education); reducing the price of schooling girls relative to the price of schooling boys by

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providing scholarships or conditional cash transfers that are more generous for girls than for boys, or reducing fees for girls relative to boys; and engaging in information and promotion campaigns intended to convince parents of the value of schooling girls. Problem 2: Consider a region in which there are two villages, Village A and Village B. In each village there are 100 poor families and 50 nonpoor families. Each family has one schoolaged child, and decides to send the child to the nearest school if the following inequality is satisfied: Tuition cost + Transport Cost + Opportunity Cost  Household’s Valuation of Future Education Benefits + Scholarship Initially Tuition costs and Scholarships are zero for all households; and Village A has a school while Village B does not, implying that Transport Costs for all households in Village A are zero, while Transport Costs would be 20 for households in Village B. The Opportunity Cost of a child’s time is 10 in a poor household (where children are expected to work and help with chores) and 0 in nonpoor households. Poor households value Future Education Benefits at 5, while nonpoor households value them at 15; this difference reflects the higher rate at which liquidity constrained poor households discount future benefits. a. Which of the four groups of households (nonpoor in A, poor in A, nonpoor in B, poor in B) would send their children to school under the initial conditions? Children Sent to School? Initial Situation Village A Village B Nonpoor Yes No Poor No No b. After each of the following policy initiatives, which of the four groups would send their children to school? •

The government builds a school in Village B (but makes no other policy changes). Children Sent to School? Build School in B Village A Village B Nonpoor Yes Yes Poor No No

•

The government institutes a means-tested scholarship program, under which a payment of 5 is made to any poor household, in either village, that sends a child to school (but builds no schools and makes no other policy changes). Children Sent to School? Means-tested Scholarship Program Village A Village B

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Nonpoor Poor

Yes Yes

No No

•

The government builds a school in Village B and charges tuition of 10 to anyone who attends that school (while continuing to charge no tuition in Village A and offering no scholarships). Children Sent to School? Build School in B and Charge Tuition Village A Village B Nonpoor Yes Yes Poor No No

•

The government builds a school in Village B, charges tuition of 15 for all nonpoor households in either village that send their children to school and pays scholarships of 5 to all poor households in either village that send their children to school. Children Sent to School? Building, Tuition and Scholarship Package Village A Village B Nonpoor Yes Yes Poor Yes Yes c. Suppose it costs 500 to build a school, and that there are no costs to administering tuition collection or scholarship programs, so that tuition fee policies add to the budget the full amount of fees collected from enrolled students, and scholarship programs cost only the full value of scholarships distributed to students who take them up. What is the net impact on the government budget of each of the four policies described in part b?

For building school in B = 500 For a means-tested scholarship program = 100 poor * 5 = 500 For building a school in B and charging tuition there = 500 – 50*10 = 0 For build a school in B, charging tuition and giving scholarships in both communities = 500+200*5–100*15 = 0 d. Under the circumstances described in this problem, which of the following equity objectives is achievable on a fixed budget of 500: • equality (across all four groups) in the offer of education services and subsidy, • equality in the receipt of education subsidy, or • equality in the receipt of schooling services? Explain. Please note that the subsidy offered to a family is the full per-child cost to the government (or other development actor) of providing the education offered (which we do not know, because we have not been told anything about the costs of running the schools) and related benefits (such as scholarships) less any payments collected from the family to help cover those costs.

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The greater the scholarship offered, the greater the offered subsidy, and the more the tuition charged, the less the offered subsidy. Equal offer of subsidy is possible. If you make schools free everywhere and offer no scholarships (or at least charge the same fees or offer the same scholarships to everyone), and esp. if you build free schools in all villages (as in part b), then you have equal offer of subsidy. [If it costs more to provide the same schooling opportunities in some places, then equal offer of subsidy would require charging higher fees in higher-cost places.] At least in this setting, equal receipt of subsidy is not possible. You can offer the same amount of subsidy to everyone but only some households will choose to receive it (unless possibly if the subsidy is very, very high). Equal receipt of schooling is possible. The last package examined above gets all kids into school. It is able to do this on a limited budget only by offering different levels of subsidy to different households. We might argue that the most compelling way to define “equal opportunity” in schooling is to equate it with “equal receipt of schooling”. While it may seem egalitarian to make free schooling equally available to all households (thus equating “equal opportunity” with “equal offer of subsidy”), this will not result in equal receipt of subsidy (since only some households will take up the offer of subsidy) and will not result in equal education outcomes, and thus does not lead to an outcome that is appealing in any satisfying sense of equality. To bring about equal receipt of schooling on a limited budget, it will often be necessary to offer unequal subsidies, in the sense that some households must be asked to pay more (or be offered smaller scholarships) than other for the same education. If the budget were not limited, we could pay everyone sufficiently large scholarships for sending kids to school that all households decide to send their children. They would then be receiving equal education and equal (large) subsidies. But that might cost a very great amount, because to draw the last few holdouts into school, we might have to raise payments to very high levels (for everyone). On a limited budget, we must devote greater subsidies to the families that are most reluctant to send children to school. Problem 3: Consider a highly decentralized government school system, in which the central government provides annual grants to school administrators. The administrators may use the grants for hiring teachers; buying textbooks, desks, and other supplies; and running any other school level programs that they wish, including demand-side programs. The grants are capitation grants, which means that the size of the grant that a school receives is equal to the number of students enrolled multiplied by a per-student grant level. School administrators are also given the authority to charge modest tuition fees if they wish. What would be the main potential benefit(s) and cost(s) of introducing into this school system an incentive scheme for principals, in which principals receive pay bonuses tied to the average scores of their students on standardized academic achievement exams? Explain.

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o Main benefit: improvement in “school quality” o Administrators might work harder at running the school in a quality way in order to improve test scores and earn more. They might show up for work more often. They might divert less of the grant money into their own pockets. They might hire more qualified teachers rather than their friends and relatives. They might supervise and discipline teachers more strictly. They might improve the curriculum and devise new ways of teaching that do a better job with students’ diverse learning needs. They might allocate money more efficiently across teachers and non-teacher inputs. (You only needed to mention some of these.) o Main costs: o reduction in enrollment, esp. among the poor and disadvantaged ▪ Administrators might refuse to enroll, or flunk out, some students who appear less likely to perform well on tests. They might raise fees to buy more supplies or offer bonuses to teachers, making school less feasible for poorer families. They might divert funds away from programs promoting education (e.g. scholarship programs and community awareness efforts) into teaching students already present. o Reduction in consumption for families who continue to attend ▪ If they increase fees to improve quality o Reduced learning of skills that are not tested in the standardized tests ▪ Administrators might (intentionally or unintentionally) give teachers incentives to “teach to the test” o Budgetary cost of paying bonuses.

Chapter 20

Chapter 20: Agricultural Research and Extension Discussion Question 1: Describe the early Green Revolution technologies. How would you describe the direction of technical change associated with the switch from the technologies farmers were using before to these technologies? Discuss how the details of this technical change affected (a) which farmers around the world were likely to benefit and (b) the nature of the direct and indirect effects of adoption. It is useful to note that the early Green Revolution technologies pertained to wheat, rice and corn. They raised yields, but only if their use was accompanied by fertilizer and steady water supply. They increased the demand for labor, especially in harvest seasons, and especially during months in which it became possible to grow a third crop per year. Initially they also increased the risk associated with cultivation. The details mattered because farmers were unlikely to benefit if they did not live in regions where wheat, rice or corn were important crops, if they had poor access to markets (so fertilizer prices were high relative to output prices), if they had no irrigation and only uncertain rainfall, if they were significantly liquidity constrained or insurance constrained. The details mattered for the nature of the direct and indirect effects of adoption, because other new technologies might not have increased as much the demand for labor (and thus not transmitted as many benefits to the landless poor), increased as much employment in off agricultural seasons, increased as much demands for the produce of the rural non-farm sector, or placed as much pressure on the environment through the use of pesticides and irrigation. Discussion Question 2: What direct and indirect effects would you want to measure for a thorough study of each of the following types of technical change? What potential barriers to adoption would you want to study? •

Adoption by food crop farmers of chemical fertilizer

In addition to studying the impact on the incomes and consumption of the adopting farm households, I would want to study the reduction in food prices and improvements in real income for net food buyers, increases in demand for labor and in wages, reductions in real incomes for farmers who do not adopt the chemical fertilizer (as output prices fall and input prices rise). I’d also want to consider the implications of the chemical use on local water quality, and the health of local flora and fauna, including humans. •

Adoption by soybean farmers of tractor-pulled plows and harvesting equipment

I would be interested in many of the same outcomes as in the previous case, but now might suspect that labor demand and wages will fall rather than rise. I might also worry about the effect of heavy machinery on the soil. •

Adoption by subsistence farmers of a new technology capable of storing grains and legumes safely for many months richard@qwconsultancy.com

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Chapter 20

I would be interested to see how effectively the storage works, whether this leads farmers to store more of their own seed, and whether incomes rise as they avoid having to incur all the transfer costs of selling at harvest time and buying seeds at planting time. Discussion Question 4: Suppose you are asked to write a report on the likely benefits and costs of shifting some government agricultural research spending away from export crops toward domestic food crops. What information would you wish to gather before writing your report? What sorts of potential benefits and costs would you consider? Good discussions will touch on the transition costs associated with re-building the research and extension systems around new types of science and new geographic locations, and on the implications of the shift for which kinds of households (poor/rich, landless/landed, rural/urban, diverse rural regions) benefit less and which benefit more from the research, either directly through adoption or indirectly through effects on goods or labor markets or the environment. Discussion Question 5: Consider an NGO working in rural development in a particular poor region of a developing country. What kinds of advocacy and liaison activities involving the national agricultural research system might it find useful? At the national level, it might advocate for more spending on agricultural research and extension, as well as construction of roads and other general policy improvements that increase profitability for the poor farmers for whom they advocate. They might also wish to serve as liaisons with the local research and extension services, helping them understand the local farmers’ needs and wants (hoping to encourage development and dissemination of technologies that are more appropriate to local farmers’ needs). Discussion Question 7: If private agents (e.g. input retailers) are quite active in extension even without subsidy, how might policymakers want to tailor public sector and NGO extension policies to complement, rather than substitute for, this private extension activity? The public sector might wish to focus on types of new technologies and types of farmers for which the private sector is least likely to supply services. These include technologies with strong public good qualities, and farmers for which the private benefits of extension efforts are least likely to outweigh the costs (i.e. farmers who are poorer, more remote, less educated). . Problem 1: You are hired by the new government of a developing country to write a report on the extent to which the current government agricultural research program is targeted toward poverty reduction, and to generate a list of potential changes in the research program that would improve its poverty reduction impact (without increasing total spending). What features of the agricultural research program would you study, and what changes would you consider? Explain. Critical policy design choices include: which crops to work on, which types of technical change to pursue, and what kind of governance structure to employ. Policy changes improve

Chapter 20

the impact on poverty if they increase the numbers of poor farmers who adopt the technologies generated under the policy, if they raise well-being for poor farmers more, if they raise wages for landless, low-skill labor more, if they drive down the prices of foods important in the consumption of the landless poor, and if they produce crops more resilient to local stresses (increasing security for buyers and sellers). Changes that might improve the poverty impact might include: shifts toward technologies that increase the value or yields of crops produced by small farmers, shifts toward technologies that increase yields of foods that are important in the consumption baskets of the poor, shifts toward technologies that tend to increase the demand for labor, shifts toward technologies that require fewer purchased inputs (so that poor market access and liquidity constraints become weaker barriers to adoption by poor farmers), governance changes that render researchers more responsive to poor farmers needs and wants (leading them to produce technologies that are more likely to be adopted by poor farmers). Problem 2: Consider a national agricultural extension service in which the agents have three sets of responsibilities: • Informing and teaching farmers about new technologies produced by the agricultural research system, • Helping farmers cope with frequent and diverse problems with insects, crop diseases and weather variations that hit their crops, and • Spreading public health messages to the farming population. The agency currently offers its services free of charge, and the agents provide services of moderate quality. Each agent is paid a fixed salary and is assigned as the sole agent in a region. The agents allocate their time across farmers within their regions as they see fit. Discuss the potential benefits and costs of a reform with two key elements: • Charging fees: Agents must start charging farmers a modest fee per scheduled extension visit. Farmers may organize themselves into groups through which they can share the costs of extension visits. Agents may visit farmers in an unscheduled fashion to inform farmers of the services they offer, and to encourage farmers to form groups, but they may not charge for such visits. Farmers pay fees only for official, scheduled extension visits. • Competition among agents: Agents will be assigned to overlapping areas. Farmers may request official visits from any of the agents available to their region, and agents’ pay is tied to the number of official farm visits they make. The pay scale is set so that agents attracting enough requests to require full time work would continue to receive the same level of pay as before, while agents who are not much requested receive less than before. Potential benefits: • By charging fees, the program recovers some cost, allowing them to expand their budget and perhaps hire more agents and reach more people. • By introducing competition, the program may strengthen incentives for agents to provide valuable, high quality extension services – they need farmers to request visits from them, thus they have an incentive to prove to the farmers that their services are valuable. Since the farmers are paying, they will be especially interested in services

Chapter 20

• • • • •

that increase their profitability. Thus agents will have an incentive to do an especially good job with the new technologies and the problem solving. Quality may also rise as worse agents drop out. Increased quality might also attract more demand (from those who can afford fees). If farmers are only willing to pay for visits if they can share cost with groups, then agents will have incentive to form groups – this would tend to increase the number of farmers reached per visit. Effectiveness may also rise as services are requested only by farmers who really want them and plan to implement advice. Any increase in quantity or quality of services provided would tend to o increase the number or size of impact on farmers whose well-being is improved through increased yields and income, reduced costs or reduced risks. o increase spillover benefits for laborers and consumers.

Potential costs: • Charging fees might cause the poor to drop out. • Charging fees would reduce the well-being impact on farmers who continue to receive services. • The reform might reduce agents’ incentives toward providing the public health and social messages, which people are less likely to want to pay them for. • Once farmers have to pay, they may be less willing to share info with non-contributing neighbors. (Note that net effects on the following are ambiguous in sign: o number of farmers reached, and related spillovers o income/well-being of farmers reached)

Chapter 21

Chapter 21: Microfinance Discussion Question 1: What assumptions about empirical reality underlie the “microfinance idea” articulated in Section 21.1A? The microfinance idea is articulated this way: “Rather than give the poor handouts, which provide them only temporary help, we can offer them loans for financing business investments. As they create or expand microenterprises …their incomes rise in a sustained fashion, allowing them to grow their families out of poverty. We may, furthermore, target the loans to women, empowering them for greater influence in their homes and communities. And we can do all this at little per-household cost because recipients will repay their loans with interest, allowing the funds to be recycled for raising many families out of poverty.” This seems to make the following assumptions that may or may not be true for a particular program design in a particular context: • that many members of the target group of poor households will wish to borrow on the terms offered by the program • that members of the target group face investment opportunities that are profitable enough that they should be able to pay back the loan with interest and still be better off (and that they have the skills and complementary assets required) • that the program loans are large enough and provide flexible enough financing that the members of the target group can undertake the investments without having to sacrifice too much consumption in the short and medium run • that members of the target group indeed take up the opportunity to borrow and invest (not put off by the risk or need to be entrepreneurial) • that the investments (which are risky) indeed pay off • that targeting loans to women makes a difference regarding how the loans are used by households • that making profitable business investments makes women better off and raises their influence within their households (rather than just giving them more to do to raise consumption for other members of the household, or even inspiring more violence against women) • that it is possible to charge an interest rate that target households are willing to pay and still cover the costs of lending Discussion Question 2: Suppose you wanted to modify a microcredit program with the aim of reaching a poorer set of households than the program currently reaches, and within the same communities. What design changes would you contemplate? Design changes that might improve outreach might include: reducing the interest rate, adding a grace period, spreading the payments out over a longer time period, providing training and other kinds of assistance with business activities, providing supplemental health care, and richard@qwconsultancy.com

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Chapter 21

helping poor borrowers cooperate with other producers in ways that reduce costs or increase revenue. It may also be useful to reduce the initial loan size (if larger loans are too daunting for the target poor) or to increase the initial loan size (if the current loans are too small to allow the truly poor to undertake profitable investments with fixed setup costs). Discussion Question 3: Suppose you are asked to participate in an evaluation of microcredit program impact, and suppose a methodology has been worked out for estimating impacts on any outcomes of interest one year after borrowers join the program. What outcomes would you wish to measure and why? If budget and the patience of my respondents allowed me to study as many outcomes as I like, I’d want to measure impacts on: business assets, business profits, total income, hours of labor devoted to the business, hours of labor devoted to other income generating activities, other household assets, child labor and schooling. This would give me a sense of the impact on well-being at that time, and also some sense of whether through asset accumulation the household is likely to enjoy continued or additional increases in income or well-being in the future. I would want to estimate the distributions of impacts on these outcomes, and not just the mean impact. Discussion Question 9: Discuss the potential benefits and costs of replacing a microcredit program that provides each of 20 women in a joint liability group with loans of $100, which they use to run individual small businesses, by a program that provides a group of 20 women with a single loan of $2,000 that they are to use in undertaking a cooperative investment in setting up a mill for grinding grain into flour (or some other small- or medium-sized food processing or manufacturing operation). Potential benefits: • By pooling the financing and cooperating, the women may be able to reap economies of scale, entering into a higher productivity and more profitable activity. If this is the case, both outreach and impact on participants’ incomes might improve. • The larger investment may also have greater capacity to raise the demand for labor and raise wages. Potential costs: • Greater capacity building expenses would probably be required, both to help the women work out an institutional structure to encourage cooperation and to help them with technical aspects of the larger investment • Possibly greater risk of complete failure within the village, both because it involves a smaller number of investment projects and because it requires cooperation among the 20 participants. Discussion Question 10: Consider a community lacking a good road connection to market. Why might construction of a high quality road to market increase the potential poverty reduction impact of a microcredit program located in the community; and why might the presence of a microcredit program increase the impact of road construction on the community?

Chapter 21

The construction of a high quality road to market might increase the potential poverty reduction impact of a microcredit program by reducing transfer costs, thereby raising output prices, reducing input prices, and increasing the profitability of the small businesses financed by microloans. (If high transfer costs keep local markets in autarky equilibrium, then no more than a few people could expand microenterprises that increase the supply of particular goods and services without driving prices down and making it unprofitable for additional people to open such enterprises.) The presence of a microcredit program might increase the impact of road construction if microloans allow people to set up small businesses transporting people or goods along the road. Problem 1: A single microcredit organization (MCI One) currently operates in a certain region. It provides loans of up to $400 and lends at an interest rate of 20 percent. It has been in operation for seven years, and has only just barely managed to achieve financial sustainability. A new microcredit organization (MCI Two) is considering entering the same region, offering loans of up to $50 and charging an interest rate of 15 percent. Other details regarding the specifics of the program it would set up remain to be determined. a. Given what we know about MCI One’s experience, explain carefully why it seems unlikely that MCI Two will be able to operate without subsidy, even after an initial startup phase. MCI One is only just breaking even after a long start-up period. This means that the interest it receives is only just enough to cover the per-dollar costs of lending, which include the personnel and transport costs of dealing with clients, the opportunity cost of its capital, and the costs associated with default. MCI Two is unlikely to be able to operate without subsidy because: • its costs are likely to be higher, because it plans to be dealing with smaller loans. The personnel and transport costs, etc., per dollar tend to be higher on smaller loans. • its revenue will probably be lower because it is charging a lower interest rate. With lower revenue and higher costs than an institution that is just breaking even, it is likely to need subsidization. b. What objective might MCI Two hope to achieve through its offer of subsidized loans at lower interest rates (than those charged by MCI One) that is not already being met by MCI One? Explain the logic behind why MCI Two might be able to achieve this objective even though MCI One has not. MCI Two might be interested in increasing the incomes and wellbeing of a poorer clientele than that reached by MCI One. Poorer clients tend to face potential investment projects with lower returns. At the 20 percent interest rate charged by MCI One, some poorer clients may not find borrowing attractive. At the lower rate of 15 percent, however, they may find borrowing attractive.

Chapter 21

MCI Two may also undertake measures to increase poorer borrowers’ potential investment returns, by, for example, providing them with some business training and advice that MCI One does not offer (increasing costs and subsidy even further). c. What concerns might MCI One have regarding the consequences for its own operations of entry by MCI Two? When MCI Two comes in offering loans at a lower interest rate, there is a chance that MCI One might lose some of its business, as borrowers pay off their loans to MCI One and switch over to MCI Two. It might see this as a loss of its own impact (even though, from a larger perspective, the borrowers are still receiving credit and profiting). It might also find that as its business shrinks and it must operate on smaller scale, its perdollar costs of operation rise, and it becomes more difficult to break even. [Note that while losing customers may reduce total profits, it does not necessarily reduce the institution’s sustainability, which depends on a per-dollar comparison of revenues and costs. A connection between total volume of lending in this community and sustainability arises if the organization has some fixed costs of operating in this market. This would imply that the per-dollar costs of lending fall as loan volume rises.] A potentially more serious set of concerns has to do with the possibility that the entry of MCI Two will cause default rates among MCI One’s borrowers to rise. This might happen through at least two channels. First, borrowers might simply not repay because they can switch to MCI Two and don’t need MCI One anymore. Second, if MCI Two, which is subsidized, also engages in undisciplined lending practices, then potential borrowers (even those who have not yet borrowed from MCI One), may get the idea that they don’t have to take credit contracts seriously, and may prove not to work very hard at repaying loans from any institution in the future. d. What choices could MCI Two make regarding its program design that would reduce its potential to create the adverse consequences for MCI One that you just described? To reduce the potential for these negative spillovers, it would be useful to implement design features that minimize the extent to which current borrowers from MCI One will find borrowing from MCI Two a viable option. First, the smaller loan size limit itself may help do this. People borrowing loans of $300-$400 may not find $50 limit loans very useful for their purposes in the first place. Second, MCI Two could even impose something like a means test, which limits eligibility for loans only to people whose income is below some level, and set this level in a way that seems to limit eligibility to a group that is not interested in MCI One loans. MCI Two may also be able to explicitly enforce a requirement that a “credit check” reveals no outstanding loans to MCI One or other lenders.

Chapter 21

In the interest of reducing spillovers through the creation of bad habits regarding loan repayments, MCI One could also pay scrupulous attention to enforcing good business practices and repayment on the part of its borrowers. Problem 2: The population of Community A includes three kinds of households. The following table describes numbers of households in each group, the income they obtain each period from sources other than business investment, and their business skill level. Group

Number of households

Group 1 Group 2 Group 3

40 40 20

Income from other sources in each period 30 30 80

Business skill level Low High High

Two types of business investment opportunities are available in Community A: small retail businesses and small sewing businesses. The returns to investments in setting up these businesses do not depend on how many people choose to undertake them. The following table describes the structure of their setup costs and the profits they generate in each of three periods, for potential entrepreneurs that have low and high business skill.

Setup cost

Profits delivered by business in each of three periods Period 1 Period 2 Period 3

Low skill High skill

50 50

25 40

0 0

Low skill

High skill

Project Description Purchase inventory for small retail operation Purchase sewing machine for tailoring business

Households have two sources of financing to cover the setup cost of an investment: a loan from the local microcredit program (taken out at time zero, before the beginning of period) and saving out of Period 1 income from other sources. Initially, the local microcredit program offers loans of 50, which borrowers must pay back in two installments of 30 each in Periods 1 and 2. This means that borrowers can finance immediate investment in a small retail business, but can finance investment in a sewing business only by adding 20 saved out of other income in period 1 to the loan of 50. Borrowers consider an investment feasible only if it does not require them to push consumption below 30 in any period. As long as consumption remains above 30 in all periods, the utility a household derives over the three-period horizon is given by the simple sum of consumption in periods 1, 2 and 3. Consumption in any period is equal to income from other sources minus any saving out of income used to help finance investment plus any business profits derived from an investment minus any loan repayments. Households seek to maximize utility as they decide whether to borrow and invest, and which investment project to undertake.

Chapter 21

a. For each group (1, 2 and 3) state which business investment, if any, they will undertake at time zero, given the conditions described thus far, and indicate what level of consumption they will enjoy in each period. Group 1 will not undertake business investment. They will enjoy consumption of 30, 30, 30. Group 2 will invest and will undertake the retail investment. They will enjoy consumption of 40, 40, 30. Group 3 will invest and will undertake the sewing investment. They will enjoy consumption of 30, 110, 140. b. State what percentage of Community A households participates in the microcredit program and fill in the following table describing the microcredit program’s impacts. The impact on consumption in any period is consumption in the presence of any microcredit financed investment minus consumption in the absence of any such investment. If they do not participate, then the impact in each period is zero. 60 percent of the community’s households participate Impact on average consumption for: Group 1 Group 2 Group 3 Microcredit program Participants Percent of microcredit program participants whose consumption is raised by at least 15 in the given period

Participate (yes or no) No Yes Yes

Period 1

Period 2

Period 3

0 10 -50 -9.8

0 10 30 16.6

0 0 60 19.8

c. Suppose evaluators are able to perfectly estimate the impact of the program on consumption in any period and for any group. Discuss how their conclusions regarding the program’s success in raising consumption might differ depending on the period in which they observe consumption. Observing only in one period offers an incomplete picture of impact. For Group 1, measurement in period 1 and period 2 yield the same answer regarding the impact while repaying the loan, but neither says anything about the extent to which the impact will continue after repayment ceases. For Group 2, even though the total impact on consumption over all three periods is positive, the impact in the first period is negative, while the participants save out of current income to augment the loan enough to finance the larger investment. d. Focus only on period 2. If evaluators consider a program successful if it raises average consumption among participants by at least 15 in period 2, would they judge

Chapter 21

this program successful? If they consider a program successful if it raises the consumption of at least half the participants by 15 and reduces consumption for no participants in period 2, would they judge this program successful? By the first criterion, the program is a success, because it raises average income among participants by 16.6. By the second criterion they do not consider the program a success, because only one third of participants experience an increase of at least 15. e. Suppose the interest rate rises so that microcredit program participants must make payments of 35 rather than 30 in periods 1 and 2. Now who participates and which projects do they undertake? G1 still does not participate. G2 still participates and undertakes the retail investment. G3 still participates but now undertakes the retail investment. f. Suppose the microcredit program is restructured to give borrowers a grace period before beginning to repay their loan. They still obtain loans of size 50, and now must pay off the loan in two installments of 40 each in periods 2 and 3. No payment is required in period 1. How does this change affect the investment choices of Group 2 households? Now G2 does not participate. Notice, however, that increasing the loan size (rather than adding a grace period) might make it feasible for G2 to undertake the higher return investment.

Chapter 22

Chapter 22: Public Health, Health Care and Health Insurance Discussion Question 2: Compare and contrast the challenges of two approaches to increasing effective use of clean drinking water in rural communities: distributing water filters for use in homes versus helping communities build clean drinking water systems that deliver water to household taps. Distributing water filters: With this intervention the challenge is to get households to use the water filters consistently and to repair and replace them when necessary. Households may lack appreciation of the benefits of these activities, and may be prevented by poverty or liquidity constraints from purchasing new filters. Helping with communal clean water investments: Here the challenge is to catalyze the cooperation required to create the new infrastructure, and to create institutions for financing and overseeing the performance of operation and maintenance activities. (As long as clean water is piped to homes, the challenges revolve much less around household choices regarding their water use activities.) Discussion Question 5: Discuss the potential benefits and costs of increasing the premium charged by a CBHI program. Potential benefits: • The increased collection of revenue on a per-beneficiary basis could be used to reduce the per-person budgetary cost of the program or to expand the coverage provided. A reduction in per-person cost could mean the ability to reach more communities on the same limited budget. Potential costs: • The increase in premium could cause some (relatively poor) people to drop out. • The increase in premium would reduce the net beneficial impact on participants.

Problem 1: When programs distribute free bed nets, they are distributing in-kind transfers. In Chapter 15 we examined the relative merits of distributing cash transfers versus food transfers (a particular type of in-kind transfer). Drawing on the analytical tools presented there, as well as the concepts presented in this chapter, articulate as carefully and completely as possible the potential benefits and costs of replacing a program that spreads information about the importance of using bed nets and distributes free bed nets to targeted households by a program that spreads the identical information and that follows the same targeting criteria, but distributes cash transfers equal in value to the local cost of buying a bed net (rather than distributing the bed nets themselves). Under what conditions are the benefits most likely to outweigh the costs? Potential benefits of shifting from info and free distribution of bed nets to info and cash distribution: richard@qwconsultancy.com

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Chapter 22

• •

• • •

Increase the perceived well-being of participants, by giving them the freedom to spend the additional income as they wish rather than tying it to the use of bed nets If the private sector is more efficient than the public sector at bringing bed nets into the community, and if private providers are competitive, then the local price of a bed net in the private sector is less than the total cost of buying and distributing the bed nets under the public distribution, potentially reducing budgetary cost. Possibly reduce leakage if non-poor people feel their collection of free bed nets is more justifiable than their collection of cash benefits. Possibly increase coverage of the poor, if they find cash more attractive than bed nets. Reduce waste of bed nets that are distributed and not used.

Potential costs: • Reduce the number of participants who acquire bed nets. o This might be especially large if it takes some effort to purchase a bed net – present bias might cause people to procrastinate, even if they believe it is a good idea to purchase a bed net. • Among those who acquire bed nets, possibly reduce the motivation to use them on a daily basis, through a sunk cost effect (though experimental evidence cited in the paper casts doubt on this) • Possibly increase leakage if the non-poor find it more attractive to try to obtain cash than bed nets. Problem 2: Consider two potential buyers of health insurance. Each maximizes expected utility and each experiences utility in any state of the world that depends on his consumption expenditure (in pesos) C and his level of health H. Each knows that he will be hit by a health shock with probability 0.5. If not hit by a health shock, he will enjoy C=100 and H=100. When hit by health shock, his health will fall to zero if he does not obtain care, but his health can be maintained at 100 if he purchases health care for 100 pesos. Potential Buyer A’s utility function is uA(C,H) = C + 2H, and Potential Buyer B’s utility function is uB(C,H) = C0.5 + 2H0.5. An insurer charges a premium p for a health insurance contract that pays the buyer 100 pesos in the event the buyer is hit by the health shock. The premium must be paid before the state of the world is revealed. a. Which potential buyer is risk neutral? Which is risk averse? How can you tell? (You may wish to review the discussion of risk and expected utility in Chapter 10.)

Chapter 22

Individual A is risk neutral, while Individual B is risk averse. It is the concavity (i.e. having a decreasing rather than constant slope) of the utility function (with respect to either of its arguments) that renders the person risk averse. b. Show that in the absence of insurance, both potential buyers would choose to obtain health care if hit by the health shock (rather than suffer the health loss associated with the shock). Both potential buyers would choose to obtain health care if hit by the health shock (rather than suffer the health loss associated with the shock), because buying care is an exchange of 100 units of currency for 100 units of health, and 100 units of health adds more to utility than 100 units of consumption (in either utility function). c. What is the expected value of the insurer’s indemnity payout to a buyer? The expected value of the insurer’s payout to a buyer is the probability of having to pay times the quantity that would have to be paid. This is .5*100=50. d. What is the highest premium Potential Buyer A would just be willing to pay for the health insurance contract? What is the highest premium Potential Buyer B would pay? Why is one willing to pay more than the other? To find the highest premium Potential Buyer A would just be willing to pay for the health insurance contract, we find the size of the premium at which the expected utility he obtains without insurance is just equal to the expected utility with insurance. His expected utility without insurance (but purchasing health care) is 0.5(100+2*100) + 0.5(0+2*100)=250. His expected utility if he buys insurance is 0.5(100-p+2*100) + 0.5(100-p+2*100)=300-p (where p is the premium). The highest premium he would pay is the premium that sets 300-p equal to 250, or p=50. For Potential Buyer B, his expected utility without insurance is 0.5(10 + 2*10) + 0.5(0 + 2*10)=25. His expected utility with insurance is 0.5((100-p)0.5 + 2*10)+0.5((100-p)0.5 +2*10)=(100-p)0.5+20. The highest premium he would pay for insurance is the premium sets these two expected utilities equal. If 25 = (100-p)0.5 + 20, then (100-p)=52=25 and p=75. Potential Buyer B is willing to pay more because he is risk averse. e. Extrapolating from what you have seen here, discuss in intuitive (i.e. nonquantitative) terms the conditions under which an insurer could break even when supplying health insurance contracts, even when the insurer incurs transactions costs in addition to the costs of expected indemnity payouts. If potential buyers were risk neutral, they would be willing to pay a premium equal to the expected value of the payout to them under the insurance contract. Potential buyers who are risk averse are willing to pay more, suggesting that even when insurers must cover transaction

Chapter 22

costs as well as the costs of providing promised indemnities, they may find it profitable to provide insurance services. Problem 3: Consider two potential buyers of health insurance who purchase health care (preventing any impact on their health) whenever hit by a health shock (much like the potential buyers in question 2). We may therefore think of health shocks as affecting only the potential buyers’ consumption expenditure, and we may describe their utility in any period as a function only of their consumption expenditure. Potential Buyer A’s utility in any state of the world is given by uA(C) = C, and Potential Buyer B’s utility is given by uB(C) = C0.5, where C equals consumption expenditure in pesos. Each faces three possible states of the world, each of which occurs with probability of 1/3. In the best state, the potential buyer is hit by no health shock and enjoys C=200. In both the intermediate and worst states of the world, he is hit by a primary health care shock, which reduces his consumption by 30 pesos. In the worst state of the world, he is also hit by a catastrophic health care shock that diminishes his consumption by 60 pesos. In the absence of insurance, then, his consumption falls to 170 in the intermediate state of the world and to 110 in the worst state of the world. An insurer offers two insurance contracts. Contract 1 pays 30 pesos in the event of a primary health shock. Contract 2 pays 60 in the event of a catastrophic health shock. a. What is the expected value of the insurer’s indemnity payout to a buyer under each contract? The expected payout under the primary care coverage contract is (2/3)*30=20. The expected payout under the catastrophic coverage contract is (1/3)*60=20. b. If offered the opportunity to purchase only Contract 1 for a premium of 20, paid before the state is revealed, would Person A accept? Would Person B? Explain. For Person A, his expected utility without insurance is (1/3)*200 + (1/3)*170 + (1/3)*110=480/3=160. His expected utility if paying 20 for contract 1 is (1/3)(180) + (1/3)(180) + (1/3)(120)=480/3=160. Person A would be willing to accept, but would not have a strong positive reason to purchase. For Person B, his expected utility without insurance is (1/3)(200)0.5 + (1/3)(170)0.5 + (1/3)(110)0.5= approximately 37.67. His expected utility when paying 20 for Contract 1 is (1/3)(180)0.5 + (1/3)(180)0.5 + (1/3)(120)0.5=37.79. Person B would indeed prefer to purchase this contract rather than remain completely uninsured.

Chapter 22

c. If offered the opportunity to purchase only Contract 2 for a premium of 20, paid before the state is revealed, would Person A accept? Would Person B? Explain. Person A’s expected utility under this contract is (1/3)(180) + (1/3)(150) + (1/3)(150)=480/3=160. This is the same as the expected utility without any insurance, so Person A would be willing to purchase this contract. Person B’s expected utility under this contract is (1/3)(180)0.5 + (1/3)(150)0.5 + (1/3)(150)0.5 = 37.911. This is greater than his expected utility without any insurance, so he would be willing to buy this. d. If offered the opportunity to purchase only one of the two contracts for a premium of 20, would Person A prefer Contract 1, prefer Contract 2 or be indifferent between the two? What about Person B? Explain. Person A would be indifferent between the two, because his expected utility is the same under the two contracts. Person B would prefer Contract 2, because his expected utility is higher under Contract 2. e. Explain as intuitively as possible why, for at least one of the two potential buyers, Contract 2 (which offers catastrophic care insurance) is more valuable than Contract 1 (which offers the same expected value of indemnity payments but covers primary care shocks). For a risk averse individual, adding a dollar to consumption in a state of the world when consumption is lower adds more to expected utility than adding a dollar to consumption in a state of the world when consumption is higher. Boosting Person B’s consumption when he has been hit by a catastrophic shock, which pushes him to a lower consumption level is, therefore, more valuable to him than boosting his consumption by the same amount in a state of the world when his consumption starts at a higher level.