Instructor Solution Manual For Public Finance in Canada, 6ce Rosen ISBN:1265255466 · ISBN-9781265255 by StudyGuide

Suggested Answers to Exercises

Instructor Solution Manual For Public Finance in Canada, 6ce Rosen Chapter 1-21With Appendix

Chapter 1 1. Canada’s system of government is decentralized in several ways. Most notably, especially relative to other federal countries, is the high share of subnational government expenditures as a share of total general government expenditures. In addition, responsibility over core areas of public services — including healthcare, education, social services, and so on — are the jurisdiction of provincial governments. Finally, except for only certain taxation sources (such as customs import duties), provincial governments have access to all the major sources of taxation, including income and consumption taxes. The historical reason for this decentralized system was the compromised required during early Confederation negotiations between British North American colonies. Leaving areas that were of local concern remained with provincial governments allowed diverse regions to adopt different policies. 2. a. This will increase the impact of government on the economy, as such a regulation will affect business spending decisions, labour force participation decisions, and more. It will not affect standard measures of the size of government since the expenditures will be done by private employers rather than the government. b. This will increase the impact of government on the economy, for reasons detailed in part a. But, unlike a requirement for private employers to provide daycare services, this will increase standard measures of the size of government. Such daycare subsidies will increase measured government expenditures. c. This will increase the impact of government on the economy, also for reasons detailed in part a. In addition, directly running daycare centres will also increase standard measures of the size of government since purchases of goods and services required to run these centres will count as government expenditures. d. This may or may not affect the impact of government on the economy since it is an intergovernmental grant and therefore doesn’t mechanically affect total general government revenue or expenditures. It will affect standard measures of the size of government by shrinking the federal government’s expenditures. Depending on the measure, it will also shrink provincial government revenues (though not own-source revenues, unless provinces respond by raising taxes). 3. Government provided loans do not initially affect overall expenditures, since they increase government liabilities and are therefore a balance sheet transaction. But debt service costs for government, which is borrowing on behalf of such individuals or businesses, will be an expense. In addition, such loans are not risk free, and covering losses will be a government expenditure. In addition, depending on the interest rate charged on such loans, there may be increased government debt services costs due to government borrowing may not be offset by payments by the individual or business receiving the loan. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 4. a. Real per capita spending has increased from less than $21,000 to over $30,000 over this period. Even excluding the COVID-related increase in spending in 2020, real per capita spending was over $25,000 in 2019. This indicates that total expenditures have increased at a faster rate than population growth plus inflation. b. The size of government has increased in terms of its real per capita size. The size of government relative to the overall economy—the fiscal burden of government, one could say — decreased from over 47 percent in 1990 to just over 40 percent in 2019. The increase to over 52 percent of GDP in 2020 is accounted for largely due to COVID-related emergency measures. Excluding that year, the share of overall economic activity accounted for by government has declined. 5. Reductions in tariffs rates will decrease customs import duty revenues of the federal government. Provincial, local, and Indigenous governments do not levy tariffs on international trade transactions, which are a strictly federal jurisdiction. But most provincial and some Indigenous governments levy taxes on consumption goods, of which imports are a part. Trade agreements may increase the total amount of taxable consumption spending and therefore may increase revenues of these governments. 6. Higher payroll taxes will likely increase government revenues and decrease provincial government deficits. Such taxes need not affect the size of provincial expenditures, however, so whether they increase the size of budgets in general depends on the measure one has in mind. These taxes affect the government’s role in the economy because they will change the cost of hiring labour or the returns to individuals for working. Whether this materially affects hours worked or employment is an empirical question. 7. Provincial governments have access to nearly all the major sources of taxation revenues. They cannot levy tariffs on imports or levy property taxes on federally owned property, but otherwise can levy taxes on income, consumption, property, and so on. Approximately half of overall provincial revenue comes from taxation sources. Local governments have very limited access to taxation and can normally only levy taxes on property within their municipal boundaries. Indigenous governments vary in terms of their access to taxation revenues. Some have access to taxation revenues including on income, on consumption through the First Nations Goods and Services Tax, or on property within reserve lands. 8. Government Expenditures before and after Intergovernmental Grants (millions of dollars) Federal Government

Provincial Governments

Local Governments

Including Excluding Including Excluding Including Excluding Grants Grants Grants Grants Grants Grants 2019 350,327 242,759 514,047 444,465 176,732 176,446 Source: Statistics Canada data table 36-10-0450-01.

Total Excluding Grants 851,470

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Suggested Answers to Exercises An increase in federal grants to provincial governments will increase federal expenditures including grants but have no effect on expenditures excluding grants. Provincial government revenues will increase, but not necessarily lead to an increase in expenditures either including grants or not. The additional federal grants in 2020 could increase provincial expenditures excluding grants if they are made conditional on provincial governments increasing their activity in certain areas, and if provincial governments do not lower their expenditures in other areas by an offsetting amount. If federal grants to provincial governments are earmarked for local governments (say, public transit support) then they will increase provincial expenditures including grants. But, in total, intergovernmental transfers will not affect total general government expenditures, unless, as mentioned, they are made conditional on increasing spending in specific areas and are not offset by reductions elsewhere.

Chapter 2 1. No. The marginal rate of substitution of beer for pizza (MRS) is 2 for Hamlet and 3 for Ophelia. This violates the necessary condition for a Pareto efficient allocation.

2. Although the economy is operating on the production possibilities frontier, the MRT will be less than the MRS because the quota causes the apples market to clear at a price exceeding the marginal cost. We can represent this situation with the following diagram.

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Suggested Answers to Exercises

3. If individuals are not permitted to substitute apples for bananas by trading or selling, then the MRS of individuals who like apples a lot will exceed the MRS of those liking apples little. If trade were permitted, the first type of individuals would acquire apples from the second type, and consequently the MRS of the first type would decline while the MRS of the second type would rise. This process would continue until the MRS is the same across individuals.

4. a. The marginal rates of substitution for coffee and for tea are constant for both Hannah and Jose. Hannah would trade ¼ pound of coffee for ⅓ pound of tea to remain equally satisfied. Similarly, Jose would trade ¼ pound of tea for ⅓ pound of coffee to remain equally satisfied. The constant MRS means linear indifference curves b. Green indifference curves are Jose’s and red indifference curves are Hannah’s.

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Suggested Answers to Exercises

c. The contract curve follows the bottom and right borders of the Edgeworth Box. At any interior point in the box, the parties will find it in their interest to trade until they reach these borders. This is because Hannah would only choose to consume tea once she has consumed all the coffee in the economy. Likewise, Jose would only choose to consume coffee once he has consumed all the tea in the economy. d. The initial allocation is not Pareto efficient. It is possible to make one better off without making the other worse off. 5. a. If John had one loaf of bread, he would be willing to give up 10 kilos of cheese for an additional loaf of bread. If Marsha had one loaf of bread, she would be willing to give up 5 kilos of cheese for an additional loaf of bread. b. The initial allocation at point a in the Edgeworth box is not Pareto efficient because John is willing to given up 2/3 of a kilo of cheese for an extra loaf of bread while Marsha would be willing to accept 1/3 of a kilo of cheese for a loaf of bread. Marsha should give John some bread in exchange for cheese.

c. Along the contract curve:

MRSbcJ 

10 5  M  MRSbcM or xbJ  2 xbM . J xb xb

Since xbJ  xbM  30, xbM  10 and xbJ  20 along the contract curve. The contract curve is a vertical line at xbJ  20.

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Suggested Answers to Exercises 6. Point a represents an equal allocation of water, but it is not efficient because there is no tangency. Point b is an efficient allocation (but not the only one).

AD:

1) the dashed line is positioned at the halfway point on the horizontal axis. 2) point b is a tangency

If Americans have a higher MRSwb than Canadians, then there are gains for residents of both countries if Canada exports water to the U.S. in exchange for bread. 7. The marginal rate of transformation between foreign and domestic movies depends on the ratio of their prices before taxes and subsidies. Because of the wedge created by the taxes and subsidies, the two price ratios are different. Therefore, the marginal rate of substitution and marginal rate of transformation are not equal, and the allocation of resources is inefficient. 8. a. Social indifference curves are straight lines with slope of –1. As far as society is concerned a ―util‖ to Augustus is equivalent to a ―util‖ to Livia.

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Suggested Answers to Exercises b. Social indifferences are straight lines with slope of –2. This reflects the fact that society values a ―util‖ to Augustus twice as much as a ―util‖ to Livia.

9. In this case, the ―Edgeworth Box‖ is actually a line because there is only one good on the island. The set of possible allocations is a straight line, 100 units long. Every allocation is Pareto efficient, because the only way to make one person better off is to make another person worse off. There is no theory in the text to help us decide whether an allocation is Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises fair. Although splitting the peanuts even between the people may be fair, it may not be fair if the calorie ―needs‖ of the people are different. With a social welfare function, we can make assessments on whether redistribution for society as a whole is a good thing. 10. Social welfare is maximized when Mark’s marginal utility of income is equal to Judy’s marginal utility of income. Taking the derivative of Mark’s utility function to find his marginal utility function yields MUM = 50/(IM1/2) and taking the derivative of Judy’s utility function yields MUJ = 100/(IJ1/2). If we set MUM equal to MUJ, the condition for maximization becomes IJ = 4IM and, since the fixed amount of income is $300, this means that Mark should have $60 and Judy should have $240 if the goal is to maximize social welfare = UM + UJ. 11. a. If the food is evenly distributed between Tang and Wilson, Tang will have 14.14 units of utility and Wilson will have 7.07 units of utility. b. If the social welfare function is UT+UW, then the marginal utilities of both should be equal to maximize social welfare. Equate MUT=1/(2FT1/2) to MUW=1/(4FW1/2) and substitute FT=400-FW. Therefore, FT=320 and FW=80. c. If the utility of both Tang and Wilson must be equal, then set UT=UW and substitute FT=400-FW and solve. Therefore, FT=80 and FW=320. 12. a. False. As shown in the text, equality of the marginal rates of substitution is a necessary, but not sufficient, condition. The MRS for each individual must also equal the MRT. b. Uncertain. As long as the allocation is an interior solution in the Edgeworth box, the marginal rates of substitution must be equal across individuals. This need not be true, however, at the corners where one consumer has all the goods in the economy. c. False. A policy that leads to a Pareto improvement results in greater efficiency, but social welfare depends on equity as well as efficiency. A policy that improves efficiency but creates a loss in equity might reduce social welfare. d. False. Moving to a point on the utility possibilities curve may not result in a Pareto improvement because one party may receive less utility on the curve than they received at the interior point. 13. a. In this particular insurance market, one would not expect asymmetric information to be much of a problem – the probability of a hurricane is common knowledge. Moral hazard could be an issue – people are more likely to build near a beach if they have hurricane insurance. Still, one would expect the market for hurricane insurance to operate fairly efficiently.

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Suggested Answers to Exercises b. There is substantial asymmetric information in the markets for medical insurance for consumers and also malpractice insurance for physicians. For efficient consumption, the price must be equal to the marginal cost, and the effect of insurance may be to reduce the perceived price of medical care consumption. That would lead to consumption above the efficient level. Because of the roles of regulation, insurance, taxes, and the shifting of costs from the uninsured to the insured, there is little reason to expect the market to be efficient. c. In the stock market, there is good information and thousands of buyers and sellers. We expect, in general, efficient outcomes. d. From a national standpoint, there is a good deal of competition and information with regards to MP3 players and music. The outcome will likely be efficient for MP3 players and music. However, some firms might exercise some market power through high brand awareness and proprietary downloading systems. e. The private market allocation is likely inefficient without government intervention. Student loan markets may suffer from asymmetric information – the student knows better than the lender whether he will repay the loan or default on it, a form of adverse selection. Government intervention does not ―solve‖ the adverse selection problem in this case (because participation in the student loan program is not compulsory), but it may create a market that would not exist without intervention. f.

The market for housing is likely to be relatively efficient. Some inefficiencies may exist, such as asymmetric information—the seller knows more about the house than the buyer—and differentiated products. But, the market has developed to mitigate these inefficiencies. For example, a buyer can employ a home inspector to help him understand more about the quality of the home. Also, a large number of homes on the market increases competition.



It is individualistic. Welfare economics focuses on individual preferences and allocations that maximize utility. If preferences are ill-formed, perhaps due to one of many psychological biases for example, then maximizing those preferences may not be appropriate. There may also be societal goals that are neglected by the framework of welfare economics.



It focuses on outcomes. Welfare economics focuses on the results of an allocation as the basis for its analysis. It does not distinguish between alternative ways in which any given allocation may be achieved. If the process through which allocations are determined matters — such as whether decisions over allocations by governments are made within a transparent and democratic process — then welfare economics will have little to say.

14.

Chapter 3 1. A benefit-cost ratio is an unsatisfactory way of describing the payoff from a project because benefits can be redefined as cost reductions, making the B/C ratio arbitrary. If there is an

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Suggested Answers to Exercises alternative project to the Oldman Dam, then the B/C ratio cannot be relied on for choosing between them. 2. a. The appropriate cost is the (estimated) equilibrium wage. Here labour is obtained at the expense (opportunity cost) of leisure. The free-market wage measures the value of leisure foregone at the margin. b. Here labour is obtained at the expense of other employers and the sacrifice involved is the value of output in the alternative jobs. Since private firms will hire until the value of marginal product equals the existing (union) wage, this wage measures the appropriate cost of labour. 3. The increased time spent at the inspection must be counted as a cost of the program. One reasonable way to estimate the value of the time would be to use the average wage rate in the province. 4. The present value of $25/0.10 = $250. Letting x = 1/(1+r) and using the sum of the infinite series provided, yields that the present value of the perpetual annual benefit (starting next year) = BX + BX2 ... Bn = B(x/(1-x)) = B(1/r) = B/r. 5. a. 1,000 = 80/  and therefore  = .08 b. If the money comes from consumer spending, use after-tax rate of interest as the discount rate: and therefore the project is admissible. But if the money comes from investment, use before-tax rate of interest as the discount rate: and therefore the project is not admissible. Finally, in the ―mixed case,‖ for a discount rate, take a weighted average: and this implies and therefore there is no net advantage to undertaking the project. c. Benefits = 80/.04 = 2,000. Present value of project = 2,000 – 1,000 = 1,000. d. Inflation is fully anticipated, and if market interest rates increase by 10 percentage points, nothing changes in real terms. 6. $100 billion invested for 50 years at 5 percent per year would generate over $1.1 trillion, which is more than the $700 billion in damage caused by the climate change. There might be other considerations offered when evaluating this proposal, but the critic is correct from a financial standpoint. 7.

At P=$1,000 the equilibrium quantity is 7,000, while at P=$600 the equilibrium quantity is 7,200. The change in consumer surplus is 2.84 million. Yes, it is worth undertaking the project because the benefits exceed the cost of $28.1 million.

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Suggested Answers to Exercises

8. The ―labour game‖ suggests that jobs and the wages paid to people in those jobs are considered by some to be one benefit of a public project. In fact, the wages are a cost and this cost can only be partially offset if the people were truly unemployed before the project. 9. The ―labour game‖ suggests that jobs and the wages paid to people in those jobs are considered by some to be one benefit of a public project. In fact, the wages are a cost and this cost can only be partially offset if the people were truly unemployed before the project. The ―green‖ jobs plays the ―chain-reaction‖ game, because they are secondary profits. 10. a. Bari is willing to pay 25 cents to save 5 minutes, so they value time at 5 cents per minute. The subway saves him 10 minutes per trip, or 50 cents. The value of 10 trips per year is $5. The cost of each trip is 40 cents, or $4 per year. The annual net benefit is therefore $1. The present value of the benefits = $5/.25 = $20; the present value of the costs is $4/.25 = $16. b. Total benefits = $20 × 55,000 = $1,100,000. Total costs $16 × 55,000 = $880,000. Net benefits = $220,000. c. Costs = $1.25 × 55,000 = $68,750. Benefits = benefit = $21,250.

. And net

d. The subway project has a higher present value. If a dollar to the ―lower-income‖ is valued the same as a dollar to the ―middle class,‖ choose the subway project. e. Let  be the distributional weight. Solve for it by setting (

)

which yields  = 3.21. Chapter 4 1.

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Suggested Answers to Exercises a. A wilderness area is an impure public good—at some point, consumption becomes rival. b. The benefits of prisons accrue to the entire population. They are a public good. c. Peacekeeping in Sudan is a public good because residents of other countries benefit (if only because they are concerned about the well-being of residents of Sudan). This benefit is also non-rival. d. Television signals are non-rival in consumption and non-excludable unless the signal is scrambled. e. An internet site is non-rival in consumption, but it is excludable. 2. a.

b. They should hire the coach for 4 hours. This is where the total MB = MC.

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Suggested Answers to Exercises

The efficient level is where the Total MB = MC which is Z*= 4/3. 4. We assume that the animal’s utility does not enter the social welfare function, hence its allocation of labour supply across activities does not matter. a. The public good is patrol; the private good is fruit. b. Recall that efficiency requires MRS Person 1 + MRS Person 2 = MRT. MRS Person 1 = MRS Person 2 = 2. But MRT = 3. Therefore, MRS Person 1 + MRS Person 2 > MRT. To achieve an efficient allocation, the animal should patrol more. 5. The GPS signal is a non-rival good: there is no additional cost in allowing citizens to benefit from receiving an accurate signal. Thus, efficiency requires GPS signals to be available at a price of zero. The receivers, on the other hand, are pieces of equipment which are rival in consumption and so should not be publicly provided for free. 6. Some ships carry more valuable cargo. They would have a higher marginal benefit curve for lighthouses than other ship owners. 7. The total tax revenue required to finance the snowplowing is R = 16Z. With distortionary taxation, the optimal provision is determined by the following condition, assuming that snowplowing does not affect tax revenues: MB1 + MB2 = MCF · MC 20 – 3Z= (1 + 0.0002441(16Z)2)·16 Z=1 8. It seems quite possible to write complete contracts for routine airport security tasks such as baggage screening. In that case, the government could set standards and monitor the Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises performance of private security firms. These firms would have a profit-maximizing incentive to adopt technologies that keep costs down while meeting the contract requirements. The argument for public production of airport security is that it may be impossible to write a contract to cover all eventualities. Furthermore, private firms might skimp on training their workers in order to increase profits. Chapter 5 1. a. SARS (sudden acute respiratory syndrome) is a contagious illness that can lead to death. Those infected can unknowingly infect others through close contact. This is a negative externality. There is no vaccine available. Publicly financed or provided public health measures, such as quarantine of infected individuals, are one possible response. b. H1N1 flu is also contagious in the same way as the common cold or other flus. Individuals with the flu can infect others, generating a negative public health externality. A flu vaccine is available which could be subsidized or be offered for free by government to those who choose to get it. The vaccinations generate a positive externality to those who choose not to get the vaccination since their risk of catching the flu is reduced. c. Fuels like firewood, dung, and charcoal for indoor cooking and heating in rural households in Sub-Saharan Africa and China can lead to severe health consequences for those who live in that household, especially women who are involved in cooking, and young children. Here, the negative externality from undertaking this activity is greatest for household members, although there may be wider implications as well. Subsidizing more efficient and less polluting stoves is one possible response. d. Driving on a congested highway generates a number of negative externalities including pollution, time delays for other drivers, and increasing the risk of accidents (and the related costs associated with this) for others. Tolls specific to congested roads or time of day are one possible government response. Other responses like gasoline taxes can indirectly help to address these negative externalities. In the case of an uncongested road, pollution externalities continue to be present but may be less than in the case of a congested road. External costs due to accidents are also likely to be significantly lower while the time delay externalities will disappear. 2. The Singh family produces a positive externality by providing the lights that others enjoy. The visitors create a negative externality for each other and the neighbourhood by tying up traffic. Resources are not usually allocated efficiently in externality situations. In this case, one can imagine charging an entrance fee, which could deal with the congestion problem. 3.

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Suggested Answers to Exercises

a. ̅ (where MBP and MCP intersect). b. See schedule MSBp. c. P * . Grant a unit subsidy of $b per party. d. Total subsidy = abcd. ―Society‖ comes out ahead by ghc, assuming the subsidy can be raised without any efficiency costs. (Cassandra’s friends gain gchd; C loses chd but gains abcd, which is the cost of the subsidy to taxpayers). 4. a . T h e e q u i l i b r i u m q u a n tity of vaccinations is 100 per month at a price of $55 per vaccination. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises c. The efficient quantity of vaccinations per month is 125. The subsidy required to achieve this is equal to the marginal external benefit at the efficient output or $16.25 (35-0.15(125)). d. The net gain to society from increasing the number of vaccinations from 100 to 125 is given by area abe or $250. There is an increase in social benefits of $1750 (area abcd), of which $453.125 are external. Additional costs are equal to area bcde or $1,500. Alternatively, private benefits increases by $1,265.625, producer surplus increases by $562.5, and external benefits increase by $453.125. Subsidy costs equal $2,031.25. Therefore, the net change in surplus is $1265.625+$562.5+453.1252031.25 = $250. The question also asks: who gains and loses under this plan? The producers gain under this plan, as do those whose risk of contracting hepatitis has been reduced (either directly because an individual received a vaccination or indirectly because there will be fewer infected individuals to come into contact with). To the extent that subsidies are financed using distortionary taxes, these taxes impose efficiency losses (or reductions in social surplus) elsewhere in the economy. 5. a. Abatement generates a 150 Mt reduction in emissions. Given E=600 Mt, the marginal cost associated with reducing emissions by one unit is $9 while the marginal benefit associated with one additional Mt reduction in emissions is $24. b. Total abatement costs are equal to $675 -- the area abc in the following figure. The total benefit associated with a reduction in emissions from 750 Mt to 600 Mt is equal to area cedb or $4050.

c. The socially optimal level of emissions is 450 Mt where the marginal benefit of an additional one unit reduction in emissions is just equal to the marginal cost of abatement. Moving to reduce emissions by one more unit generates additional abatement costs (slightly greater than $18) while the additional benefit generated (the reduction in damage) is valued at just less than $18. Therefore, it is not socially optimally to reduce emissions below 450 Mt.

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Suggested Answers to Exercises d. With the emissions tax, the firm pays $12 on each Mt of emissions. So, in the absence of any abatement activity, the tax bill equals $9,000 (750 Mt x $12). However, the tax bill can be reduced if some abatement activity occurs. As long as the marginal abatement cost is lower than the tax, there is an incentive to reduce emissions. In the presence of the tax, the level of emissions falls to 550 ($12 = MAC = 45-0.06E). Lowering emissions below 550 Mt generates additional abatement costs in excess of tax savings and would not be undertaken. The tax would need to be increased to $18 per Mt in order to achieve the socially optimal level of emissions. 6. Private Marginal Benefit = 10–X Private Marginal Cost = $5 External Cost = $2 Without government intervention, PMB = PMC; X = 5 units. Social efficiency implies PMB = Social Marginal Cost = $5 + $2 = $7; X = 3 units. Gain to society is the area of the triangle whose base is the distance between the efficient and actual output levels, and whose height is the difference between private and social marginal cost. Hence, the efficiency gain is ½ (5–3)(7–5)=2. A Pigouvian tax adds to the private marginal cost the amount of the external cost at the socially optimal level of production. Here a simple tax of $2 per unit will lead to efficient production. This tax would raise ($2) (3 units) = $6 in revenue. 7. a. If you know who was cooking, the externality is easy to identify, and depending on how many students are involved, the costs of negotiation should be fairly small. Assuming you could establish property rights, the Coase Theorem may apply. b. The Coase theorem is not applicable because the number of affected individuals may be very large and the cost of negotiation may be excessive. c. The Coase theorem is applicable because the number of individuals affected is small. 8. This is an example of an infra-marginal externality. Consider a simple example to illustrate. The private marginal demand for gardens, G, (measured in number of garden beds) is given as PMB in the figure below. The private marginal cost of supplying gardens is given by PMC. The marginal external benefit curve captures the additional external benefits generated to others from additional flower beds. Absent government intervention, the number of flower or garden beds in the neighbourhood equals G*, where PMC = PMB. The efficient number of flower beds is the number that ensures the social marginal benefit from an additional flower bed just equals the social marginal cost (which in this example equals PMC). Note that because the external benefits are exhausted at a relatively low level of G, the efficient G is the same as achieved in the competitive equilibrium (i.e. G*). In this case there is no market failure and no government intervention required.

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Suggested Answers to Exercises

9. a. Under proposal 1, Azul and Madrid both reduce emissions from 50 units to 41 units. Azul incurs abatement costs equal to $405 (area A in the panel a below) while Madrid incurs abatement costs of $810 (areas A+B in panel a), for total abatement costs equal to $1215. Under proposal 2, Azul and Madrid each reduce emissions until his MAC just equals the $120 fee. Azul reduces emissions by 12 units while Madrid reduces his emissions by 6 units. Azul incurs abatements costs equal to $720 (area xys in panel b) while Madrid incurs costs equal to $360 (area wzs in panel b) for a total cost of reducing emissions of $1080. Under proposal 3, the government initially gives Azul and Madrid 41 permits each. If Azul and Madrid do not trade permits, the outcome and abatement costs would be the same as under proposal 1. However, under a cap-and-trade scheme, Azul and Madrid are free to trade permits. Given the initial distribution, Azul’s marginal abatement cost is lower than Madrid’s. This gives Azul an incentive to reduce his own emissions and sell some of his permits to Madrid. Azul and Madrid will trade permits until MACA = MACM, which is the cost-effective solution. Total emissions will fall by 18 units. After trading, Azul will hold 38 permits and Madrid will hold 44 permits. The market price for permits equals $120 and ensures that marginal abatement costs are equalized. At this price, Madrid will purchase 3 permits from Azul, allowing him to reduce emissions by 6 units rather than 9. This abatement costs are the same as the solution achieved with the emissions fee. Azul incurs abatements costs equal to $720 (area xys in panel b) while Madrid incurs costs equal to $360 (area wzs in panel b) for a total cost of reducing emissions of $1080. b. From an efficiency perspective, proposals 2 and 3 both bring about a reduction in emissions equal to 18 units with a total of $1080 in abatement costs. Proposal 1 achieves the same emissions reduction but at higher cost. Thus, from an efficiency perspective, proposals 2 and 3 are preferred to 1. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises c. Consider some of the distributional consequences for Azul, Madrid and the government. Under Proposal 1, Azul incurs abatement costs of $405. And Madrid incurs abatement costs of $810. In the case of the emissions fee, Azul incurs higher abatement costs equal to $720 and pays $4560 ($120 x 38 units) in emissions fees to the government. Madrid incurs relatively lower abatement costs of $360 and pays emissions fees equal to $5280. The government receives a total of $9840 in emissions fees. Under proposal 3, the government receives no revenue since permits are distributed free of charge. Azul is better off (relative to proposal 2) because instead of having to pay taxes, he receives a payment of $360 for the 3 permits he sells to Madrid. Madrid is also better off relative to proposal 2 since he avoids paying emissions fees to the government. Madrid must pay $360 for the purchase of the extra permits.

10. This could be a very sensible policy, because it may be substantially less expensive to reduce emissions from those old polluting cars than to install expensive technology at a company. It should be established that the source of these pollutants is not important in affecting their impacts. Also, the cars purchased must really be removed from the road, rather than to the back yard or shipped to other provinces where auto emissions are not a problem.

Chapter 6 1. The table below shows Canadian income shares by quintile for in 2020:

Income Quintile

Market Income (before taxes and transfers)

Total Income (before taxes and after transfers)

After-tax Income (after transfers)

Lowest quintile Second quintile Third quintile Fourth quintile Highest quintile

3.6 9.7 16.4 25.3 44.9

6.9 12.7 17.9 24 38.5

7.8 14.6 19 23.8 34.8

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Suggested Answers to Exercises Source: Statistics Canada, data table 36-10-0587-01.

a. See table below for cumulative income shares: Cumulative Income Shares Income Quintile

Market Income (before taxes and transfers)

Total Income (before taxes and after transfers)

After-tax Income (after transfers)

Lowest quintile Second quintile Third quintile Fourth quintile Highest quintile

3.6 13.3 29.7 55 100

6.9 19.6 37.5 61.5 100

7.8 22.4 41.4 65.2 100

b. See Lorenz Curves below:

Note that the Lorenz curve based on after tax, after transfer income lies everywhere closer to the line of complete income equality while the Lorenz curve using market income lies furthest away. The tax-transfer system has quite a significant impact on the cumulative income shares and in redistributing income. The redistributive impact of in-kind benefits are, however, not captured by these data.

c. If we look at the Gini coefficient, we see that government taxes and transfers have reduced income inequality. While the Gini coefficient is a useful summary measure, it does not provide any information about changes in income shares at different points in the income distribution. Consider the case where the Lorenz curves for market income and income after taxes and transfers crossed. The conclusion about whether income inequality has worsened or improved because of government policies would now depend on where you were in the income distribution. This would be evident if income shares or Lorenz curves were used but not so if only the Gini coefficient measured were considered. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises This question was the topic for Andrew Leigh’s 2007 paper, How Closely do Top Income Shares Track Other Measures of Inequality, published in The Economic Journal 117, F619-F633. There is a strong and significant relationship between top income shares and broader inequality measures, such as the Gini coefficient. This suggests that panel data on top income shares may be a useful substitute for other measures of inequality over periods when alternative income distribution measures are of low quality, or unavailable. 2. Reasons for why more women than men live in poverty including: 

Unpaid work: women spend 50% more time in unpaid work—a reality often referred to as a ―second shift‖—which impacts their earnings potential because women are more likely than mean to attempt to balance the challenges of paid and unpaid work by reducing paid work. The biggest contributor to this is that women take on more unpaid caregiving responsibilities (caring for young children and elderly adults) mean more women drop out of the labour force or work part-time which has life-long affects on women’s income.



Lone parent families are more likely to be headed by women, where there is only one potential earner and have at least one dependent child to support, meaning that the income of the one earner has to stretch further than in other families.



Indigenous women living off reserves have a unique set of intersecting experiences (e.g. gender-based violence, colonialism, sexism and misogyny, child alerts) that interact and lead to experiencing poverty at high rates especially off reserve where they lack the societal and cultural supports.



Newcomer and immigrant women face language and cultural barriers and limited social networks. Too often their foreign credentials and professional qualifications are not recognized by Canadian employers.

3. Canada’s Dimensions of Poverty Hub (https://www.statcan.gc.ca/en/topics-start/poverty) shows that broader measures are included in three areas: 

Dignity goes beyond just deep income poverty, but also includes unmet housing needs, unmet health needs, and food insecurity.



Opportunity and inclusion goes beyond low income measures to include the bottom 40% share of income, youth engagement, and literacy and numeracy.



Resilience and security includes the median hourly wage, asset resilience, and low income entry and exit.

Progress is mixed across these measures. 4. The term ―fair‖ is very hard to define precisely. A fair distribution of income might be one in which all people have the basic necessities of life: food, clothing, shelter. Alternatively, a distribution is fair if the processes used to generate it are fair—e.g., equal access to education. In either case, a fair outcome is not necessarily one in which people end up with equal amounts of income or wealth. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

821

Suggested Answers to Exercises 5. Utilitarianism suggests that social welfare is a function of individuals’ utilities. Whether or not the rich are vulgar is irrelevant, so part of the statement is inconsistent with utilitarianism. On the other hand, Stein’s assertion that inequality per se is unimportant is consistent with utilitarianism. 6. If the processes used to generate the income distribution are fair, then one might expect to see mobility in the income distribution as earnings would vary with individuals’ efforts and talents. A snapshot of the income distribution does not take into account changes in income over the life cycle, or the fact that individuals may have low incomes because they chose to work fewer hours, or in low effort jobs. The utilitarian approach has been criticized for emphasizing the snapshot approach. Most welfare programs provide financial support for individuals and families at levels which are below the ―poverty line‖ although deciding what constitutes poverty is very subjective. 7. a. To maximize W, set marginal utilities equal; the constraint is Is + Ic = 100. So, 400 – 2Is = 400 – 6Ic substituting Ic = 100 – Is gives us 2Is = 6 (100 – Is). Therefore, Is = 75, Ic = 25. b. If only Chen matters, then give money to Chen till MUc = 0 (unless all the money in the economy is exhausted first). So, 400– 6 Ic = 0, hence, Ic = 66.67 Giving any more money to Chen causes their marginal utility to become negative, which is not optimal. Note that we don’t care if the remaining money ($33.33) is given to Shi or not. If only Shi matters, then, proceeding as above, MUs = 0 if Is = 100; hence, giving all the money to Shi is optimal. c. MUs = MUc for all levels of income. Hence, society is indifferent among all distributions of income. 8. a. See the following figure:

822

Suggested Answers to Exercises

As above, to maximize W, set marginal utilities equal given the constraint is yM + yS =20,000. Setting MUM = MUS , gives us the social welfare maximizing income distribution of yM = yS=10,000. Social indifference curve are straight lines with a slope of -1 (given by -MUM/MUS ).

823

Suggested Answers to Exercises

As above, to maximize W, set marginal utilities equal given the constraint is yM + yS =20,000. However, in this case, when setting MUM = MUS , we find that the social welfare maximum is achieved when Will’s income is 4 times the income of Grace. Given a total income of 20,000, the social welfare maximizing income distribution is yM = 16,000 and yS=4,000. Social indifference curve are straight lines with a slope of -1 (given by -MUM/MUS ). In the case of the Rawlsian social welfare function, the welfare maximum is achieved by having complete utility equality. This requires unequal incomes but in this case yM = 4,000 and yS=16,000. 9.

825

Suggested Answers to Exercises

Note that the utilities possibility curve looks different from the standard case since it has a positive slope over some of its range (in contrast to the UPC illustrated for question 5). When Wyatt has $4,000 and Gurpret has $16,000, we are on the positively sloped portion of the UPC. By redistributing some income, both individuals can have higher utility (i.e. Pareto redistribution). By redistributing $1,000, both Wyatt and Gurpret are better off. Gurpret would be willing to undertake this transfer themselves. However, if Wyatt has $16,000 and Gurpret has $4,000 we are on the negatively sloped part of the UPC where it is not possible to redistribute income to make one person better off without making someone else worse off. Given this distribution of income, Wyatt would not volunteer to transfer $1,000 to Gurpret (and Gurpret would not be willing to transfer $1,000 to Will either). Students can ponder how society would redistribute income given an additive or utilitarian social welfare function. 10. a. False. While society is indifferent to whether one unit of utility (one ―util‖) goes to Lanh or Jahdahdieh, it is not indifferent to how a dollar is distributed. This would depend on the additional utility Lanh would receive from an extra dollar (their marginal utility of income) in comparison to the increase in utility Jahdahdieh would receive from an extra dollar (their marginal utility of income). Society would prefer to give the dollar to the person who gets the biggest increase in utility since this increases social welfare the most. b. True: By giving an extra ―util‖ to Jonathan, social welfare increases by 8 while an extra unit of utility (or happiness) to Lanh increases social welfare by 1. This social welfare function weights more heavily increases in Jahdahdieh’s happiness. c. True, if the two individuals have utility functions. In this case, then with this type of social welfare function (the maximin social welfare function), there is always scope to increase social welfare whenever there is a difference in utility levels between the two individuals. However, if the two individuals have different utility functions (like in question 6d), then this social welfare function calls for an equal distribution of Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

826

Suggested Answers to Exercises utility, not income. 11. Peregrine participates in the program as long as P1P2ca > cef.

Chapter 7 1. The three main uses of public debt are: a. Shock absorber, such as when during periods of recession, war, pandemic, etc., government borrow to finance current activities. b. Macroeconomic stabilization, such as during recessions or booms when governments change tax rates or expenditure levels in an attempt to affect the economies overall pace of economic growth. c. Aligning costs and benefits of government spending, such as debt-financing a bridge or other infrastructure that has long-lived benefits. Debt allows the costs of such a project to be shifted to future generations that also receive benefits. 2. The effect of each of the following event has on public debt levels is: a. Recession increasing unemployment: to the extent that government tax rates and program expenditure programs are not adjusted in response, public debt will rise due to declining government revenues from lower employment (and therefore lower incomes) and from rising government expenditures from employment insurance payments. b. Private-financed bridge: public debt will not increase, since the debt from this particular project will not be on the government books but on the private corporation. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

827

Suggested Answers to Exercises c. A loan guarantee to a company that goes bankrupt: while the loan guarantee itself does not affect measured public debt, upon the bankruptcy of the corporation the government will need to repay the loan to the creditor. This would likely come with an increase in public debt. d. Interest rates increase: to the extent that higher interest rates increase government deficits, public debt levels will increase. 3. This country’s debt is 80 percent of its GDP, since 2/2.5 = 0.8. 4. A balanced budget does not imply public debt levels will remain constant. In particular, accrual accounting procedures mean that spending on long-lived capital and infrastructure projects are not included in current expenditures. Government may borrow for such projects even if they are not borrowing to cover any gap between revenues and current expenditures. 5. a. A 25 percent tax on employment income raises $2,500 from the Young and $3,750 from the Middle-aged. This could provide a $6,250 benefit to the Old. b. The income after taxes and transfers for the Young, Middle-Aged, and Old generations are $7,500, $11,250, and $6,250, respectively. c. Assuming no discounting, lifetime incomes are $25,000 ($10,000+$15,000). d. Assuming no discounting, lifetime before-tax and transfer incomes are $31,250 ($10,000+$15,000+$6,250). e. If debt was used to finance the elderly benefit, then taxes would not be required and the burden would depend on when debt is repaid and who is liable to fund that repayment. If the $6,250 in benefits was funded from equal borrowing of $3,125 from the Young and the Middle-Aged. If this was then repaid in the following period (when the Young are middle-aged and the Middle-Aged are old, etc.), then ignoring interest payments the initially Young and Middle-Aged would be no better or worse than no elderly benefit, the initially Old would benefit by $6,250, and the future Young would have lifetime incomes $3,125 lower (the tax levied to repay the borrowing from the initially Young and Middle-Aged). 6. We will use

to answer this question.

a. Balanced budget in each period. The tax rate in a year of strong economic growth is 10 percent. The tax rate in a year of poor economic growth is 13.33 percent. The total excess burden in the strong year is dollars. The total excess burden in the poor year is dollars. Total excess burden is then dollars. b. Balanced budget across both periods. The tax rate required is 11.58 percent (from 220/1900). The deadweight loss in the strong year is dollars. The deadweight loss in the poor year is dollars. Total excess burden is then dollars.

828

Suggested Answers to Exercises c. This demonstrates the simple idea that stable tax rates are more efficient than variable ones required to balance in all years. 7. If the economic growth rate is 4 percent and the interest rate is 3 percent, then a sustainable primary budget balance of (

)

That is, a deficit of 0.385 percent of GDP can be sustained without increasing debt levels from the current 40 percent of GDP level. The overall budget balance would be this minus interest payments on the debt, which equal percent of GDP. The overall balance would therefore be -1.98 percent of GDP. 8. If interest rates and growth rates are constant, then starting from Equation 7.2 provided in this chapter, we have

Repeated substitution starting from (

yields )

∑

(

)

If interest rates equal economic growth rates, then this simplifies to ∑ Chapter 8 1. The share of government expenditures accounted for by subnational governments is the expenditure decentralization ratio. Since France’s ratio was 19.8 while Canada’s was 67.8, this measure implies Canada’s system of government is significantly more decentralized than France’s. 2. a. Points QA and QB give the number of firefighters hired in municipalities A and B, respectively, when the constant marginal cost is W1. b. QA´ and QB´ (where QA´ = QB´) are the number of firefighters hired after amalgamation in each municipality. Municipality A experiences a welfare loss equal to ABC. The additional firefighters result in benefits equal to ACQA´QA at a cost of ABQA´QA. Municipality B experiences a welfare loss to A´B´C´ – the fall in costs equals C´B´QBQB´ and the loss in benefits equals A´B´QBQB´. c. The more elastic the demand curves for firefighters in both municipalities, the smaller the welfare loss that occurs when both are required to hire the same number of firefighters. To illustrate this draw more elastic demand curves through points A and B´ (points before uniformity is required) and observe the decrease in the areas ABC and A´B´C´. This reflects a decrease in the welfare loss. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

829

Suggested Answers to Exercises

3. Some of the assumptions are: 

No externalities arise from local government behaviour



Individuals are completely mobile



People have perfect information with respect to each community’s public services and taxes



There are enough different communities so that everyone can find one with public services meeting their demands



The cost per unit of public services is constant, so that if the quantity of public services doubles, then the total cost also doubles

4. An increase in fiscal benefits to residents of one region may lead to higher rates of inmigration to that region than would have occurred if only labour productivity affected individual location choices. In the diagram below, the net productivity loss from this inefficient migration is illustrated as the shaded region marked ―TFP losses‖.

830

Suggested Answers to Exercises 5. a. To the extent that autos tend to be used within a given jurisdiction only, it would make sense for provinces and municipalities to control pollution regulations in order to better match controls to local needs. To the extent that it costs producers less to comply with national-level regulation, a given car is driven in many provinces, or that pollution created in one jurisdiction affects residents in another, it may make sense for the federal government to be in charge. b. Consistent standards across provinces would appear to make sense. c. Provision of weather satellites should be a federal responsibility because there are economies of scale: a single satellite can provide information to users all across Canada. d. Public refuse collection is a natural function for municipal government. 6. The theory of federalism indicates that one of the main purposes of decentralization is to allow people to select bundles of public services and taxes that suit them. The more diverse their tastes, the greater the benefits of being able to pick different bundles, and hence, the greater the benefit to decentralization. Hence, the finding is consistent with the theory. 7. a. A decrease in transfer payments from the federal government should decrease the overall spending by the provincial government because of an inward shift of the budget constraint. b. Replacing conditional grants with unconditional ones could affect the composition of spending if the conditional nature of the grant caused provinces to spend more on social assistance than they otherwise would have. c. If we measure quality as effectiveness per dollar spent, then quality may rise if the conditions associated with the old grant prevented provinces from using the most effective method of delivering the service or may fall if provincial governments fail to take into account the impacts of their social assistance programs on residents of other provinces. 8.

831

Suggested Answers to Exercises

9. AB is the budget constraint before the grant program. ACD is the budget constraint when the grant, equal to AC (=$X), is unconditional. AC´D is the budget constraint when the grant is a matching grant, but closed ended and equal to $X. With the unconditional grant the highest level of welfare is achieved at point P on indifference curve i2. With the closed-ended matching grant, welfare is maximized at point C´ on a lower indifference curve, i 1. If some point along C´D is the maximizing point, the unconditional grant and closed-ended matching grant have a similar effect on consumption.

832

Suggested Answers to Exercises

10. The treatment of non-renewable resources is a contentious issue in Canada. Like the personal income or sales tax, resources generate revenues for provincial governments, and in that respect, should be included if full equalization is the guiding principle. Inclusion of resource revenues in equalization may, however, reduce a province’s resource tax effort and may create a disincentive to further develop resource bases. Another argument against partial or full inclusion focuses on the impact of rising energy prices for the aggregate cost of equalization to the federal government. More detailed discussion can be found in Smart, Michael. "Equalization and resource taxation," in Paul Boothe and Francois Vaillancourt, eds., A Fine Canadian Compromise: Perspectives of the report of the Expert Panel on Equalization and Territorial Formula Finance, Edmonton: Institute for Public Economics, 2007 and in R. Boadway’s submission to the Expert Panel on Equalization and Territorial Financing. 11. This problem uses equalization data provided in an Excel spreadsheet called ―Rosen 6ce_ExcelData_Chapter8_Exercise11‖. The correct calculations are available in an Excel worksheet called ―Rosen 6ce_ExcelSolutions_Chapter8_Exercise11‖. a. The provinces of PEI, Nova Scotia, New Brunswick, and Manitoba are deficient in all bases according to these calculations. Quebec and Saskatchewan are deficient in all bases except for natural resources. Alberta is the only province with a surplus in all five tax bases. b. Based on these illustrative calculations, the total amount of equalization required is $20.577 billion. All provinces are recipients except Ontario, Alberta and BC. In practice, actual equalization entitlements are calculated using a weighted average of the three years prior to the year in question. Other bells and whistles include the fiscal capacity cap, the ceiling in the annual growth of payments, and a few other adjustments. c. If included Alberta’s revenues increase by $5 billion, then the revenues to be equalized increase from about $113.516 billion to $118.516 billion. Assuming provincial shares of the tax base are unchanged, total equalization increases to Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

833

Suggested Answers to Exercises $20.756 billion – an increase of about $0.179 billion. All provinces experience an increase in entitlements except Ontario, Alberta and BC who remain non-recipients. Quebec’s equalization increases the most by $122 million and accounts for roughly 68% of the increase in total equalization.

834

Suggested Answers to Exercises

Data for Exercise 11 corresponds to fiscal year 2019/20

Distribution of Tax Bases, by Province and Revenu NL

Personal Income Taxes

1.22

0.29

2.01

1.45

19.50

41.04

Business Income Taxes

0.62

0.15

1.18

0.88

19.09

46.12

Consumption Taxes

1.34

0.36

2.28

1.85

20.25

39.18

Natural Resources

7.01

0.00

0.13

0.48

23.16

1.58

Property Taxes and Miscellaneous

1.31

0.26

1.85

1.27

17.89

41.09

Population Shares

1.40

0.42

2.59

2.07

22.69

38.81

Solution: Part a) Tax base deficiencies (positive equals deficiency)

Personal Income Taxes

0.18

0.13

0.58

0.62

3.19

-2.22

Business Income Taxes

0.78

0.27

1.40

1.19

3.61

-7.31

Consumption Taxes

0.06

0.30

0.23

2.45

-0.37

Natural Resources

-5.61

0.42

2.46

1.60

-0.46

37.24

Property Taxes and Miscellaneous

0.09

0.16

0.73

0.81

4.80

-2.28

Personal Income Taxes

$216

$160

$708

$759

$3,905

-$2,720

Business Income Taxes

$261

$89

$473

$401

$1,214

-$2,461

Consumption Taxes

$63

$70

$345

$258

$2,777

-$417

Natural Resources

-$433

$32

$190

$123

-$36

$2,875

Property Taxes and Miscellaneous

$78

$149

$671

$739

$4,387

-$2,081

Fiscal Capacity Shares

1.35

0.28

1.94

1.46

19.37

40.12

Part b) Equalization entitlement for each tax base

Deficiency

0.05

0.14

0.65

0.62

3.32

-1.30

Basic Equalization Entitlement ($M)

$186

$501

$2,386

$2,280

$12,247

Part c) If Alberta introduces a sales tax, and we assume the distribution of tax bases are unchanged, then only the consumption tax revenues increase. The totals are then: Personal Income Taxes

$ 122,299,341

Business Income Taxes

$ 33,667,520

Consumption Taxes

$ 118,516,973

Natural Resources

Property Taxes and Miscellaneous

$ 91,379,680

<-- only this is different

7,720,085

The effect on equalization is as follows: Fiscal Capacity Shares

1.35

0.29

1.95

1.46

19.38

40.10

Deficiency

0.05

0.13

0.64

0.61

3.31

-1.29

1-35

Suggested Answers to Exercises Basic Equalization Entitlement ($M)

$189

$504

$2,401

$2,292

$12,369

Change in Entitlements

$15

$11

$122

Equalization entitlements increase for all receipients. The reason is there is more revenues to be equalized than before.

Bonus marks for students that adaquately explain how the fixed growth rule would lead those provinces with relatively large consumption tax bases to see decreases in equal

Excel data

Chapter 9 1. a. There is a 95 percent chance of no illness, in which case income is $30,000, and a 5 percent chance of illness, in which case income is $10,000 because of the $20,000 loss. Thus, expected income is (0.95)(30,000) + (0.05)(10,000) = 29,000. The utility of having income of $29,000 with certainty is 11.66, but the expected utility is only (0.95)U(30,000) + (0.05)U(10,000) = (0.95)(11.695) + (0.05)(10.597) = 11.64. b. An actuarially fair premium would be $1,000 since there is a one in twenty chance that the insurance company will have to cover losses of $20,000. If the individual buys insurance for $1,000, then they have certain income of $29,000 and the utility of $29,000 is 11.66. Setting the expected utility equal to 11.64 and solving for income yields approximately $28,388, indicating that the individual is indifferent between bearing the risk and having expected income of $29,000 or purchasing insurance with a certain income of $28,388. c. If the insurance costs $30,000 - $28,388 = $1,612, the individual is indifferent between having insurance and not having insurance, so $1,612 is the most they’d be willing to pay (allow some difference for rounding). 2. a. P=100-25Q = 50, hence Q = 2 for efficiency. The total cost is 100. b. With 50 percent coinsurance, the individual pays $25 per visit and the quantity demanded is 3 visits per year. The individual’s out-of-pocket costs are $75 and the insurance company pays $75 ($25 per visit, 3 visits per year). 3. Since the variation in health among the elderly is likely to exceed the variation in health for the population as whole, and patient-doctor confidentiality provides patients with private information about their health, adverse selection may be particularly severe for elderly cohorts. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

1-36

Suggested Answers to Exercises 4. a. Nathan’s actuarially fair premium is equal to $1,500 since the insurance company has a 10 percent change of having to cover $15,000 in losses. For Samantha, the actuarially fair premium is $3,000 since the firm has a 20 percent chance of having to cover a $15,000 loss. b. Suppose the firm charges everyone a premium of $1,500, based on the belief that everyone in the risk pool has a 10 percent chance of incurring a $15,000 loss. Both Nathan and Samantha will purchase insurance given this premium; it is a particularly good deal for Samantha. Suppose there are a number of individuals like Nathan and Samantha who purchase insurance from the firm (similar to the example illustrated in Table 9.2). Over the course of the year, the firm will actually be making higher payouts than expected since there are Samantha types in the risk pool whose risk is 20 rather than 10 percent. Over time, the firm’s payouts will be higher than originally anticipated. In response the firm increases the premium. If the premium increases such that the Nathan types are no longer interested in purchasing insurance, the adverse selection problem results and the low-risk types drop out of the market. c. Compulsory, government-run health insurance program can avoid the problem of adverse selection by requiring mandatory participation. In this way, low risk types are prevented from dropping out of the market. High risk types will be better off compared to purchasing insurance in a private market setting (where low risk types dropped out) as the premium (or tax contribution) will likely be lower. Low risk types however need not be better off. 5. a. See the following figure. The potential source of market failure in this example is imperfect or poor information. Assume a private market for colon cancer screening tests. The informed demand is denoted by DI. It reflects the true private marginal benefit schedule associated with colon cancer screening tests. The uninformed demand DU captures the perceived private marginal benefits, which in this example lies below DI as individuals with poor information underestimate the benefits of screening tests. The supply curve reflects the private marginal cost curve, which in this example also equals the social marginal benefit schedule. Given the lack of information, the equilibrium quantity of screening tests purchased each year is X0. The efficient level of screening tests is X*, determined as the level of tests where the true private marginal benefit is equal to the private marginal cost. Note that in this example there is no difference between private and social marginal costs (and benefits). X* ensures that surplus is maximized.

1-37

Suggested Answers to Exercises

The inefficiency is captured by area abc. This area represents the additional surplus or net benefits that could be obtained if the number of screening tests increased from Xo to the efficient level. b. In cases where there is a lack of information (or poor information), the government could undertake an annual information campaign that outlines the benefits of colon cancer testing in an effort to essentially shift the uniformed demand curve closer to the informed demand curve. In Ontario, Cancer Care Ontario has developed screening guidelines for various cancers including colon cancer. The current recommendation is that all Ontarians aged 50 and over be screened for colorectal cancer. A letter is sent to all eligible Ontarians to inform them of the benefits of screening, the screening guidelines, and to encourage individuals to discuss screening with their family physicians. Family physicians also help disseminate information and awareness to their patients and may use various systems (like an online screening activity report) to help track screening and follow-up with their patients. 6. There are several ways to correctly answer this question. Health spending is different because consumers’ payments for health services are not related to the amount of service they consume. Also, consumers sometimes lack full information. For example, when people are sick, they may just follow the doctor’s orders, regardless of the cost to the health system. Paternalism, income redistribution, and externalities are also potential factors differentiating health care from most other goods and services. Asymmetric information (both adverse selection and moral hazard) are particularly important challenges facing a health care system. 7. The Canada Health Act contains five conditions or principles that provinces must follow to qualify for federal grants: The principles outlined are: i. universality ii. accessibility iii. comprehensiveness iv. portability

1-38

Suggested Answers to Exercises v. public administration Past studies have shown that the financial penalties imposed have been small relative to the size of health spending. Despite this, it is the continued support of the public and the provinces for the Act that has helped to maintain Canada’s publicly funded health system. 8. Since healthier individuals may be unwilling to pay the high cost of insurance when the premiums are based on a population average risk, the regulation by itself does not prevent the lower risk individuals from choosing reduced coverage. However, the government uses a taxfinanced fund to compensate insurers facing relatively high claims. Companies can thereby afford to pool risk classes with a full insurance contract at a price that is acceptable to lowrisk individuals and they have no incentive to try to exclude high risk individuals. Thus, the regulation may help reduce the gap in coverage caused by the adverse selection problem. 9. Concern over the Canadian health care system would be justified if health outcomes are not improving as health spending increases. To determine whether media reports are justified, we could collect cross-country data on indicators of population health. Data which allow us to compare indicators such as average life expectancy and infant mortality rates can give us a better idea of how Canada’s health system is doing over time, relative to health outcomes and spending in other countries.

Some of the exercises have no single ―correct‖ answer. The answers provided here outline only a few possibilities. Chapter 10 1. a. Let E be total employment, LF be the total labour force, U be total unemployment (U = LF – E), and POP be the working age population. Therefore er = E/POP and pr = LF/POP, and er/pr = E/LF. Consequently, 1 – E/LF = U/LF = ur. b. ur = 1 – (0.55/0.60) = 0.083 c. new ur = 1 – (0.55/0.61) = 0.098

1-39

Suggested Answers to Exercises

It is assumed that employment does not change because the real wage remains constant. Initially, total unemployment is the distance ab. An increase in the participation rate shifts the labour supply cure to the right to S" and the total number of unemployed increases to ac. 2. Here is a plot of the data:

1-40

Suggested Answers to Exercises One-in-four Canadians are now on long-term unemployment, which speaks to a persistent impact from this pandemic that will leave scars on labour markets for years to come. Further government support will likely come, but as is the case in the U.S., the deferral period for mortgages and household debt payments (credit cards, lines of credit, etc.) is ending, and the federal coffers aren’t bottomless. Which means that we are bound to see defaults ahead, with repercussions for consumer spending and service-sector jobs that depend on people’s disposable incomes. The Bank of Canada wrote a piece about long-term labour market scarring that is a worthwhile read about the concerns: https://www.bankofcanada.ca/wpcontent/uploads/2021/02/remarks-2021-02-23.pdf 3. A higher benefits rate reduces the cost of job search for EI eligible workers, so the unemployed may search longer. The effect might be smaller if the change is expected to be temporary. A higher benefit rate may induce unemployed workers who are currently ineligible for benefits to get a job so that they can access these higher benefits in a future unemployment spell. If the increases rate is temporary, this effect may not arise at all. 4. a.

Should Harry get laid off, expected benefits are 0.55 x 0.1 x 12,000= $660. Ron’s expected payout is calculated in a similar way (0.55 x 0.08 x 12,000) and is equal to $528.

b. Yes. Harry pays a premium of $594 and has an expected payout equal to $660, so Harry in effect receives a subsidy. Ron, on the other hand, faces a smaller probability of layoff and a lower expected payout of $528 but pays the same premium. Ron is making a net contribution. The employment insurance, as it is currently designed, redistributes income from Ron to Harry. c. Ron would pay a premium equal to $528 and Harry would pay a premium of $660. 5. If  is the gross replacement rate, m is the income tax rate, and t is the payroll tax rate, then the net replacement rate is ((1 – m)  )/(1 – m – t). If  is 0.5, m is 0.25, and t is 0.10, the after-tax EI replacement rate is 0.577. A higher after-tax replacement rate may reduce the amount of effort which unemployed workers devote to finding a new job, thereby increasing the unemployment rate. 6. This question is designed to do two things: get students thinking about the efficiency and equity rationales relating to benefits for parental leave and generate some discussion surrounding how to impose limits and why. Some reasons for parental leave include promoting and ensuring continued labour market participation of parents (an efficiency argument relating to efficient labour market adjustment policies), equity considerations (supporting families, reducing financial hardships for single parents and so on). Some discussion may emerge relating to potential abuses of the program and the potential for horizontal inequities to emerge if the case was allowed. Consider a single mother who gives birth to twins. Should the single mother be able to make two claims? What about a couple who have one child but this child has colic, sleeps poorly and is sick a lot? See Jill Mahoney’s article ―Parents of twins lose their bid for twice the benefits,‖ Globe and Mail, June 16, 2011, for a real-world example. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 7. a. If lr = 0.02 and du = 4.5, then ur = 0.083. b. If lr = 0.021 and du = 4.5, then ur = 0.086. The unemployment rate would increase because the number of workers laid off would increase, while the rate at which laid off workers find new jobs remains constant. c. If lr = 0.020 and du = 4.75, the ur = 0.087. The unemployment rate would increase because the rate at which unemployed workers find new jobs would decline, while the rate at which workers are laid off from their jobs remains constant. 8. a. If employers’ premiums are based on their layoff rates, they would have an incentive to report the termination of an employee as a voluntary quit rather than as a layoff. If unemployment insurance benefits only go to those who are laid off, workers have an incentive to report a job termination as a layoff. Thus, there will be conflicts between workers and firms over whether job separations are quits or layoff. Adjudicating these disputes is costly. b. New businesses do not have a track record on which to base their premiums. An industry average might be used, but since most new firms are small and many go out of business within their first five years, using an industry average would tend to subsidize new employers at the expense of established employers. c. The layoff rate for a small employer could be very erratic, say jumping from zero to 75 percent if the firm laid off three of its four employees. Thus, premiums for small firms, if based on their past layoff rates, could vary widely over the business cycle. d. The laid-off employees of bankrupt firms would be eligible for EI benefits but the bankrupt firm would not be paying higher premiums. The remaining firms would have to pay for the benefits received by the employees of the bankrupt firm. Chapter 11 1. The quote ignores possible effects of a pay-as-you-go system upon savings rates. In addition, it ignores possible distortions in labour supply behaviour both on the part of the currently working generation and the generation that is considering retirement. 2. The equation relates taxes paid into the pension system to the dependency ratio and the replacement ratio, that is, t=(Nb/ Nw)*(B/w). If the goal of public policy is to maintain a constant level of benefits, B, rather than a constant replacement ratio, (B/w), then taxes may not need to be raised. If there is wage growth (through productivity), then it is possible to maintain B at a constant level, even if the dependency ratio is growing. By rearranging the equation, we can see that B=t*w*(Nb/ Nw)-1. That is, increases in wage rates (the second term) offset increases in the dependency ratio (the third term). Thus, constant benefits do not necessarily imply higher tax rates. 3. Using equation 11.2, maintaining the benefits relative to average wages over time requires taxes to rise in proportion to the ratio of elderly individuals to workers. That is, the relative Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises change in tax rates between 1990 and 2050 must equal the relative change in . The relative change in the number of people aged 65 or older to people aged 20 to 64 increases by a factor of . Therefore, the tax rate must increase by this same proportion: . Alternatively, if the tax rate were kept constant then benefits relative to wages would instead decrease by a factor of 1.715. 4. If the contribution rate increase only goes to pay for higher benefits, then the savings rate will not increase. If the Canada Pension Plan fund increases as a result of the increase in the contribution rate, then the national savings rate will tend to increase. This increase in the national savings rate could be offset if individuals decide to reduce their personal savings rates or if governments decide to incur higher deficits. 5. a. The problem does not provide information about the utility function, so the optimal point is where the indifference curve is drawn tangent to the budget line, which can occur at different values depending on how the curve is drawn. In the following diagram, the optimal point involves saving $8,000 and future consumption consists of period 2 income ($5,000) plus savings with interest ($8,800).

b. If Social Security takes $3,000 from the individual in the first period and pays them this amount with interest in the second period, then private savings falls from $8,000 to $5,000. There would be no change in optimal consumption values. 6. If the implicit rate of return from the public pension is lower than the private return, the budget line becomes flatter at the endowment point as present consumption falls from, say, $20,000 to $17,000 when $3,000 is taken for social security. This middle segment of the budget line is flatter, reflecting the lower rate of return on public pensions compared to private saving. For savings beyond the $3,000 taken for public pensions, the private rate of return is available, so the budget line is parallel to the original line. This would cause the optimal point to change and put the individual on a lower indifference curve. In the following graph, the effect is to increase private saving slightly. However, if the new optimal point were to lie to the right of the first optimal point, savings would decrease.

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Suggested Answers to Exercises

7. The OAS/GIS performs a redistribution role. It ensures that all seniors have some retirement income. The CPP/QPP can be viewed as a forced savings plan to overcome the myopia and the problem of the Samaritan’s Dilemma. It also provides inflation protection for retirement income and is an alternative to the private annuity market which may be affected by adverse selection. The rationale for having the two different programs is that they perform different functions. Because GIS is means tested, increases in CPP benefits result in lower GIS payments. 8. The expanded pension benefits—called Additional CPP—will increase the maximum pensionable earnings threshold (by 14 percent) and, in addition, increase the share of earnings replaced by the pension is increased from one-quarter to one-third. To fund this increase in benefits, CPP contribution rates will increase, and proceeds will fully fund the higher benefits. In practice, there are two different maximum pensionable earnings thresholds and two different contribution rates. Up to the base CPP earnings ceiling (the YMPE) the contribution rate for employers and employees will gradually increase by one percentage point each by 2023 (to a combined 11.9 percent from its previous 9.9 percent). For earnings beyond that ceiling but up to a higher second ceiling there will be a combined 8 percent contribution rate. Above the second ceiling, no CPP contributions are made as those earnings are still not pensionable. Upon retirement, the benefits an individual receives will be based on the contributions that they made using their best 40 years of earnings. This fully funded approach is different than the partial funding of base CPP, whereby contributions are accumulated in an investment fund whose returns help offset higher future expenditures to beneficiaries. 9. If CPP assets earn a rate of the return , then fund assets in year is given by , where are expenditures not covered by contributions. Divide through by and use the assumption that to see . And since, by assumption, we know that we can further have ( ) . If assets are a constant ratio to expenditures of 7.5 then we further have ( ) . Rearranging this expression to isolate for yields . This result means that, under these assumptions, the CPP fund must earn an average rate of return equal to 5.9 percent to ensure the asset to expenditure ratio remains at 7.5.

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Suggested Answers to Exercises

Some of the exercises have no single ―correct‖ answer. The answers provided here outline only a few possibilities. Chapter 12 1.

The topic of creating a more responsive on reserve income assistance program was the subject of a two-year consultation process that was reported on in the document Indigenous Services Canada, First-Nations-Led Engagement on Income Assistance 2018 to 2020, National Summary Report, 2021. https://www.sac-isc.gc.ca/DAM/DAM-ISC-SAC/DAMSOCIAL/STAGING/texte-text/fn_led_engagement_Income_assistance_20182022_nsr_1622210062197_eng.pdf, referenced in the text. Section 4 suggests several ways forward within five overarching themes of 

Provisions



Capacity building



Case management and pre-employment supports



Community-based wraparound, ancillary and holistic services



Self-determination/governance and Traditional Knowledge

2. See five reasons below: 1. Some jurisdictions report average annual cases (some of which use the calendar year, others using the fiscal year), while other report cases on March 31. 2. Some jurisdictions report number of applications, while others report beneficiaries, which include everyone in the household of the applicant. The number of beneficiaries will vastly exceed the number of applicants or cases. 3. Some jurisdictions only report those who receive a partial benefit; others do not. 4. Some jurisdictions include on reserve data; others do not. 5. How jurisdictions include assets and other sources of income affects eligibility and therefore cases. The stricter the tests, the fewer the cases and therefore not comparing the same need. 3.

Zasha’s max benefit is $814 (see Table 12.3). Also, note that in Ontario the monthly earnings exemption is $200 (see LO5). NE=(300-0.43-4.86-200)+((48+13)-(48+13))=$94.71. So, the monthly income assistance benefit is: B=Max(B) – NE = 814-94.71=$719.29

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Suggested Answers to Exercises a. With the part time job, Hendrix would work 25 x 4 = 100 hours a month. At a wage of $11 per hour, Hendrix would generate $1100 in earned income. Their welfare benefit would be equal to 0: B = 600 – (0.75 x 1100) < 0. They would no longer be on welfare if they took the job.

The slope of the XZ is equal to the absolute value of the wage rate. The slope of segment SP is flatter since along that segment, for each additional hour worked, Hendrix gets less than the wage because of the clawback or implicit tax on earnings. b. (i) Hendrix is better off (i.e., is on a higher indifference curve) when they take the job. Note that while Hendrix is on a higher indifference curve when they take the job, this indifference need not be tangent. This is because we have assumed that Hendrix is choosing between only two options: not working and being on welfare (point P) or working the part time job with 100 hours a week and being at point V.

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Suggested Answers to Exercises

(ii) Hendrix is better off not taking the job and remaining on social assistance.

c. Note that along segment AP the budget line has the same slope as XZ, since there is no clawback. Along segment BA the clawback has kicked in, so this segment is parallel to SP. The level of income where the social assistance reaches zero is higher and equal to $1200. If Hendrix takes the job they reach point K—they receive $1100 in earned income plus $100 in social assistance. It is possibly that this might yield higher utility than point P, depending on how the indifference curves are shaped.

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Suggested Answers to Exercises

d. Consider the figure from b (i) above. Taking the job yields income of $1100, but Hendrix must also spend some of this money on daycare. If day care costs $5 a day, $500 of their earned income must go to daycare expenses, leaving them with exactly $600, which is what they would get if they stayed on social assistance. Some alternatives are a bigger earnings deduction, a lower clawback or a deduction for childcare expenses. 5. a. Their benefit = $150 – 0.25 (earnings) Solve for H: 0 = $150 – 0.25 (5H), or H = 120. If they work 120 hours per month or more, their benefit is zero.

b. Their benefit = $150 – 0.25($5/hr)(60 hr.) = $75

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Suggested Answers to Exercises

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Suggested Answers to Exercises e. Uncertain. If Emery worked less than 100 hours per month under the previous welfare program, then they may or may not be better depending on their preferences for consumption and leisure. If Emery worked more than 100 hours per month under the previous welfare program, then they will be better off. f.

Disability and poverty are important social issues that have yet to have a satisfactory resolution. Some argue that providing generous benefits create work disincentives. Others say that those who are diagnosed with a disability not only face medical impairments and functional activity limitations that reduce productivity and limit their ability to maintain consistent work hours, employment, and labour market attachment, but also that employers discriminate against people with disabilities. To the extent that either of these are true, workfare requirements impose unfair barriers to people with disabilities because they are either unable to meet the work requirements or unable to find employers willing to employ them. This is why in modern day income assistance programs, workfare requirements are usually waived for people who are designated as having a disability.

6. Such a system will be less responsive to income shocks than the income assistance system, which can respond to an immediate income shock. Income assistance also generally does not require you to file taxes, while this benefit does. Income assistance also classifies income according to exempted income and ensures that some income is not counted, whereas this scheme includes all income, including tax benefits. There is no earnings exemption. Lowincome income assistance recipients with children who receive income from child benefit are likely to receive less on this program, as are many with disabilities. 7. The water crises on First Nations reserves can only be solved through ongoing investment in water infrastructure and in operation and maintenance. In the short-term the provision of bottled water is necessary. As each individual and household needs different amounts of water depending on whether they have children, how much they cook, etc., a cash benefit will be unable to appropriately adjust to differential need for clean and potable water. Chapter 13

1. There are numerous rationales given for government provision of education. Even though education is primarily a private good, many argue that educating a child provides external benefits. However, the existence of a positive externality implies that government should subsidize education rather than making it free and mandatory. Other rationales are based on equity, including a belief in commodity egalitarianism. The rationales do imply a lower level of provision of higher education versus primary and secondary. Higher education has higher private benefits and fewer externalities, therefore requires a lower level of provision. Finally, problems of asymmetric information can lead to capital market imperfections in the market for loans and underinvestment in education. Government intervention in the market for student loans can help to address this problem for higher levels of education where the individual taking out the loan is also the student. However, this form of intervention does not fully resolve the problem of underspending at lower levels of education, since the person responsible for the loan is not typically the student, but it rather the parent.

2. Liquidity constraints, positive externalities, the importance of quality (merit good), and structural inequities that lead to the underpayment of childcare workers.

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Suggested Answers to Exercises

3. It may be that national income is increased purely though private returns to education summed up across the economy. If this is the case, one could not use an externality-based argument to justify subsidization. However, if education quality increases the growth rate of national income outside of the returns that accrue to individuals who consume the education, then private decisions will yield a lower than efficient level of education quality. This reasoning would allow for government subsidization that would improve the quality of education.

4. Parents’ education background, family income, and other socioeconomic characteristics are typically found to have significant effects on the educational performance of students. Failure to take into account these characteristics when examining school test results means that the effects of socioeconomic background and school performance are mixed together and cannot be separately identified. For example, a school may be unfairly ranked based on test results because its student population is drawn primarily from a poorer neighbourhood. However, when compared against other schools with similar student populations in terms of socioeconomic background, the school might outperform its peers. Several challenges may result from this. The most relevant may be in exasperating informational problems in the market for education. If parents sort children into schools with higher unconditional test scores, this may not improve educational outcomes if the reasons for the higher scores are unrelated to true school quality. This is related to there being insufficient information for informed decisions by parents in certain circumstances. Another problem may concern the signaling value of graduating from schools with high unconditional test scores. If scores are higher in communities with high socioeconomic status, then the higher signaling value of graduating from those schools could exacerbate inequality—for reasons unrelated to a given student’s own individual abilities.

5. a. The family’s budget constraint is given as AB where point A is the quantity of all other goods that can be purchased if the family spends all its $50,000 on these goods ($50,000 / price of all other goods). Point B represents the maximum amount of private education that can be purchased if all income is devoted to education (i.e., $50,000/price of education).

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Suggested Answers to Exercises b. By participating in the project, the family gets $8,000 in education (or quantity ep). The entire $50,000 in family income can be spent on all other goods. Thus, the consumption possibilities set expands to include point x. c. Without public education, the family choose to purchase e* in private education. With the introduction of the public education option, the family choose a new consumption bundle at point x. Note that while x lies on a higher indifference curve, the quantity of education consumed has fallen. d. The $8,000 voucher can only be spent on education. However, unlike the public education option illustrated above, the family can use the voucher for private or public education. The new budget constraint for the family is given as AxC. Compared to the case where there is no voucher (and no public education), the family will increase its consumption of education above e* as long as education is a normal good.

6. Public goods are (1) non-rival and (2) non-excludable. Non-rivalry implies that one person’s consumption of a good or service does not detract from another person’s opportunity to consume that same good or service. Education is rival since the educator’s time spent teaching one person cannot simultaneously be used to teach another person. Nonexcludability implies that it is infeasible to exclude any person from consuming the good or service. Education is excludable since physical barriers (doors on school buildings, for example) can easily exclude individuals from receiving educational services. This implies that education is a private good. The level of public support and funding received by providers of this good is not relevant to determine what it a public or a private good.

7. Advantages: tailor educational services to local tastes and circumstances; accountability is also enhanced where there is strong local control. Disadvantages: inequality in access to financial resources may result, such as due to unequal distribution of property tax bases; benefits of education are also not all private, so there are spillovers beyond the local community and under provision may result from the presence of this positive externality.

8. Provinces do not capture part of the return to higher education—future income streams and taxes that flow from the education—and underspending on post-secondary education may occur if left to the provinces alone. High levels of education and national standards facilitate mobility and contribute to social and economic development, and to a sense of nationhood. Thus, since benefits of higher education extend beyond provincial borders, important externalities accompany provincial spending. The federal government can play a role in helping to address these externalities. The federal government’s support of post-secondary education can also be justified based on the public good aspect of knowledge generated from research. The benefits of this public good certainly spill over provincial borders and are more likely to be national in scope.

9. Discussion should identify the variation in private rates of return to different degree programs (e.g., dentistry and education). Consider the extent to which government and university regulations, coupled with low tuition fees (in some cases), allow individuals fortunate enough to gain admission to programs to capture ―rent‖. Consider the reasons (externalities in some cases) for providing greater subsidies for individuals to enter certain professions or areas of study. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises

10. Students are encouraged to think about what social benefits and costs may be excluded from the analysis and how these exclusions might increase or lower social costs and benefits. The efficiency costs associated with using tax revenues to fund education are not accounted for. The efficiency benefits associated with correcting various externalities relating to education are not accounted for, nor are the gains from addressing information problems. Note also that these estimates do not control for unmeasured attributes of individuals. Possibly people with, for example, high levels of charisma are able to find work immediately upon completing a BA, while people who struggle to find work upon graduation from university go on to further education. These unmeasured attributes could create a negative bias in the estimated returns to higher degrees. Finally, the value of achieving equity objectives through education is not captured here. Chapter 14 1. a. The worker’s assertion is correct if the demand for their services is perfectly elastic. The demand for these services would be perfectly elastic if there were perfect substitutes available and no differentiation. If the tax is generally enforced, it is unlikely that there would be perfect substitutes available, so the worker’s assertion is unlikely to be correct. If, however, there is a substantial amount of tax evasion, and clients can readily substitute underground economy services for tax compliant services, or utilize services in other nearby cities, the worker’s assertion may be correct. b. The statutory incidence of a tax does not determine its economic incidence. Levying the tax on patrons would not make a difference except in so far as it alters the extent of compliance or administrative costs.

2. a. A part-time worker with annual income of $9,000 pays no taxes since everyone gets a $10,000 deduction. Her marginal tax rate is 0% and her average tax rate is 0%. b. A retail salesperson with annual income of $45,000 has taxable income of $35,000 and pays $1,750 in taxes (5 percent of taxable income). As a percentage of income, the average tax rate is 3.89% ($1750 is 3.89% of $45,000). Her marginal tax rate is 5%. c. An advertising executive with annual income of $600,000 pays $2,500 in taxes since no tax is levied above $50,000 in taxable income. As a percentage of income, the average tax rate is 0.42%. Her marginal tax rate is 0%.The tax is initially progressive, but because of the cap on taxable income, becomes regressive. 3. The tax reduces the demand for petroleum products. Since the sector is capital intensive relatively more capital than labour will be released to other sectors of the economy. Hence in a closed economy the relative price of capital must fall. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 4. Tax theory tells us that the statutory incidence and the final incidence may be very different. Hotel owners and employees may bear the tax burden if they are forced to lower their beforetax prices to compensate for the tax. This depends on the elasticities of the supply and demand curves. 5. In the competitive case, the full tax is paid by the consumer because the supply curve, given by MC, is perfectly elastic. With a monopoly, the tax is shared between the consumer and the producer depending on the elasticity of demand. (If the tax is imposed on the consumer, the demand curve falls by $u, and the result is the same in both cases).

6. These reports about demand sensitivity suggest that there is a very elastic demand curve for goods sold over the Internet. Because of this high elasticity, the incidence of a tax levied on Internet sales is primarily borne by producers, not consumers. 7. a. Set 2000 – 200 Pc = 200 Pc, so Pc = $5 and Qc = 1000 packs. b. Consumer price = Producer Price + $2. Let Pn be the producer price. Then 2000 – 200 (Pn + 2) = 200 Pn Producer receives $4 per pack; Consumer pays $6 per pack. Quantity sold = (200)(4) = 800 packs. Tax revenue = (tax/pack)(no. of packs) = (2)(800) = $1600. Half of this revenue comes from consumers, half from producers. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises

8. a. The equilibrium price can be calculated by setting the quantity supplied equal to the quantity demanded: QD = a - bP QS = c + dP If QD = QS, then the equilibrium price can be determined as follows:

a  bP  c  dP a  c  (b  d ) P ac P bd

The equilibrium output can be determined by substituting the equilibrium price into either the supply or demand equation. Substituting into the demand equation:

Substituting into the supply equation:

b. If a unit tax of u dollars is imposed on the commodity, then it doesn’t matter which party it is imposed upon (the consumer or producer); the new equilibrium will be the same in either case. If the unit tax is imposed upon the consumer, then the price the consumer pays is u higher than the price received by the supplier. The consumer’s price without the tax, PC, and price that includes the tax, PCT, are:

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Suggested Answers to Exercises

Similarly, the price received by the producer in the absence of the tax, PP, is u lower than the price received with the imposition of the tax, PPT. These prices are expressed below:

The equilibrium that prevails after the imposition of the tax can be found by setting PCT = PP or PC = PPT -- in the end, both approaches will yield the same answer. First, we can derive the solution setting PCT = PP:

P CT  P P a 1 c 1   Q  u   Q  b b d d a c 1 1   u    Q b d b d  da  bc  dbu  b  d   Q db  db  da  bc  dbu Q bd Next, setting PC = PPT:

P C  P PT a 1 c 1   Q   Q   u b b d d a c 1 1   u    Q b d b d  da  bc  dbu  b  d   Q db  db  da  bc  dbu Q bd

Therefore, both approaches lead to the same outcome. 9. The employers will end up bearing the entire burden if either the supply of labour is perfectly elastic or the demand is perfectly inelastic. Since neither of these conditions Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises

is likely to hold, one expects that workers would bear part of the burden of an increase in CPP premiums. 10. This finding implies that the labour supply of European soccer players is highly elastic. These soccer players will pay little in taxes. 11. The budget constraint with a 25% tax on food and music is

Y  (1.25) PF QF  (1.25) PM QM , which is equivalent to writing

Y  PF QF  PM QM , 1.25

i.e., an income tax rate of 20%. 12. The ability of high earners to shift their income taxes on to consumers would reduce the progressivity of personal income taxes in the upper deciles of the distribution, assuming that the consumers of high-end professional labour have, on average, lower incomes than the professionals themselves. 13. When all capital-labour ratios are the same, inputs released by any sector may be absorbed by the others without changing the relative prices of capital and labour. Accordingly, the sources of income are not altered. Incidence is determined solely by the use of income. The consumers who purchase relatively large shares of taxed output will bear more of the tax. Chapter 15 1. a. Originally the tax is $24 per carton of 200 cigarettes, or 200 percent of the pre-tax price per carton of around $12. After the new legislation, the tax is $10 per carton, which is 83 percent of the pre-tax price of $12. The original tax was higher than after the tax reduction by a factor of 2.00/0.83; since excess burden increases by approximately the square of this, it was higher by a factor of 5.81. Thus, a tax reduction from $24 to $10 reduced the excess burden by 83 percent, [1–1/5.81]. b. If the original price did not incorporate all costs, then part of the tax can be viewed as a Pigouvian tax, which, in effect, has a negative excess burden. 2. As illustrated in Figure 15.3, the magnitude of excess burden can be measured using the concept of equivalent variation. The amount of income that would need to be taken from an individual to make them just as worse off as under a tax depends on how sensitive an individual is to price changes. That is, it depends on how the marginal rate of substitution changes for different quantities consumed. If barley, for example, is highly substitutable for corn then the marginal rate of substitution between the two does not change much for different quantities of barley consumed and therefore the indifference curve is relatively flat. If barley must be consumed in fixed proportions to corn (i.e., they are perfect complements) then the indifference curve is L-shaped. In the former situation, points E2 and E3 (in Figure 15.3) are far apart, and the equivalent variation is large. In the latter situation, points E2 and E3 are the same and the equivalent variation is zero. The more substitutable a taxed product is for others, the greater the excess burden.

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Suggested Answers to Exercises 3. The following diagram illustrates a lump-sum tax that lowers an individual’s budget constraint, resulting in optimal consumption choices at point B. Total government revenue in terms of kilograms of corn is indicated by the line segment BC. The concept of equivalent variation requires we compare this to the income reduction resulting in the same level of utility as at point B. This is the same budget constraint as under the lump-sum tax, and therefore there is no excess burden.

4. A tax on height may be considered a form of lump-sum taxation only to the extent that this tax does not introduce marginal distortions between individual choices. Such a tax, for example, would not affect the marginal trade-off between consumption and labour even though it may affect a person’s optimal quantity of consumption and labour chosen (since their income would be lower). This would not be a lump-sum tax, however, if individuals could respond to the tax in a way that would change their height. For example, changing their nutritional intake could (over time) affect one’s height. 5. a. Since land is fixed in supply, we expect no excess burden when it is taxed. b. If the demand for personal computers is elastic, then the subsidy for personal computers will create substantial excess burden, relative to the size of the subsidy. c.

The demand for smartphones is probably quite elastic, as they are luxury goods with many substitutes, and hence the tax should result in substantial excess burden. (This would not be true, however, for a Pigouvian tax imposed to cover the cost of disposal of electronic goods—see the chapter on ―Externalities‖.)

d. The excess burden of a subsidy for investment in ―high-tech‖ could be large if significant investment capital is attracted from unsubsidized investments into the high-tech sector due to an investment subsidy (i.e., many investment decisions are affected). e. Some consumers may switch from purchasing bottled water to pouring tap water into reusable bottles. But many may switch from buying bottled water to soft drinks which are untaxed, resulting in substantial excess burden. f.

A tax on all computer software will have a smaller excess burden (relative to revenues collected) than a tax on one particular type of software. This is because it is easier to substitute away from one type of software than from software in general. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 6. a. At the equilibrium, Qb  240 and Pb  24 . Hence the elasticity of demand (in

 24    1.5 and the elasticity of supply is  240 

absolute value) is   15

 24    1.  240 

  10

b. Using the approximation formula from the text, excess burden is approximately equal to (1 / 2)

24  240  (0.15) 2  38.88 . This approximation is exact only for small tax  1   1   1.5 

rates. The actual excess burden in this example is 32.97. c. The excise tax results in a new equilibrium, where Qb  220 .18 and Pb  22.02 . The tax revenues equal 0.15x220.18x22.02 = 727. The average excess burden is the excess burden divided by tax revenue, i.e. 38.88/727 = .05. 7. a. The value of the marginal product of capital in the corporate sector is given by VMPc=100-Kc, and the value of the marginal product of capital in the noncorporate sector is given by VMPn=80-2Kn. With 50 units of capital altogether in society (Kc+Kn=50), and no taxation, capital should be allocated so that the values of the marginal products in each sector are equalized. Thus, setting VMPc=VMPn gives 100Kc=80-2Kn and substituting in the constraint of 50 units gives 100-50+Kn=80-2Kn or Kn=10. This implies that Kc=40. This is illustrated in the following diagram:

b. If a unit tax of $6 is leveled on capital employed in the corporate sector, the after-tax value of the marginal product in the corporate sector falls. It is now given by Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises VMPc’=100-Kc-6=94-Kc. Now setting VMPc’=VMPn gives 94-Kc=80-2Kn and substituting in the constraint of 50 units gives 94-50+Kn=80-2Kn or Kn=12. This implies that Kc=38. This is illustrated in the following diagram:

Thus, ΔK=2 and the tax wedge is t=$6, so the excess burden is ½(2)($6)=$6. 8. If Nigeria subsidizes gasoline, the price of gasoline goes to (1-s)PG in the following graph. Rectangle ovur is the subsidy paid by the government, while osur is the increase in consumer surplus from the subsidy. The excess burden is svu, the amount of the subsidy that is paid but does not translate into consumer surplus. Because excess burden is created with a subsidy, the subsidy was wisely removed.

9. This is not a good way to think about the squared term. The way in which the presence of the t-squared makes the tax more ―important‖ is that when the tax increases, the excess burden increases with its square. Thus, when the tax doubles, the excess burden quadruples. 10. Given a 10 percent tax on airplane tickets, Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises a. EB = 0.5(1.1)($91B)(0.12) = $500.5 million b. In the short run, the relatively inelastic supply means ε will be close to zero and EB is small. In the long run, ε approaches infinity and EB is larger than in the short run. c. If air travel creates a negative externality, then the reduction in air travel caused by the tax will generate a marginal social benefit that reduces the overall social burden of the tax. 11. The following diagram shows the effect of the price ceiling. Point b gives the price and quantity without the price ceiling. Consumer plus producer surplus equals gbh. With the price ceiling, producers supply the amount represented at point d, and consumer plus producer surplus is now represented by gadh. Consumer plus producer surplus has been reduced by abd. This is the excess burden due to the price ceiling. (In addition, there has been a transfer of surplus from producers to consumers equal to cdef.) Now consider the effect of the tax on a substitute good. This will cause a shift in demand for the good with a price ceiling—from D to D´. The loss in consumer plus producer surplus grows from abd to a´b´d, or by the amount a´b´ba.

Chapter 16 1. From the point of view of efficiency, a commodity whose demand is completely inelastic should face a very high tax rate. However, this is not necessarily ―socially desirable.‖ Concerns with equity and due process must also be taken into account. 2. Assuming that all other commodities (except for cable and satellite television) were untaxed, then optimal tax policy suggests the commodities should be taxed according to the inverse elasticity rule. Goolsbee and Petrin (2004) find that the elasticity of demand for basic cable service is -0.51, and the demand for direct broadcast satellites is -7.40. Applying the inverse elasticity rule would imply that: ⁄

⁄

Thus, tax rates on basic cable should be 14.5 times higher than tax rates on satellite television because basic cable is inelastically demanded, while demand for satellite television is highly elastic. Among the assumptions that go into the inverse elasticity rule are that goods are neither complements nor substitutes, and that the elasticities are the Hicksian compensated elasticities rather than the Marshallian uncompensated elasticities. In this case, it is likely that Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises the first of these assumptions is false—basic cable and satellite television are likely substitutes for each other. The Hicksian and Marshallian demand elasticities are likely to be close to each other because the income effects are likely to be small for this commodity. 3. Total excess burden could be reduced without changing revenues by reducing the corporate income tax and raising the general sales tax, until the marginal excess burden is the same for both taxes. 4. The elasticity of demand for X is demand for Y is

and the elasticity of . Hence efficient taxation requires

. This implies . The revenue requirement is . Using the pre-tax prices and quantities and R=1000, the optimal tY is (approximately) given by the solution to , i.e. . The optimal value of t X is then .46 x .17 = .08. 5. a. It is true that a proportional tax on all commodities (including leisure) is equivalent to a lump sum tax. To illustrate, consider the simplest example where there are only two goods: consumption goods and leisure. The budget constraint is equal to: pCC+wL=I, where pC and w are the prices of consumption goods and leisure, C and L are the quantities of consumption and leisure, and I is income. Then a proportional tax on all goods changes the budget constraint to: (1+τ)pCC+(1+τ)wL=I, or rearranging, pCC+wL=I’, where I’=I/(1+τ)<I. Thus, a proportional tax on all goods does not change relative prices and is equivalent to taking away income. So, it is equivalent to a lump sum tax. b. It is (usually) false that efficiency is maximized when all commodities are taxed at the same rate; this will not be true if leisure is untaxed. Imagine a more complicated budget constraint: pCC+pFF+wL=I. If leisure cannot be taxed, then a tax on commodities leads to a budget constraint of (1+τ)pCC+(1+τ)pFF+wL=I, which does change the relative price of leisure compared with food or consumption goods. Thus, it is not a lump sum tax. Instead, the inverse elasticity rule given in equation (16.9) would suggest that the ratio of the tax rates are inversely related to the ratio of the compensated demand elasticities for all commodities that can be taxed. That is, (tC/tF) =(ηF/ηC). c. It is true that average cost pricing for a natural monopoly allows the enterprise to break even, but the outcome is inefficient. Figure 16.3 in the textbook shows the typical natural monopoly problem, with an initial fixed cost, and an ever-declining marginal cost curve. In this case, the average cost curve is always declining, but above the marginal cost curve. Setting P=AC results in an output level of ZA and zero economic profits. The figure illustrates, however, that the marginal benefit of more output exceeds the marginal cost, so the efficient level of production occurs at P=MC, or an output level Z*>ZA. The deadweight loss is the area between the demand curve DZ and marginal cost curve, going from ZA to Z*. If output were at the efficient level, however, there would be economic losses rather than zero profits.

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Suggested Answers to Exercises d. One notion of horizontal equity is that people in equal positions should be treated equally by the tax system. Under this traditional notion of horizontal equity, the fact that Tom’s workplace provides free access to a fitness room suggests this kind of compensation should be taxed; Jerry pays ―full taxes‖ on his compensation while Tom does not. Another notion of horizontal equity relies on the utility definition of horizontal equity. This concept says that if two individuals have the same utility without taxes, they should have the same utility with taxes, and the taxes should not affect the utility ordering. One implication of the utility definition is that any existing tax structure does not violate the notion of horizontal equity if individuals are free to choose their activities and expenditures. If Tom and Jerry have free choice between the two different jobs (and identical preferences), then the net after-tax rewards (including amenities) must be the same at both jobs; otherwise there would be migration. In this case, the before-tax wage on Tom’s job adjusts for the fact that there is a fringe benefit. 6. To the extent that tallness is genetically determined and correlated with income, making personal taxes contingent on height is less distortional than taxing income directly, since incomes can be affected by labour choices. Hence, basing taxation on height makes sense from an optimal tax perspective. However, it is objectionable because it violates the principle of horizontal equity: people who are the same in all relevant respects should be taxed equally. 7. The theory of optimal taxation indicates that the tax rate should be relatively lower on the spouse who has the more elastic supply of labour. For example, a part-time worker may be more sensitive to the tax rate than the principal earner in a family. There is some evidence in the United States that female labour supply is more elastic than male labour supply. These observations suggest that the excess burden on a family is reduced when the spouses are taxed separately, each facing their own appropriate marginal tax rate. 8. The amount of the transfer received by each individual is ( ). Therefore, Jia’s net income (and thus their consumption) is ( ) and their utility equals . Substituting the labour supply functions and the ( ) values of Jia’s and Jess’s wages into Jia’s utility expression gives , which can be simplified further to give . In a similar manner Jess’s utility can be written as . Using the expressions for Jia’s utility and Jess’s utility in the social welfare 2 function allows us to write W  24(1  t )  80t (1  t ) . By trying different values of t it is apparent that the optimal tax rate is about 29 percent. The solution can be confirmed using calculus. The tax rate is positive because the social welfare function places a higher weight on Jia’s utility and they earn a lower wage than Jess, making some redistribution desirable. The tax rate is not 100% because this rate would discourage labour effort by too much. In fact, at t  1 Jia and Jess would supply no labour and would have identical utilities of zero! 9. Using the Ramsey rule, Hence, and 10. The first possible definition of horizontal equity is that people in equal situations should be treated equally. Prior to 1988, a business person could spend $5,000 on their own meals and entertainment when with clients. This $5,000 in benefits would not be included with their Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises $45,000 in taxable income. Another employee who spends $5,000 on entertainment and eating out has to pay taxes on $50,000 of income since they had no ―business‖ entertainment and meal expenses. Two individuals who were ―equally situated‖ were treated differently. The tax system arbitrarily favoured business people, and continues to do so to a lesser extent after 1988. Since the tax treatment of entertainment and meal expenses re-orders the utilities of individuals in Canada, it also violates the utility definition of horizontal equity. 11. The beard tax was progressive because it was a function of social position, which was probably a good proxy for income. Because the tax attempted to treat people with the same income similarly, it satisfied some level of horizontal equity, even though it penalized those with a preference for facial hair. It’s hard to know about the efficiency consequences unless one knows more about the price elasticity of demand for the privilege of having a beard. If the elasticity was small, then it would be an efficient tax. 12. The marginal benefit of underreporting is equal to the taxes saved, which is simply the person’s marginal tax rate, or MB = t. The expected marginal cost of underreporting $1 of income is equal to the product of the probability of getting caught and the fine per dollar of underreporting, or MC = ρ*Marginal Penalty. The optimal amount of underreporting, R* equals zero if MC ≥ MB. Thus, if ρ*Marginal Penalty ≥ t, then there will be no underreporting. With ρ = 0.02 and t = 0.35, the inequality becomes 0.02*Marginal Penalty ≥ 0.35, or Marginal Penalty ≥ $17.50. With a fine of $17.50 (or more), Sharlene would not cheat on her taxes. 13. a. It is an easy tax to administer, since an inspector can readily check the number of windows. b. Because wealthier people have larger houses, and larger houses have more windows, this tax would tend to target the well off, satisfying vertical equity. c. People could brick up the windows on their homes. d. The excess burden would arise from the utility loss resulting from diminished sunlight and fresh air into the homes. Chapter 17

1. Personal Income tax revenues have grown as a share of GDP over time for several reasons. First more people are working, particularly women. Second, people are earning more money in the form of income. Third, our society has come to value the government to provide a social safety net, including universal health care, education, and income supports which has increased the need for tax revenues. The trend is likely to continue as the average age of the population increases. 2. Step 1: Calculate total income for Jarminder=100,000+2,000=$102,000 Step 2: Calculate net income for Jarminder=102,000-18,000-8,000=$76,000 

To determine how much of their childcare expenses Jarminder can deduct, note that for a child age 6, the maximum allowable is $8,000. The maximum claimable amount Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises can’t exceed 2/3 of earned income which is 2/3×100,000 (earned income)=$66,667. Jarminder can claim the entire amount of their childcare expenses Step 3: Calculate taxable income: $76,000 The amounts for CPP and EI only reduce tax owed and do not affect taxable income.

3. Of the $4,000 of earnings that Sam has, they are able to invest (1-tI)×earnings in the market, or (1-0.25)×$4,000=$3,000. Assume that when they save the money in a taxable account, they have to pay taxes each year on the interest, and the interest is treated as ordinary income and taxed at 25%. In this case, their after-tax rate of return is (1-tI)×r, or (1-0.25)×8%, or 6%. Thus, after 10 years of investment, the amount of money in the taxable savings account is $3,000×(1.06)10=$5,372.54. If they invest the money in an RRSP, the money is initially tax free and accrues at the before-tax rate of return, although there is a tax liability at the end. Thus, the amount from the RRSP is $4,000×(1.08)10×(1-0.25) =$6,476.77. 4. It is not clear that this is a meaningful measure of average income. The Haig-Simmons definition of income used to calculate taxable income excludes many types of income, such as interest on state and local bonds, some dividends, capital gains, employer contributions to benefit plans, some types of saving, and gifts and inheritances. Further, the H-S income is subject to exemptions and deductions before arriving at ―taxable income,‖ which significantly reduces the denominator of the calculation from actual income. 5. Suppose Jean buys the cannabis stock for $1,000 at the start of period 1. At the start of period 2 they have two options. a. Hold the cannabis stock one more period, then sell. b. Sell the cannabis stock, buy the psychedelic stock and hold it for one period. In both cases, it is assumed that all assets are sold, and any taxes paid at the end of period 2. What are the returns to option a)? At a 10 percent rate of appreciation, the cannabis stock is worth $1,210 after period 2, the capital gain is $210, and assuming a 40 percent tax rate applies to the taxable half of capital gains, the capital gains tax is 20 percent of $210, or $42. Thus, Jean is left with $1,210 – $42, or $1168, after tax. If Jean follows strategy b), the value of the cannabis stock at the start of period 1 is $1,000, the capital gain is $100, and the tax $20. Thus, Jean has $1080 left over to buy psychedelic stock. Now, if r is the rate of return on psychedelic stock, what are the after-tax proceeds (V) from selling the stock at the end of period 1? V = Value of psychedelic stock – taxes = (1 + r)($1080) – [.4 × 0.5][(1 + r)($1080) – ($1080)] = (1 + r)($1080) – [.4 × 0.5][($1080)] = $1080 + 0.8r($1080)

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Suggested Answers to Exercises Setting V = $1168 (same as cannabis stock) $1168 = $1080 + 0.8r($1080), and r = 10.19% Thus, the psychedelic stock must pay a ―premium‖ of 0.19% (10.19% – 10%) over the cannabis stock in order to overcome the cost of realizing the capital gain. This is the source of the ―locked-in effect‖ – people can generate a higher rate of return by holding onto their existing stocks, in order to avoid triggering a capital gains tax liability. 6. Employee-provided dental care plans result in the consumption of dental services of a value roughly equivalent to the cost of the plan and this value should be taxed under the HaigSimons criterion. Allocation of the cost of these plans to the employees as a taxable benefit would provide for fairer treatment between those with and without such plans. Inclusion as a taxable benefit is likely to cause a decrease in dental plans as a fringe benefit and in the consumption of dental services, and to an increase in taxable income and the consumption of other goods and services. 7. Since the tax credit for charitable donations increases to 29 percent once they exceed $200, the effective ―price‖ decreases for donations above $200. As long as the people’s ―demand‖ for charitable donations is downwards sloping, a decrease in the price of donations will increase the amount that people donate. This explains why heads of organization dependent on charitable contributions think that it’s important to have a relatively high tax credit. 8. a. See section ―Tax Deductions and Tax Credits‖. The CWB attains its maximum value of $1,395 when income equals $8,365 (calculated as x=1395/0.26+3000). It is not clawed back until income is $22,944 so the range of earnings that the credit is at its maximum value is between $8,365 and $22,944. The credit is reduced to $0 at $32,224 b. The following table shows how the CWB and the income tax affect the EMTR. The EMTR is negative at low-income levels due to the CWB, which encourages entry into the workforce. The EMTR rises above the income tax rate at an income of $22,944 due to the CWB clawback. This increase may discourage part-time workers from increasing their work hours.

Change in MTR

Income

Tax Provision

EMTR

3000

CWB

-26

5000

Income tax

+30

8365

CWB maximum

+26

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Suggested Answers to Exercises

22944 32224

CWB clawback End of CWB clawback

+15

-15

9. This question can be answered directly using the information in Table 17.6. See Excel spreadsheet ―Rosen 6ce_ExcelSolutions_Chapter17_Question9‖. 10. All three couples have identical incomes of $80,000. Only Alyss and Will have a child under the age of 18. Before the proposal, the taxes of Alyss-Will and Paulina-Halt are .2×40,000+.4×40,000=$24,000, while Cassandra-Horace pay .2×60,000+.4×20,000=$20,000. After the proposal, Alyss shifts $20,000 of her income to Will, so their taxes are .2×60,000+.4×20,000=$20,000, while Paulina-Halt cannot shift income as their son is 18. Cassandra-Horace continues to pay $20,000 in taxes. Neither the pre-existing tax system, nor the proposal can satisfy both Principles 2 and 3. The pre-existing system violates Principle 2 because Alyss-Will and Paulina-Halt pay different taxes than Cassandra-Horace; but it is ―child neutral‖ (Principal 3) since Alyss-Will and Paulina-Halt pay the same taxes. The proposed system violates Principal 2 and Principal 3 (Alyss-Will now pay lower taxes than Paulina-Halt). Whether ―child neutrality‖ is an appropriate fairness criterion for taxation is debatable. 11. a. The nominal after tax rate of return is reduced to 7.2 percent from 12 percent by the 40 percent tax rate. The real after-tax return equals the nominal after-tax return minus the rate of inflation, 7.2 – 5 or 2.2 percent. b. With a 3-percentage-point increase the nominal return is 15 percent, and the nominal after-tax return is 9 percent. With the rate of inflation now at 8 percent, the real aftertax rate of return becomes 1.0 percent. c. In general, if the inflation rate increases by P percentage points, the nominal rate of interest, in, must increase by [1/(1–t)] P percentage points if the real after-tax rate of interest, ir, is to be kept constant. With the increase in inflation from 5 percent to 8 percent, in needs to increase by 5 percentage points, from 12 to 17 percent. 12. A global or citizen-based taxation system. Chapter 18 1. Figures 18.2 and 18.3 can also be used to illustrate the possible effects of a reduction in the marginal tax rate on the income-leisure decisions of a high-income individual. In each of these diagrams the upward rotation from TH to TD reflects a reduction in the marginal tax rate applied to the taxpayer. As the two diagrams illustrate, such a change may result in a decrease in work, as in Figure 18.2, when marginal tax rates are reduced, or a increase in work, as in Figure 18.3.

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Suggested Answers to Exercises

2. Apollo’s after-tax budget constraint is pC  (1  t ) A  (1  t ) w(T  l ) , where l denotes hours of leisure, C represents units of consumption and p is the price of consumption. This equation can also be written as (1  t ) A  (1  t ) wT  pC  (1  t ) wl .

6. The U.S. Immigration Act of 1965 reduced the possibilities of Canadians to move to the United States in response to net wage differentials. Hence, the elasticity of total hours of work supplied in Canada may have decreased as a result. Consequently, personal income taxation would cause relatively less excess burden than in the absence of the Act and an optimal policy response would be to increase personal tax rates. Davies and Winer find some evidence that this happened. 7. Using the definition of elasticity and its midpoint formula, if the after-tax share increases by 0.08%, taxable income should decrease by 0.096%. (1.2 × % change in after tax share = % change in taxable income). Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 8. If individuals view their loss in labour income taxes as offset by the benefits of public services, labour supply falls by AB hours. This is the compensated change in hours with respect to a change in the net wage rate. 9. This finding is completely consistent with the life-cycle model of consumption behaviour. Basically, this model suggests that consumption behaviour is dependent upon permanent income and is not strongly affected by temporary changes in income. The fact that the temporary tax cut had no strong effect on consumption behaviour is not surprising, since they have no effect on permanent income. If the government wishes to use tax policy to stimulate consumption, then the permanent income hypothesis would dictate that it must employ permanent tax cuts to alter permanent income. 10. Increasing tax rates will not increase tax revenue if European tax rates are on the righthand side of the Laffer Curve (Figure 19.6), where the tax rate exceeds tA. 11. a. The supply curve is given by S = -100 + 200wn. The before-tax wage is w = 10, and the after-tax wage is wn = (1-t)w = (1-t)10. The difference, then, between the beforetax and after-tax wage for any tax rate is w - wn = 10t. This is the tax collected per hour of work. The tax revenue for any given hours of work is then the product of the tax collected per hour of work and the quantity of labour supplied: Tax Revenue

= 10t*(-100+200(1-t)10) = -1,000t + 20,000t -20,000t2 = 19,000t - 20,000t2

The tax rate t = 0.7 is beyond the revenue maximizing point (this can be shown by computing tax revenue for a slightly lower tax rate, like t=0.69. Thus, to increase tax revenue the government would want to lower taxes. See point A in the following figure:

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Suggested Answers to Exercises

b. Taking the derivative: dTax Revenue/dt=0 yields 19,000-40,000t=0, or t = (19,000/40,000), or t = 0.475 as the revenue maximizing tax rate. 12. The net effect on private saving is ambiguous. For consumers who would have saved more than the $15,500 in any case, there is no pro-saving substitution effect associated with the plan, and the income effect can go in either direction. For other types of savers, the net effect depends on a positive substitution and an ambiguous income effect. Moreover, to the extent that tax revenues are used for capital formation, public saving may decrease even if private saving increased, with an ambiguous result for social (public + private) saving. 13. A rational person will increase savings in reaction to reduced interest rates, as suggested by the financial columnist, if the income effect is stronger than the substitution effect. This would result in a downward-sloping supply of savings curve. 14. a. There are horizontal equity concerns between how homeowners and renters are treated through the application of asset tests. Economic theory suggests that the imputed value of the service provided by this asset (principal residences) should be included in disposable income following an approach similar to that outlined by Diewert et al. (2020). However, income assistance programs may not be able to effectively calculate Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises the imputed value for homeowners. As a result, for horizontal equity asset tests should recognize costs of renting b. If the tax system were changed so that the imputed value from principal residences were included in taxable income, then all programs would be able to easily calculate this value and include it as part of the asset test. 15. High marginal tax rates reduce, not only the net-of-tax expected return, but also the variance of the net return. If investors are risk-averse, the reduction in uncertainty cause by income taxation may encourage risk-taking. Chapter 19 1. Ad valorem taxes are levied as a fixed proportion of an item’s value while unit taxes are a fixed amount per unit of an item. Gasoline taxes of 10 cents per litre levied by the federal government is an example of the latter while the retail sales tax of 6 percent levied by the Government of Saskatchewan is an example of the former. 2. You save $31,500 – (1.05×16,000) = $14,700. Your consumption in the second period is therefore equal to (1+(1-.2)×.08)×$14,700/1.05 = $14,896. You pay sales taxes of $800 in the first period and $744.80 in the second period. Your tax on interest income is $235.20. 3. Under an income tax, Amy's burden is $1,000*t in the first period, and .08[(1-t)$1000-200]t in the second period (e.g., her investment income is taxed). Shirley's burden is identical in the first period, $1,000*t, but is lower in the second period, equal to .08[(1-t)$1000-300]t. This is because Shirley consumed more in the first period and saved less. Thus, Amy has a higher lifetime tax burden because she has higher investment income. Under a proportional consumption tax, Amy and Shirley have the same lifetime tax burden, $1,000*, where  is the consumption tax rate. 4. a. We can conclude that an income tax generates an excess burden if it creates a tax wedge between the amount a borrower pays and the amount a lender receives. With a 25% income tax and an interest rate of 8%, lenders receive (1 – t)r = 6%. Since interest paid is tax deductible, borrowers pay (1 – t)r = 6%. Therefore, there is no tax wedge and no excess burden. b. If interest payments are not tax deductible, then borrowers pay 8%, while lenders receive 6% after taxes. Since there is a wedge between the two rates, the income tax creates an excess burden in this case. c. If the income tax rate is t = 0.25, then (1+) = 1/(1-0.25) = 4/3, so the equivalent consumption tax is  = 1/3. A consumption tax leaves unchanged the market of return because the receipt of interest income by itself does not create a tax liability. If interest payments are not tax deductible, there is no wedge between the rate lenders receive and the rate borrowers pay, so there is no excess burden. d. If interest payments are tax deductible, then there is a wedge between the rate lenders receive and the rate borrowers pay, so the tax creates an excess burden. With a consumption tax rate of 1/3, borrowing $1 and paying 8% interest causes the tax liability Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises to fall and the after-tax interest rate borrowers must pay is (1 – t)r = (2/3)0.08 = 5.36%. In this case, the wedge between what the rate lenders receive (8%) and the rate borrowers pay (5.36%) is even larger than for a 25% income tax when interest payments were not tax deductible, so the excess burden is larger. Note that there is an excess burden associated with an income tax only when interest payments are not tax deductible, while there is an excess burden associated with a consumption tax only when interest payments are tax deductible.

5. Sale by producer Y to producer Z $600 $30 $10 $20

Sale by producer Z to consumers

Sale value a. GST collected b. GST credit c. GST remitted

Sale by producer X to producer Y $200 $10 0 $10

Sale by producer Y to producer Z $600 $30 $10 $20

Sale by producer Z to consumers

Sale value a. GST collected b. GST credit c. GST remitted

Sale by producer X to producer Y $200 $10 0 $10

$1,600 $80 $30 $50

$1,600 0 0 0

Producer Lumberjack Furniture Maker Wholesaler Retailer Total

Value Added $100

GST 5

Input Tax Credit 0

Net Tax Due 5

400

200 100 $800

35 40 105

25 35 65

10 5 40

Value Added

GST

Input Tax Credit

Net Tax Due

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Suggested Answers to Exercises Lumberjack Furniture Maker Wholesaler Retailer Total

$100 400

5 25

0 5

5 20

200 100 $800

35 0 65

25 0 30

10 0 35

8. Retail sales taxes of some provinces, such as British Columbia and Saskatchewan, levy taxes on inputs purchased by businesses and not just on final consumers. The federal GST, and any provincial system harmonized with it as an HST, exempts business inputs and charges a tax only on the final value of a product for consumers. Equivalently, the GST is a value-added tax while the retail sales taxes in BC and Saskatchewan are not. This has the effect of compounding the tax burden throughout a supply chain and therefore also distorts business investment and production decisions. 9. If an additional excise tax is levied on an item that generates an external cost on others, then this may be improve economic efficiency. To the extent that the external cost is not incorporated into the production and consumption decisions in this market, there may be an overconsumption of the item that results in a deadweight loss – as explored in Chapter 5. An excise tax, so long as it does not exceed the magnitude of the marginal external cost at the efficiency level of consumption, will decrease consumption and remove the deadweight loss. 10. The statement is misleading because it ignores the business part of the Hall-Rabushka tax. Capital incomes are generated by businesses; effectively, the H-R tax captures this income at its source. Note, however, that investment expenditures are expensed under the H-R proposal. Hence, only returns to capital in excess of normal returns are taxed. 11. In order to tax ―accrued‖ income, assets of all types would have to be valued annually to determine unrealized gains and losses. This would be extremely complex, difficult, and costly for taxpayers and tax collectors. A personal consumption tax applies only to those amounts spent on consumption. Where gains and losses are not realized through the sale of real and financial assets, they do not enter into the calculation of the tax base. Nor is there a need to calculate depreciation (CCAs) since a full deduction is permitted in calculating the tax base when real and financial assets are purchased. Chapter 20 1. Any and all gifts and bequests are included in taxable income according to the Haig-Simons definition of income. The deceased and recipient are separate individuals, and if the individual is the taxable unit, the bequest increases the recipient’s ability to consume or add to his net wealth. It is irrelevant that the deceased was never allowed to deduct the $100,000. Because of the ―lumpiness‖ of some gifts and bequests, in a tax system with progressive rates, it may make sense to permit a recipient to average large gifts and bequests over several years. That gifts and bequest are not included in the taxable income of the recipient under Canadian tax law is a good topic for discussion. If the bequest was dictated in some fashion, reducing their ability to pay, there might be an argument for deductibility. But if the bequest was discretionary, it should not be.

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Suggested Answers to Exercises 2. Both the donor and recipient need to be considered. Wealth transfer taxes increase the price the donor must pay for each dollar transferred. Relative to the price of leisure, the price of wealth transfers has increased. A donor may choose to work less and save less. However, if the objective is to leave family members with a specified amount, net of tax, a donor may work more and save more. Similarly, with full loss offsets, donors wishing to leave substantial fortunes to their family may be encouraged to increase risk to realize higher returns. This is like the effect of a tax on interest income when the objective of an individual is to save a ―targeted‖ amount. If wealth transfer taxes reduce the amount for the recipient, this will have an income effect that increases work effort. The tax may also increase the need for the recipient to save. 3. The effect of the change in tax rates would depend upon the mobility of homeowners and businesses. Homeowners would be tempted to relocate to avoid higher taxes, while businesses might be induced to move in to take advantage of the more attractive tax rates. The long-run and short-run effects might be different, too, as house prices adjust, and people have more opportunities to move. The mobility of homeowners in turn depends upon the size of the city – in Vancouver tax rates vary substantially across lower mainland municipalities, but Toronto is a hard-to-escape-from ―mega-city.‖ 4. Yes, the first individual bore the burden of the tax increase while the second did not. Because the future tax payments are incorporated into the price of the house, the second individual was able to purchase the (same) house at a lower price. The previous owner effectively ―pays‖ the tax. If both individuals are in homes with the same market value and receiving the same public services, horizontal equity requires that their tax payments should be the same. 5. The change from a property tax to a land value tax would lower the tax rate on building structures. As this would encourage new construction, downtown parking may become scarcer. If contractors re-allocate construction from Hamilton to Toronto, land prices in Hamilton could be expected to fall. 6. From a capital tax view, the increase in the city’s property taxes may cause some mobile factors of production — people and capital investments — to move to places with lower taxes. This would create excess burden. Landowners would bear a large share of the higher property tax, since land is an immobile factor. Under a user fee view, the property tax increase is equivalent to paying a price for the benefit of accessing the tunnel and, hence, it would not induce an exit of people and capital. In this case, the tax is neutral and has no important distributive consequences. Since the tunnel would be used mainly by residents in the Northeast part of the city, a capital tax view is probably more appropriate than a user fee view. 7. Development charges oblige the sellers and buyers of houses to internalize the cost of infrastructure in a new neighbourhood. This is a more precise way of matching the benefits and costs of public services than a property tax can achieve. Development charges improve efficiency and satisfy the benefit principle. 8. The ―user-fee‖ view of property taxes regards property taxes as payment for local public services. The statement ―its presence would raise property values and the extra tax revenues would easily repay the construction costs‖ reflects this view—that people pay for the recreational services made available by the part with their property taxes. The statement is not consistent with the ―traditional view‖ or the ―new view,‖ both of which ignore the local services aspect. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 9. There are several reasons why property taxes will continue to be an appropriate target for criticism by those who seek fair and efficient taxes. Four were listed in the text: 1. Housing market transactions typically occur infrequently, the property tax must be levied on an estimated value. For some, the tax is perceived as unfair if this valuation is not made appropriately. 2. The property tax is highly visible. Moreover, the payments are often made on a quarterly or an annual basis, so each payment comes as a large shock. 3. The property tax is perceived as being regressive. It is reinforced by the fact that some property owners, particularly the elderly, do not have enough cash to make property tax payments and may therefore be forced into selling their homes. 4. Taxpayers may dislike other taxes as much as the property tax, but they feel powerless to do anything about the others. It is relatively easy to take aim at the property tax, where it is levied locally. In contrast, mounting a drive against, say, the federal income tax is more difficult, if for no other reason than a national campaign would be necessary and, hence, involve large coordination costs. 10. Royalty systems aim to extract a share of the resource rent. This reflects the value of the resource less the necessary costs to extract or produce it. In the case of oil and gas in Alberta, moving to higher cost types of deposits means that the resource rent – at any give price – will be lower than would be the case with lower cost of extraction deposits. A falling ratio of government royalty revenues to industry revenues is not evidence of the government extracting a smaller share of resource rents since costs of extraction is rising. 11. The B.C. stumpage system is not an ideal royalty system because it charges a fee on the volume of timber extracted. In recent years, this was approximately $20 per cubic meter. Because this is a levy on the quantity of production, it affects the producer’s marginal costs of production and therefore may be relevant in providing a competitive advantage compared to producers in the U.S. that may face higher costs. An idealized royalty system that extracts a share of resource rents would not affect costs in this way and therefore may be less susceptible to the same critique. Some argue B.C. has important elements of this, as it auctions rights to extract timber and therefore extracts resource rents through this mechanism. To the extent that such auctions are competitive, a low stumpage fee would not be a cost advantage. Chapter 21 1. There are several reasonable descriptions of the patterns reported in Table 21.1. In particular: the importance of corporate taxation for public finances varies over time, falling from 17.8 percent of government revenues at the end of World War II to 6.1 percent in 1995. This share had risen to 10.7 percent by 2020 due to increased profits from economic growth and the 1987 tax reforms that broadened the tax base and reduced investment tax credits. 2. This statement suggests that corporations are people, with independent abilities to pay, a view that parallels the legal status of corporations. The conventional view described in the text notes that only real people – customers, employees, shareholders – have an independent ability to pay. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 3. The calculations follow: a. Corporate income tax equals 26.5% of $200 = $53. Hence dividends equal $147. b. See line c). c. See line f). d. See line h). e. The combined rates are slightly higher than the personal income tax rates. f.

The integration is close but not exact. It remains a partial integration system. Person 1 (20 PIT Rate)

Person 2 (42 PIT Rate)

Dividends

$147

Gross up (38%)

55.86

Taxable Income

202.86

a) Federal PIT before credit

30.43 (@15%)

58.83 (@29%)

b) Federal tax credit

30.43 (@15%)

0.00

28.40

d) Provincial PIT before credit

10.14 (@5%)

26.37 (@13%)

e) Provincial tax credit

20.29 (@10%)

f) Provincial PIT after credit

-10.15

6.08

g) Combined CIT and PIT

42.85

87.48

21.43% > 20%

43.74% > 42%

c) Federal PIT after credit

h) Total tax rate

The effective tax rates exceed the marginal personal income tax rates; therefore the dividend tax credit does not fully integrate personal and corporate income taxes. 4. The answers are as follows: a. Corporate tax equals 0.5×200=100 and dividends equal 200-100=100. Personal taxes for the first individual are 0.2×100=20, for an effective total tax rate of 120/200 = 60%, and for the second individual are 0.4×100=40, for an effective tax rate of 140/200=70%. b. With perfect integration of corporate and personal taxes, the effective total tax rate is identical to the personal marginal tax rate faced by each individual: 20% and 40%. c. Tax integration causes the effective tax rate to fall from 60% to 20% (a 40percentage-point reduction) for the first individual while the rate falls from 70% to 40% (a 30-percentage-point reduction) for the second. Hence, the individual with the lower marginal personal income rate gains more from integration. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 5. In static equilibrium, owners of capital would bear a relatively large burden of a corporate tax increase. Recall the analysis of a partial factor tax in Chapter 15; the effects depend on factor substitution and output responses, and factor supplies are fixed. If we take into account dynamic effects, however, then labour would bear some burden also, since the tax might lower the capital stock and hence the marginal product of labour. In an open economy such as Canada’s, the impact on the capital stock might be particularly important. Note, however, that the effect of a capital tax on saving is, strictly speaking, ambiguous. Hence, while in the short run higher-income classes might suffer, this result could be weakened in the longer run. 6. The answers are as follows: a. The real value of depreciation allowances,  of equation (22.1), falls. b. When  falls, the user cost of capital increases. c. Index depreciation allowances. 7. The user cost of capital is given by equation (21.6) in the textbook, C=[(r+δ)(1--k)]/[(1θ)], where r=after tax rate of return in the capital market, δ=economic depreciation, θ=corporate tax rate, Ψ is the value of capital cost allowances, and k is the investment tax credit. The value of Ψ is , while k=0. Substituting the numbers from the problem into the formula, gives the user cost: C=(.08+0.1)(1.28)/.65=0.20. Since the project’s return, 30%, is higher than this user cost of 20%, the company does invest in the project. 8. The tax holiday biases company investments toward shorter-lived forms of capital. To see the reason, first consider capital that has a short life, such that it is fully depreciated by the time the holiday period ends. Suppose the tax rate θ equals zero during the holiday. In that case, θ and  are both zero in equation (21.6) of the textbook and so capital bears no tax. Now consider capital that has an economic life beyond the holiday period. Even though the firm is tax exempt during the holiday, it must pay taxes on the income generated by the investment after the holiday is over. If depreciation allowances for tax purposes are relatively high, then the tax savings generated by the allowances that remain after the holiday is over may be inadequate relative to the income-generating capacity of the capital. In effect, the firm has had to shift the bulk of its tax savings from depreciation allowances to a period during which the savings have no value because the tax rate is zero during the holiday. See Mintz, Jack (1990) ―Corporate Tax Holidays and Investment‖ The World Bank Economic Review 4(1): 81–102. 9. a.

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Suggested Answers to Exercises

10.

If foreign taxes are deductible, XYZ would pay $200,000 in domestic taxes. If foreign taxes are creditable, XYZ would pay $50,000 in domestic taxes. A tax credit makes the firm’s tax liabilities independent of their location and thereby does not bias the firm’s international investment decision. A tax deduction results in the tax liability being greater Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises on the foreign investment than on an equivalent domestic investment, thereby biasing the investment decision toward the domestic country. 11.

Yes, such a shift to complete integration would be consistent with the Haig-Simons criterion. We would expect the change to increase the amount of capital in the corporate sector, increase the distribution of corporate earnings and reduce retained earnings, and reduce the ratio of debt to equity.

Online Appendix – Public Choice 1. a. Below, the preferences for each person.

b. C wins in every pair wise vote. Thus, there is a stable majority outcome, despite the fact that persons 1, 2, and 3 have double-peaked preferences. This demonstrates that although multi-peaked preferences may lead to voting inconsistencies, this is not necessarily the case. 2. a. The outcome of the first election (M vs. H) is M. The outcome of the second election (H vs. L) is L. The outcome of the third election (L vs. M) is M. Majority rule leads to a stable outcome since M defeats both H and L. Giving one person the ability to set the agenda would not affect the outcome in this case. b. With the change in Eleanor’s preference ordering, majority rule no longer generates a stable outcome. In a vote between M and H, the outcome is H. In a vote between H and L, the outcome is L. In a vote between L and M, the outcome is M. So, giving one person the ability to set the agenda affects the outcome. For example, Abigail prefers H, so she might pit L against M first in order to eliminate L and avoid having L defeat H. Rosen: Public Finance, 6Ce © 2023 McGraw Hill Ltd.

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Suggested Answers to Exercises 3. When there is a vote over five options, there is the chance that a potential majority vote is split between four relatively preferred options, and the fifth option wins. The winning option may have been voted down if it had been a two-way vote with any of the other options. Further, if preferences are not single-peaked, cycling and inconsistent public decisions may emerge. 4. a. Neither issue would pass with majority voting as in both cases, two voters of the three would vote against each issue because they receive negative net benefits. This is not efficient because issue X has a positive total net benefit and should be funded. b. With logrolling, voters A and B can trade votes. A will vote for issue Y if B votes for issue X, but C will not vote for either project. Both issues will pass with two votes for and one against. This is not efficient because issue Y has a negative total net benefit. c. If side payments were allowed A could pay B to vote for issue X (A would not pay C because C would require a higher payment than B), and B could pay A or C to vote for issue Y. This would result in the same inefficient outcome as in b. d. If side payments were allowed A would have to pay B at least 1 to vote for issue X. A would only be willing to pay less than 6. B would have to pay A or C at least 3, but no more than 4 to entice him to vote for issue Y. 5. The six criteria are as follows: 

It can produce a decision whatever the configuration of voters’ preferences. Thus, for example, the procedure must not fall apart if some people have multipeaked preferences.



It must be able to rank all possible outcomes.



It must be responsive to individuals’ preferences. Specifically, if every individual prefers A to B, then society’s ranking must prefer A to B.



It must be consistent in the sense that if A is preferred to B and B is preferred to C, then A is preferred to C.10



Society’s ranking of A and B depends only on individuals’ rankings of A and B. This assumption is known as the independence of irrelevant alternatives.



Dictatorship is ruled out. Social preferences must not reflect the preferences of only a single individual.

The impossibility theorem states that it is impossible to find a voting rule that satisfies all of these criteria without voting paradoxes arising. But if any of the six criteria is dropped, a decision-making rule that satisfies the other five can be constructed. But whether or not it is permissible to drop any of the criteria depends on one’s views of their ethical validity.

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Suggested Answers to Exercises 6. When the policy changed to allow and encourage female voting, female voters became the majority, so it is sensible that the median voter is now a woman. Given this, the median voter theorem suggests that politicians should shift their positions to more closely align with the views of women. 7. a. Three percent a year. b. Assuming that the public sector uses only labour as an input, the price of the public good increases by 3 percent a year. c. The size of government increases. For further discussion of this phenomenon see the paper by W.J. Baumol, ―Macroeconomics of Unbalanced Growth: The Anatomy of Urban Crisis,‖ American Economic Review, 1967.

8. a. With the demand curve of Q=100-10P and a perfectly elastic supply curve at P=2, the milk is sold at a price of $2, and a quantity of 80 units is sold. b. The marginal revenue curve associated with the inverse demand curve P=10-(1/10)Q is MR=10-(1/5)Q, while the marginal cost curve is MC=2. The cartel would ideally produce a quantity where MR=MC, or 10-(1/5)Q=2, or Q=40. The price associated with a cartel quantity of 40 units is P=10-(1/10)×40, or P=6. c. The rent associated with the cartel is the product of the marginal profit per unit and the number of units produced. The marginal profit per unit of milk is $4 (=$6 price $2 marginal cost), while 40 units are produced. Thus, the rents equal $160. d. The most the cartel would be willing to contribute to politicians is the full economic rent of $160. The cartel situation, the quantity of milk produced is too low from society’s point of view. The deadweight loss triangle is computed using the difference between the cartel output and competitive output as the ―base‖ of the triangle, and the difference between the cartel price and competitive price as the ―height.‖ Thus, the triangle is equal to (1/2)×(80-40)×($6-$2)=$40. e. As Figure OA1.5 in the textbook shows, the deadweight loss could now go as high as the sum of the conventional deadweight loss and the rents, or $160 rents + $80 DWL = $240. This is because, as noted in the text, ―rent-seeking can use up resources – lobbyists spend their time influencing legislators, consultants testify before regulatory panels, and advertisers conduct public relations campaigns. Such resources, which could have been used to produce new goods and services, are instead consumed in a struggle over the distribution of existing goods and services. Hence, the rents do not represent a mere lump-sum transfer; it is a measure of real resources used up to maintain a position of market power.‖

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Suggested Answers to Exercises 9. When a cartel raises its price, any individual firm has an incentive to cheat, that is, to increase its production beyond its agreed-upon quota. If the firms can get the government to enforce the cartel, then they can maintain the high price without having to worry about cheating. 10. a. When each actor pays $5, Moe’s preferred quantity is 4 hours, Larry’s is 7, and Curly’s is 2. Their preferences are single-peaked and thus the median choice (4 hours) prevails. This is close to the optimal level of 5, where MB = MC. b. In this case, Moe’s preferred choice is 6, Curly’s is 6, and Larry’s is 3. Majority rule selects 6 as the winning choice, which exceeds the efficient quantity of 5.

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