Instructor’s Manual to accompany
Public Finance, Seventh Edition, by Harvey S. Rosen
Suggested Answers to End-of-Chapter Discussion Questions
Some of the questions have no single “correct” answer – reasonable people can go off in different directions. In such cases, the answers provided here sketch only a few possibilities.
Chapter 1 - Introduction
1. a. Putin’s statement is consistent with an organic conception of government. Individuals and their goals are less important than the state.
b. Rehnquist makes a clear statement of the mechanistic view of the state.
2. a. A person with an organic conception of the state might react favorably, arguing that even if an individual owner is worse off because he must show only French movies, the nation is better off because it achieves more unity.
b. A libertarian would certainly reject this policy and the reasoning behind it -- there is no “national interest” independent of the interests of individuals, and people should have the right to run their lives in the way that they prefer -- including seeing whatever movies they want.
c. A social democrat would try to balance these two aims, and it is hard to predict how he or she would come out.
3. The mechanistic view of government says that the government is a contrivance created by individuals to better achieve their individual goals. Within the mechanistic tradition, people could disagree on the obesity tax. Libertarians would say that people can decide what is best for themselves - whether to consume high calorie food - and do not need prodding from the government. In contrast, social democrats might argue that people are too short sighted to know what is good for them, so that government-provided inducements are appropriate.
4. a. If the size of government is measured by direct expenditures, the mandate does not directly increase it. Costs of compliance, however, may be high and would appear as an increase in a “regulatory budget.”
b. It’s hard to say whether this represents an increase or decrease in the size of government. One possibility is that GDP stayed the same, and government purchases of goods and services fell. Another is that government purchases of goods and services grew, but at a slower rate than the GDP. One must also consider coincident federal credit and regulatory activities and state and local budgets.
c. The federal budget would decrease if grants-in-aid were reduced. However, if state and local governments offset this by increasing taxes, the size of the government sector as a whole would not go down as much as one would have guessed.
5. The inflation erodes the real value of the debt by 0.021 x £311 billion or £6.5 billion. The fact that inflation reduces the real debt obligation means that this figure should be included as revenue to the government.
6. The federal government grew by $450 billion. However, because the price level went up by 16 percent, in terms of 2001 dollars this amounted to a real increase of $224 billion (=$1.86 trillion - 1.16*$1.41 trillion=$1.86 trillion-$1.64 trillion). Note that the increase in prices of 16 percent in the Rosen text (p. 18) differs from official sources. According to the 2004 Economic Report of the President (Table B-60), the CPI-U was 177.1 in 2001 and was 144.5 in 1993, an increase of 22.5 percent, not 16 percent. If one uses these numbers, government spending increased in constant 2001 dollars from $1.72 trillion in 1993 to $1.86 trillion, or $140 billion. As a proportion of GDP, federal spending in 1993 was 21.2 percent and in 2001 it was 18.2 percent. Hence, by one measure, the size of government fell and by the other measure, it grew. To get a more complete answer, one would want data on the population (to compute real spending per capita). Also, it would be useful to add in expenditures by state and local governments, to see if the total size of government fell. Also, although it would be harder to measure, one would want to try to gain some sense of how the regulatory burden on the economy grew during this time period.
Chapter 2 – Tools of Positive Analysis
1. The reality that astronomers are trying to understand is not influenced by any “policies” that astronomers might implement. That is, planets and stars do act any differently when they are being analyzed, whereas people can change their behavior. Moreover, the parameters with which astronomers must deal are constant over time (at least in the “short-run” of hundreds of years), while the parameters in economics can quickly change over time and across geography.
2. A change in the marginal tax rate changes the individual’s net wage. This generates both an income effect and a substitution effect. As long as leisure is a normal good, these effects work in opposite directions. Hence, one cannot tell a priori whether labor supply increases or decreases. One could ask taxpayers to describe how they would change their behavior under the proposal, but it is hard to imagine that this would yield useful results. In a social experiment, a control group would confront the status quo, and an experimental group would face the new tax regime. This is clearly infeasible. Econometric investigation of labor supply seems the best approach, particularly if data associated with past changes in tax rates can be brought to bear on the problem.
3. Generally, economic outcomes are affected by a number of variables some of which are observed and others of which are unobserved. Economists often cannot perform
(e.g., the Negative Income Tax experiment or the RAND Health Insurance Experiment), a number of unintended behaviors can arise because people know they are in the experiment for a short amount of time and because of lack of generalizability. In the medical example here, brain impairment may be due to a number of factors that are either observed are unobserved. Ecstasy users clearly are not a random sample of the population, but are likely to differ in terms of their attitudes towards risk, their discount rates, and potentially many other ways. Hence, one cannot definitively conclude whether brain impairment is due to Ecstasy or some variable that is correlated with Ecstasy use. There are numerous non-experimental methods that may be helpful in inferring the causal effect of Ecstasy. For example, if there were a plausible “instrumental variable” (perhaps the punitiveness of the drug laws in a state) that was correlated with the supply of Ecstasy but not otherwise correlated with the outcomes of interest, one may be able to estimate the causal effect of Ecstasy on long-run developmental problems.
4. The text points out the pitfalls of social experiments: the problem of obtaining a random sample and the problems of extending results beyond the scope of the experiment. Participants in the study had found it to their advantage to be a part of the experiment, which may have resulted in a self-selected population unrepresentative of the wider group of health care consumers. In addition, the RAND Health Insurance Experiment was of limited duration, after which the participants would move to some other health plan. This design could induce certain behavior in the short-run that would not necessarily be present if the health insurance coverage were permanent rather than transitory. Further, physicians’ “standard practices” are largely determined by the circumstances of the population as a whole, not the relatively small experimental group.
5. First, it is important to note that the numbers on page 32 of Rosen’s text actually show the surplus, not the deficit. That is, the negative surplus of $221.2 in 1990 is actually a deficit, while the positive surplus of $236.4 is a surplus. There is a very weak, negative relationship between surpluses and interest rates (the correlation coefficient is -.043), or put differently, a weak, positive relationship between deficits and interest rates. However it is expressed, it is weak -- by “eyeballing” the data, it might appear that larger deficits lead to lower interest rates (for example, by comparing the data from 1980 with the data from 2000). One clearly would need more data to investigate this question. One would want to look at deficits relative to some benchmark, such as GDP. One would want to express both interest rates and deficits in real terms, rather than nominal terms. One would like to control for other factors that can affect interest rates, such as monetary policy and the level of economic activity. Finally, one would want to determine which way the causality runs – do larger deficits cause higher interest rates, or do higher interest rates cause larger deficits (since, by construction, one of the largest items in the federal budget is interest on the debt).
Chapter 4 – Public Goods
1. a. Wilderness area is an impure public good – at some point, consumption becomes nonrival; it is, however, nonexcludable.
b. Water from a municipal water supply is both rival in consumption and excludable. My consumption of water precludes you from consuming the same water, thus it is rival. The municipality can control who consumes water by shutting off the flow to customers, thus it is excludable. This is a useful question for showing that not all publicly owned facilities are public goods.
c. Medical school education is a private good. d. Television signals are nonrival in consumption.
e. An Internet site is nonrival in consumption (although it is excludable).
2. We assume that Cheetah’s utility does not enter the social welfare function; hence, her allocation of labor supply across activities does not matter.
a. The public good is patrol; the private good is fruit.
b. Recall that efficiency requires MRSTARZAN + MRSJANE =MRT. MRSTARZAN=MRSJANE =2. But MRT=3. Therefore, MRSTARZAN + MRSJANE >MRT. To achieve an efficient allocation, Cheetah should patrol more.
3. A pure public good is nonrival in consumption, thus it is necessary to determine whether or not this is the case with the highway. That is, if the additional cost of another person “consuming” the highway is zero, then it is a public good. So, as long as the highway is not congested, then it can be considered to be a public good. However, adding another motorist to an already congested roadway can cause traffic jams that cost motorists more time to travel the highway, which would represent nonzero costs to having an additional person use the highway. Therefore, the congestion of the roadway determines whether or not we could designate it as a public good. Note that we are assuming throughout that the highway is nonexcludable.
To determine whether or not the privatization of the highway is a sensible idea, it is necessary to consider the advantages and disadvantages of such an action. First, if the market structure is such that privatizing the highway would result in a monopolist in control of the highway, then this would be inefficient. Also, it would be difficult for the government to write a complete contract for maintaining the highway, which would also cause inefficiencies that would result from the privatization of the road. However, if the government owns the highway, it might not have the appropriate incentives to maintain it properly. In such a case, even ownership by a private monopolist might be a sensible solution.
4. The benefits of maintaining the incomes of the poor accrue largely to the recipients of welfare, not to society as a whole. Thus, it is implausible to think of welfare (or the administration of the welfare system) as a public good. Unless there is a “warm-glow” from income redistribution, there is little basis for thinking that the provision of TANF,
whole. In terms of administration of welfare, it is hard to say whether or not it should be publicly or privately administered. Private administration might be less costly. On the other hand, private administrators might have an incentive to deprive deserving individuals of benefits in order to cut costs. It could be difficult to write a contract to prevent this kind of behavior, because one cannot specify in advance every conceivable set of circumstances under which welfare should be granted. This kind of subjectivity was present in the 1960s, when caseworkers had a great deal of discretion in terms of which households to offer assistance to. This subjectivity led to accusations of discrimination and, from the 1970s onward, there has been far less subjectivity in terms of defining eligibility. Since that time, eligibility is fairly mechanically related to income, assets, family structure, and a number of other observable factors. Given the current system, it seems less difficult today to monitor a private firm than it would have been in the 1960s.
5. A lower cost is a necessary (but not sufficient) condition to conclude that prisons should be privatized. A policy maker should be concerned both with costs and quality of prisons. Although, in principle, one could write a contract that is concerned about the quality of prisons (e.g., whether the prisoners are treated decently, whether security is adequate, and so on), Hart, Shleifer and Vishny (1997) note that it is sometimes impossible to write a complete contract because one cannot specify in advance every possible contingency. The key is whether the administration of prisons is a fairly “routine” activity where complete contracts can be written, or whether there are too many contingencies.
6. As noted on page 65 of the textbook, the experimental results of Palfrey and Prisbrey (1997) suggest that there is some free riding, but some people do contribute. Those authors found that, on average, people contribute a portion of their resources to the provision of a public good, and there is some free riding. That was the case in Manchester, Vermont. Also, Palfrey and Prisbrey found that when the experimental game was repeated, people were more likely to free ride. This also happened in Manchester -- in the second year, participation was less.
7. There is no compelling reason for museums to be run by the government from the theory of public goods; thus, it is appropriate to think about privatization. Admissions to museums are clearly excludable. And viewing the artwork is also rival, because there is congestion when too many people are consuming the good. Thus, museums may be thought of as a private good rather than public good. In the United States, many great museums are run privately (not for profit), and they seem to do quite well. In terms of private versus public production, the text points out that this decision should be based on relative wage and material costs in the public and private sector, administrative costs, diversity of tastes, and distributional issues. There is no compelling reason to think the private sector would have higher costs than the public sector. In regards to diversity of tastes, a profit-maximizing private sector museum would likely be more responsive to consumer tastes than the public sector – e.g., adopting new technologies that make the museum more enjoyable for the typical customer. In regards to distributional issues, it is
likely that the private sector would be less responsive than the public sector. The notion of commodity egalitarianism, however, is a stretch for museums.
8. If households are allowed to supplement public education with private lessons, then the budget constraint in Figure 4.5 of the textbook is modified by drawing a line starting at point x (consuming only public education) that runs to the southeast and is parallel to AB. The figure below is then similar to the analysis of in-kind benefits like food stamps.
ep
BA A
Other Goods
Education FIGURE 4.8a – Supplement public
If parents pay for the public schooling (rather than perceiving it as being free), and the schooling was paid for with a lump sum tax, then the budget constraint shifts in by an amount that depends on the household’s share of the tax burden. If the household’s tax burden exactly equals the cost of public school, the budget constraint is no longer the line segment AB but rather the segment CDB, where the segment DB runs along the original budget constraint, except that the minimum amount of schooling consumed is eP.
9. In this case, the apartment’s temperature is a public good because for the “society” of Rodolfo and Mimi, the temperature is nonrival and nonexcludable. Both get to “consume” a warmer house, and neither can exclude the other from this. The marginal benefit for society is the sum of Rodolfo’s and Mimi’s marginal benefit – e.g., $20 at 66 degrees, $17 at 67 degrees, $13 at 68 degrees, $8 at 69 degrees, and $4 at 70 degrees. The marginal benefit for society equals the marginal cost at 67 degrees; for temperatures higher than that, the marginal cost is greater than the marginal benefit for society.
D C ep BA A Other Goods Education FIGURE 4.8b – Parents pay for “free”
10. Thelma’s marginal benefit is MBTHELMA=12-Z, and Louise’s is MBLOUISE=8-2Z. The marginal benefit for society as a whole is the sum of the two marginal benefits, or MB=20-3Z (for Z≤4), and is equal to Thelma’s marginal benefit schedule afterwards (for Z>4). The marginal cost is constant at MC=16. Setting MB=MC along the first segment gives 20-3Z=16, or Z=4/3, which is the efficient level of snowplowing. Note that if either Thelma or Louise had to pay for the entire cost herself, no snowplowing would occur since the marginal cost of $16 exceeds either of their individual marginal benefits from the first unit ($12 or $8). Thus, this is clearly a situation when the private market does not work very well. Also note, however, that if the marginal cost were somewhat lower, (e.g., MC≤8), then it is possible that Louise could credibly free ride, and Thelma would provide the efficient allocation. This occurs because if Thelma believes that Louise will free ride, Thelma provides her optimal allocation, which occurs on the second segment of society’s MB curve, which is identical to Thelma’s MB curve (note that Louise gets zero marginal benefit for Z>4). Since Louise is completely satiated with this good at Z=4, her threat to free ride is credit if Thelma provides Z>4.
Chapter 5 - Externalities
1. Classical economics explicitly requires that all costs and benefits be taken into account when assessing the desirability of a given set of resources, so Gore’s statement is false. The notion that rescuing the environment should be “the central organizing principle for civilization” provides no practical basis for deciding what to do about automobile emissions (or any other environmental problem), because it provides no framework for evaluating the tradeoffs that inevitably must be made.
2.
a. The number of parties per month that would be provided privately is P. b. See schedule MSBp.
c. P*. Give a per-unit subsidy of $b per party.
d. The total subsidy=abcd. “Society” comes out ahead by ghc, assuming the subsidy can be raised without any efficiency costs. (Cassanova’s friends gain gchd; Cassanova loses chd but gains abcd, which is a subsidy cost to government.) 3. 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.
b. It is unlikely that property rights could be enforced in terms of catching tropical fish on the Amazon River. The question states that hundreds of divers illegally catch these fish and sell them on the black market. If the property rights were given to the divers, it is not clear who is actually harmed (perhaps “society as a whole”) by the depletion of exotic fish. Given the large number of people who are harmed (in a small amount), and the large number of people who are engaging in this activity, it is not clear how bribes would flow from “society” to the “divers.” c. There are too many farmers and too many city-dwellers for a private negotiation. d. Too many people are involved for private negotiation and impossible to figure out
how to transfer bribes.
4. a. The price of imported oil does not reflect the increased political risk by effectively subsidizing authoritarian regimes like those in Saudi Arabia.
b. The tax would estimate the marginal damage (e.g., the increased instability in the Middle East, etc.) by importing oil from Saudi Arabia.
c. The supply of vouchers is vertical at 140 billion. The demand curve is downward sloping. For every gallon of gasoline, you either have to buy a voucher or use up one of your own. In either case, this increases the opportunity cost by 75 cents.
5. The per-unit taxes, which range from 12-27 cents per ounce, are far below the marginal external cost of $1.19 per ounce. Although the deadweight loss is smaller than with no tax at all, the allocation is still far from the socially efficient level. The current allocation produces too much alcohol at too low of a price.
6. By establishing a market for air pollution rights, the Chicago Board of Trade has applied the Coase Theorem. The potential efficiency of the outcome may be laudable, but the distributional impact may be unpalatable to some.
7. a. When the Little Pigs hog farm produces on its own, it sets marginal benefit equal to marginal cost. This occurs at 4 units.
b. The efficient number of hogs sets marginal benefit equal to marginal social cost, which is the sum of MC and MD. At 2 units, MB=MSC=13.
c. The merger internalizes the externality. The combined firm worries about the joint profit maximization problem, not the profit maximization problem at either $0.75 140 billion D S PVOUCHER QVOUCHER
d. Before the merger, the LP farm produced 4 units. By cutting back to 2 units, it loses marginal profit of $3. On the other hand, the Tipsy Vineyard’s profits increase by $20. Thus, profits increase by $17 altogether.
8. 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 Costs = $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.
9. In the absence of persuasive evidence on positive externalities for higher education, there is no reason for the government to provide free tuition. True, taxes on wages may distort education decisions (see Chapter 16), but virtually all taxes distort some decision making, and it is unlikely that it is optimal to subsidize tuition at 100 percent.
10. a. By regulating the number of permits to 50 units, then the demand curve implies that 50=100-10P, or P=$5.
b. Because it would cost ACME more money to reduce pollution than buy a permit ($8 versus a market price of $5), ACME buys the permit. By doing so, it saves $3 in costs.
Chapter 6 – Political Economy
1. a. Below, the preferences for Person 1 and Person 2 are drawn. Same procedure is used for the other three people.
b. C wins in every pairwise 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. The votes by the Senators from the northeast and south to subsidize each other’s interests are consistent with the logrolling model. The senators from the affected states made the deal for advantage their constituents at the expense of other regions.
3. a. Three percent a year.
b. Assuming that the public sector uses only labor as an input, the price of the public good increases by three 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 Crises,” American Economic Review, 1967.
4. Yes, it is consistent, because the theory says that when unanimity is required, no decisions are likely to be made. A majority system might be more suitable, although it is subject to cycling and other problems.
5. If these figures are true, then the predictions of the median voter theory are not accurate – that is, majority voting will not reflect the preferences of the median voter but rather the median participating voter. The reason for this is because of the different turnout rates for individuals in different income categories. Consider this simple example: suppose that voters have single-peaked preferences, and they are trying to determine how much should be spent on national defense. Their preferences are listed as follows:
Andrew: $500 Bob: $700 Charlie: $850
The median voter theorem predicts that a majority vote will result in $750 being spent on defense (which is reflective of Bill’s preferences, since he is the median voter). However, if there are different participation rates by different groups (in this case, the groups are determined by the first letter in the person’s name), then the preferences of the median voter (Bill) are no longer reflected in the majority vote. Suppose that Andrew and Anne don’t vote – then a majority vote will result in $800 of defense spending.
6. 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.
7. Given the U.S. experience with the Budget Enforcement Act of 1990, we would expect the EU deficit limits to be ineffective. We would expect “accounting tricks” to mask the size of the deficits (such as itemizing various budget items as “unexpected emergencies”), and if that didn’t work, we would expect the deficit rules to be ignored. This is apparently what is happening. When Germany exceeded the deficit target, no moves were taken to levy the required fines.
8. Since rents, by definition, are the returns above a normal return, then when the licenses are put on the market, their price will be the value of the rents. Hence, the owner of the peanut license, whoever he or she is, only makes a normal return. Put another way, the license is an asset that earns a normal rate of return. If the peanut license system were eliminated, efficiency would be enhanced. But the elimination would, in effect, confiscate the value of this asset. It is not clear that this is fair. One could also argue that when someone buys this asset, the purchase is with the understanding that there is some probability that its value will be reduced by elimination of the program; hence, it is not unfair to do so.
9. a. With the demand curve of Q=100-10P and a perfectly elastic supply curve at P=2, then 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 6.5 in the textbook shows (page 130), 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 on page 131, “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.”
10. Niskanen’s model of bureaucracy is illustrated in Figure 6.4 of the textbook. In the aftermath of September 11th, the new concerns over food safety would likely shift the V curve upward (that is, the value placed on each level of Q). Assuming that C curve (costs per unit of Q) does not change, then this shift increases the actual number of food inspectors hired. It is also likely that the slope of the V curve changes, with each marginal unit of Q becoming more valuable. Thus, the V curve not only “shifts” upward, but becomes steeper as well. Both of these effects – the shifting of the V curve and the change in the slope – lead to greater values of Q under the bureaucracy model. The change in the slope leads to a greater value of Q*, the efficient level of output. Thus, the optimal number of FDA employees and the actual number of FDA employees are likely to rise.
11. The lesson in The Economist, that Democrats flourish when they move toward the center, is basically a description of the median voter rule.
Chapter 7 – Income Redistribution: Conceptual Issues
1. Utilitarianism suggests that social welfare is a function of individuals’ utilities. Whether the rich are vulgar is irrelevant, so this part of the statement is inconsistent with utilitarianism. On the other hand, Stein’s assertion that inequality per se is unimportant is inconsistent with utilitarianism.
2. 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 Charity matters, then give money to Charity until MUc = 0 (unless all the money in the economy is exhausted first).
Giving any more money to Charity causes her marginal utility to become negative, which is not optimal. Note that we don’t care if the remaining money ($33.33) is given to Simon or not.
If only Simon matters, then, proceeding as above, MUs. 0 if Is = 100; hence, giving all the money to Simon is optimal. (In fact, we would like to give him up to $200.)
c. MUs = MUc for all levels of income. Hence, society is indifferent among all distributions of income.
3. The main conceptual problem with the poverty gap is that it doesn’t account for the income effect on labor force participation rates. The poverty gap is calculated assuming there are no behavioral responses; e.g., that labor income would remain unchanged even after the income was transferred to the poor population, but economic theory predicts that this will not be so. In fact, if the poor household were given enough income to bring it out of poverty, we would believe that the household would work less as a result of receiving this transfer. This complicates the analysis, of course, because once the household works less, then it will generate less labor income, thus lowering its overall income. This means that the poverty gap actually understates the amount of money necessary to alleviate poverty in the United States. In addition, the poverty gap is based on the official poverty line, which is thought to be an ad-hoc measure of the true “needs” of a family.
4. A day care center is an example of an in-kind compensation. The figure below is similar to Figure 8.2 in the text. The original budget line is G1 H1 If the employee received $5,000 cash, the budget line moves to G2 H2 . An employee who uses the day care center may not be $5,000 better off. The employee consumes at point A, but would be better off at point B, which represents consumption after a cash transfer of $5,000.
5. a. This would increase the incomes of the providers of computer equipment and the individuals who maintain the equipment. In the long run, this might also increase the incomes of the students who use the equipment. Moreover, giving a laptop to
all seventh graders (rather than poor seventh graders) may simply “crowd-out”
computer transfers from parents to children. One could imagine that nowadays many children do have a computer at home, paid for by the parents. This government transfer may simply result in less parental transfer to the child.
b. Providing free after-school programs for children in impoverished families largely acts as an in-kind transfer for poor, working households. The program is of little value for unemployed households, as the alternative would be childcare at home. For those who are employed, and paying for childcare, this program provides an alternative and effectively changes the after-tax, after-working-cost wage. This also may affect work behavior on the extensive margin. The likely “losers” from such a program are childcare providers, who see a reduction in demand for their services. In principle, this reduction in demand could lower the hourly childcare cost for all workers with children, though this effect is likely to be modest because most impoverished families do not have a very large labor force attachment and, thus, their effect on the childcare market as a whole is likely to be small.
6. a. False. Society is indifferent between a util to each individual, not a dollar to each individual. Imagine that UL=I and UJ=2I. Then each dollar given to Jonathan raises welfare more than the same dollar given to Lynne.
b. True. The social welfare function assumes a cardinal interpretation of utility so that comparisons across people are valid.
c. False. Departures from complete equality raise social welfare to the extent that they raise the welfare of the person with the minimum level of utility. For example, with the utility functions UL=I and UJ=2I, the social welfare function W=min[UL,UJ] would allocate twice as much income to Lynne than Jonathan. 7. Initially the price of food was $2 and the price of other goods was $1. The black market
for food stamps changes the price of food sold to $1. In Figure 7.2 of the textbook, as one moves to the “northwest” from point F, the segment will now have a slope (in absolute value) of 1 rather than 2. The black market may make the individual better off if the best point on her budget constraint AFD was initially at the corner solution of point F, and the black market certainly does not make her worse off. It is important to note that the black market does not always make the recipient better off. If the (absolute value) of the marginal rate of substitution (MRS) were between 1 and 2, the indifference curve would not “cut” into the new part of the budget constraint with the black market.
U0 F A Food Stamp Allotment D Other Goods Food FIGURE 7.7a – Black market where food
stamps are sold for fifty cents on the dollar, no better off
Sell food stamps for other goods on black market
If the MRS were less than (or equal to) 1 in absolute value, the person would be made better off and would reduce food consumption by selling the food stamps on the black market.
8. Pareto efficient redistribution is a reallocation of income that increases (or does not
decrease) the utility of all consumers. With these two consumers, Marsha’s utility increases as Sherry’s utility increases. Thus, it may be possible to reallocate income from Marsha to Sherry and raise both of their utility. With Sherry’s initial utility function of US=100YS1/2, her utility with $100 of income is US=100($100)1/2, or US=1,000. With Marsha’s initial utility function of UM=100YM1/2+0.8US, her utility with $100 of income is UM=100($100)1/2+0.8(1,000), or UM=1,800. If the social welfare function is additive, then initial welfare is W=US+UM=1,000+1,800=2,800. If $36 is reallocated from Marsha to Sherry, then Sherry’s income is now $136 and Marsha’s is now $64. With Sherry’s utility function, her utility with $136 of income is US=100($136)1/2, or US=1,166.190. With Marsha’s utility function, her utility with $64 of income is UM=100($64)1/2+0.8(1,166.190), or UM=800+932.952=1,732.952. In this case, Sherry’s utility increases from 1,000 to 1,166.190, while Marsha’s utility falls from 1,800 to 1,732.952. Social welfare increases with this redistribution, going from 2,800 to 2,899.142. Thus, this redistribution increases social welfare, but is not Pareto efficient redistribution.
Chapter 8 – Expenditure Programs for the Poor
U1 U0 A Food Stamp Guarantee D Other Goods Food FIGURE 7.7b – Black market where food
stamps are sold for fifty cents on the dollar, higher utility
Sell food stamps for other goods on black market
1. a. Note that the figure below shows the correct shape of the budget constraint, but the numbers themselves are outdated. With a wage rate of $10 per hour, Elizabeth earns $100. Because the deduction in California is $225, none of her earnings are counted against the $645 welfare benefit. Thus, her total income is $745 (=$100+$645).
b. The actual welfare benefits collected by a person equals B=G-t(Earnings-D), where B=actual benefits, G=welfare grant, t=tax rate on earned income, and D=standard deduction. Thus, (Earnings-D) is the net earnings that are taxed away in the form of reduced benefits. When benefits equal zero (B=0), the expression becomes 0=G-t(Earnings-D), which collapses to: Earnings=G/t+D. This is known as the “breakeven formula.” In the California context here, the expression becomes Earnings=$645/0.5 + 225, or Earnings=$1,515. With a wage rate of $10 per hour, this corresponds to 151.5 hours of work per month.
c. The diagram shows the correct shape of the budget constraint, but the “577” figure should be replaced with “645” and the “9” hours should be replaced with “22.5”. d. The diagram above shows one possibility – in this case, Elizabeth is both working
and on welfare – but she collects a reduced welfare benefit in this case.
2. One could gather data on the earnings of those in the program, as well as earnings data from nonparticipants. Regress the earnings variable on demographic variables and other factors that determine earnings (such as education and experience), and a variable that indicates whether the individual participated in the training program. Factors that affect local employment conditions, such as unemployment levels, may help explain earnings, but they may also explain participation in the program. The econometric strategy should be chosen carefully to account for this.
3. If the quantity of leisure consumed by X appears as an argument in the utility function of Y, then X’s consumption of leisure creates an externality. If the externality is negative (i.e., Y likes X to work), then a wage subsidy of X might induce him to work the efficient number of hours. Alternatively, a workfare program might achieve the same goal by simply forcing X to work. However, to the extent that the feasible quantity of labor supply is determined less through market incentives now, workfare would be less efficient.
4. He participates in the public housing program as long as P1P2ca>cef.
5. As illustrated below, the budget constraint with food stamps has a “notch” in it, similar to the analysis of Medicaid in Figure 8.9 of the textbook. At the notch, the marginal tax rate is greater than 100%. One key difference from the figure in the textbook is that the marginal tax rate on earned income for Medicaid is 0% until the “Medicaid notch,” while the marginal tax rate on earned income for food stamps is 24% until the “food stamp notch.” The reason the food stamp notch exists at all is that there is a “gross income test,” where a recipient is ineligible if income is higher than the limit. The characterization in the Rosen textbook on page 189 that “at some point near the poverty line, food stamps worth about $1,250 are suddenly lost” implicitly assumes that childcare costs are quite high. This is likely to be true for many households. In the year 2004, this monthly (annual) gross income limit was $1,994 per month ($23,928 per year) for a family of four, while the monthly guarantee was $471 ($5,652 per year). Assuming the family had earnings at the limit of $1,994 of earnings during the month, and after applying a 20% earnings deduction and a $134 monthly standard deduction, the household would receive a monthly (annual) benefit of $32 ($384). We arrive at this number using the equation B=G-t(E-.2E-D)=471-.3(.8*1994-134)=$471-$438.36=$32.64, which is then rounded down to $32. In this case, B=actual benefits
Increasing annual earnings by $1 from $23,928 to $23,929 would reduce food stamp benefits from $384 to $0; hence the “food stamp notch.” This notch would be even higher if the household qualified for a childcare deduction, child support deduction, or shelter deduction. The childcare deduction ranges between $175 and $200 per child per month. Assuming this family of four consisted of a mother and three children, each with $175 of monthly childcare costs, then B=G-t(E-.2E-D-C)=471-.3(.8*1994-134-525)=$471-$280.86=$190.14, which is then rounded down to $190. The modification here is that C=childcare costs. This amount corresponds to an annual food stamp benefit of $2,280. Figure 8.5 below draws the budget constraint using annual levels for the food stamp program, using 2004 rules and assumes no childcare expenses.
6. For an individual who is not working while on welfare, in this case the highest indifference curve touches the budget constraint on the right vertical axis. Note that the marginal rate of substitution (MRS) does not necessarily equal the after-tax wage rate at the time endowment – rather, it is possible that the person would want to consume more leisure than the time endowment but is obviously constrained from doing so.
Statutory food stamp maximum = $5,652 Food stamp notch; eligibility
determined separately from benefits. Notch = $384 Other Goods or
Annual Income
Leisure FIGURE 8.5 – The food stamp “notch”
with 24% tax rate on earned income
Statutory TANF benefit
Other Goods
Leisure FIGURE 8.6 – Individual is on welfare and
does not work at all
U0
7. In all cases, the demand curve for housing slopes downward.
a. If the price of low income housing gets bid up but there is no increase in the stock of housing, then the supply curve is perfectly inelastic, e.g., vertical.
Q0
D0 S
PHOUSING
QHOUSING
FIGURE 8.7a – Demand curve shifts outward, perfectly inelastic supply
P0
D1 P1
b. If there is no increase in the price of housing, but there is an increase in the stock of housing, then the supply curve is perfectly elastic, e.g., horizontal.
Q0
D0 S PHOUSING
QHOUSING
FIGURE 8.7b – Demand curve shifts outward, perfectly elastic supply
P0
D1
c. If there is an increase in both the price and quantity of housing, then the supply curve slopes upward.
According to Sinai and Waldfogel, there is partial crowding out, consistent with case c above. Although the underlying housing stock itself is probably quite inelastic in the short-run, the number of rental homes can be more elastic as (potential) landlords convert vacation homes or vacant homes into rental units.
8. a. When Eleanor’s hours (earnings) go from 0 to 1,000 ($0 to $8,000), she qualifies for an additional earned income tax credit (EITC) worth $3,200 (=0.4*8,000). Thus, her income goes up from $0 to $11,200. Note to instructors – the
distinction between earnings and income may cause confusion in the students’ answers.
b. When Eleanor’s hours (earnings) go from 1,000 to 1,500 ($8,000 to $12,000), she qualifies for the maximum EITC (according to Figure 8.8 in the textbook). She receives the full EITC when her earnings exceed $10,510, at which time the credit equals $4,204 (=0.4*$10,510). The earnings between $10,510 and $12,000 face neither a subsidy nor phase-out from the EITC. Thus, her income goes up from $11,200 to $16,204.
c. When Eleanor’s hours (earnings) go from 1,500 to 2,000 ($12,000 to $16,000), she moves into the range where the EITC is phased out. According to Figure 8.8
Q0
D0 S PHOUSING
QHOUSING
FIGURE 8.7c – Demand curve shifts outward, upward sloping supply curve
P0
D1
Q1 P1
in the textbook, she receives the maximum subsidy of $4,204 until her earnings exceed $14,730. For the marginal earnings between $14,730 and $16,000, the EITC is reduced at a 21.06% tax rate. Thus, her EITC falls by $267.46 from $4,204 to $3,936.54 (=4,204-0.2106*(16,000-14,730)). Her income rises from $16,204 to $19,936.54.
Chapter 9 – Social Insurance I: Social Security and Unemployment Insurance
1. With adverse selection, insurance contracts with more comprehensive coverage are chosen by people with higher unobserved accident probabilities. To make up for the fact that a benefit is more likely to be paid to such individuals, the insurer charges a higher premium per unit of insurance coverage.
2. There are many possible implications of a voluntary Social Security system. One possibility is that people would save less for retirement, betting that society would not put up with having great numbers of elderly poor. Part of the effect of the Friedman program, then, would depend on the government's credibility when it promises not to bail out people who do not save enough to survive during retirement.
3. Use the basic formula for balance in a pay-as-you-go social security system: t =(Nb/Nw)*(B/w).
Call 1990 year 1 and 2050 year 2. Then t1 = .267*(B/w)1
t2 = .458*(B/w)2
It follows that to keep (B/w)1=(B/w)2 we require t2/t1=.458/.267=1.71. That is, tax rates would have to increase by 71 percent. Similarly, to keep the initial tax rate constant, we would require (B/w)2/(B/w)1=.267/.458=0.58. Benefits would have to fall almost by half. 4. If Social Security benefits are partially taxed for those who have other income over a
certain level, then there is an implicit means test in receiving full, untaxed benefits. However, there is no explicit means test for eligibility for the program. Everyone receives benefits, though some recipients must pay some tax on them. Thus, the two statements are somewhat inconsistent with each other.
5. Austen’s quote seems like it could relate adverse selection, but perhaps more likely, to moral hazard. The quote “If you observe, people always live forever when there is any annuity to be paid them” in a sense sounds like they act differently (e.g., better diet, more exercise, etc.) when an annuity is to be paid – the idea of moral hazard. In contrast, adverse selection suggests that people who expect to live a long time to be the ones who purchase annuities. A recent paper by Finkelstein and Poterba (NBER working paper, December 2000) found that “mortality patterns are consistent with models of asymmetric information” and that annuity “insurance markets may be characterized by adverse selection.”
6. Equation (9.1) relates taxes paid into the Social Security 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.
7. The statement about how the different rates of return in the stock market and government bond market affect the solvency of the trust fund is false. If the trust fund buys stocks, someone else has to buy the government bonds that it was holding. So, there is no new saving and no new capacity to take care of future retirees.
8. Diamond and Gruber’s calculations suggest that the additional year of work (and delayed retirement) lowers the present discounted value of expected Social Security wealth by $4,833. If the adjustment were actuarially fair, Social Security wealth would neither rise nor fall. Since wealth falls, the adjustment is actuarially unfair.
9. For those who argue that the scheme for financing Social Security is unfair because people with low earnings are taxed at a higher rate than those with high earnings, the key issue is that the cumulative payroll tax of 12.4 percent is capped for each person, after which the payroll tax is zero (this ignores the 2.9 percent uncapped Medicare tax, however). The earnings ceiling in 2004 is $87,900. Hence, Social Security payroll taxes as a share of earnings fall after the ceiling is passed – thus, the Social Security payroll tax may be thought of as regressive. The opponents to this view note that the above analysis only focuses on taxes paid, not benefits received. As shown in Table 9.3, Social Security redistributes from high earners to low earners, and the formula for the primary insurance amount offers extremely high replacement rates to very low earners, and much lower replacement rates to high earners. Thus, the net tax payment (taxes minus benefits) is likely to be progressive, not regressive. One critical assumption in this kind of analysis is how one computes lifetime benefits – e.g., do we assume that low earners and high earners live the same number of years?
10. Let G stand for the individual’s gross earnings. The question assumes that the person faces a marginal tax rate of 15% and a payroll tax of 7.45%. Thus, the person’s after-tax earnings (denoted by N) are N=(1-tearn-tpayroll)G, or N=(1-0.15-0.0745)G, or N=0.7755G. It is assumed that the gross unemployment benefits, U, are equal to 50 percent of before-tax earnings, or U=0.5G. Net unemployment benefits, B, take out income before-taxes, so B=(1-tearn)U=(1-tearn)0.5G=(1-0.15)0.5G=0.425G. The percentage of the individual’s after-tax income that is replaced by UI is therefore equal to B/N, or 0.425G/0.7755G, which is approximately 54.8%. Unemployment benefits are about 55% of the individual’s previous after-tax income. The effects of unemployment insurance on unemployment are a matter of considerable debate. While the high replacement rates from UI may increase the duration of unemployment, the longer search time may reduce recurrence of unemployment by allowing time for a worker to find a better job match. Empirical
studies seem to show that the hazard rate into employment spikes up around the time that benefits run out – perhaps suggesting that job matches are not really improving.
Chapter 10 – Social Insurance II: Health Care
1. The quotation contains several serious errors. First, concern with health care costs does not mean that health care is not a “good.” Economists do not care about the cost of health care per se. Rather, the issue is whether there are distortions in the market that lead to more than an efficient amount being consumed. Second, it makes a lot of difference how money is spent. One can create employment by hiring people to dig ditches and then fill them up, but this produces nothing useful in the way of goods and services. Thus, employment in the health care sector is not desirable in itself. It is desirable to the extent that it is associated with the production of an efficient quantity of health care services.
2. a. Those who have a relatively high probability of needing the insurance are the ones who are most likely to buy it. This raises the premium, which in turn, leads to selection by people who have an even higher probability of using it. The cycle continues until the price is so high that virtually no one purchases the policy. b. Employer-provided health insurance is deductible to the employer and not taxed to
the employee.
c. Because of the tax subsidy, individuals may purchase more than the efficient amount of health insurance. That is, they “over-insure.” An interesting example of how the tax system leads to overinsurance is given in a recent Wall Street Journal (January 19, 2004) article by Martin Feldstein. He gives an example of two different California Blue Cross health plans – identical in all respects except for the deductible and annual premiums. The low-deductible plan (the “generous” plan) has a deductible of $500 per family member, up to a maximum of two and an annual premium of $8,460. Thus, the maximum out-of-pocket expense is $1,000. The high-deductible plan (the “less generous” plan) has a deductible of $2,500 per family member, up to a maximum of two, and an annual premium of $3,936. Thus, the maximum out-of-pocket expense is $5,000. Note that the premium savings of $4,524 actually exceeds the maximum incremental deductible payment of $4,000 (which would only occur if the family had very high health expenses). In principle, the high deductible plan is unambiguously better. But the traditional tax rules could lead an employer to choose the low deductible policy. If the employee faced a marginal tax rate of 45% (the sum of federal, state, and payroll tax rates), then if the $4,524 premium saving was turned into taxable salary, the individual’s net income would only rise by $2,488. Thus, families with high expected medical expenses do better with the “generous” plan, even though it is more costly in terms of premiums.
b. Now the individual pays only $5 per visit.
Dd = 4.22 – (0.044)(5) = 4 visits, with out-of-pocket costs of $20. Insurance company pays ($45)(4) = $180
Total expenditure = $200, double its previous level.
4. Examining Figure 10.1, we can see why health care costs increased for the state of Tennessee. As insurance coverage increases, this lowers the cost of medical expenses for those who were previously did not have insurance, which increases the overall amount of medical services they consume. Before receiving insurance, these people demand Mo units of medical services, and the amount they pay is represented by the area OPoaMo. But after receiving insurance coverage, they demand M1 amounts of medical services, paying only OjhM1, while their insurance pays jPobh. The increase in insurance payments is sizable for two reasons – first, by providing coverage, it pays for the majority of the already sizable medical expenses incurred by this group, and second, the introduction of insurance makes the group consume even more medical services. In short, if the people who designed the Tennessee program had realized that the demand curve for medical services is downward sloping, they would not have been surprised at the consequences of their program.
To explain why HMOs have been unable to contain long-run health care costs, it is necessary to consider the effect of technology on health care costs in the long-term. The inherent problem is that the market for medical care places a large premium on using the latest and most-developed medicines and machinery for treating patients. These technologies tend to be expensive. Hence, while introducing HMOs can lead to a once and for all decrease in the rate of change in health care costs, there is nothing that an HMO can do to lower the cost of continually providing the latest in medical treatments. 5. The goal of making the Medicare prescription drug benefit a one-time, permanent
decision is to reduce the adverse selection problem (note: the current “Medigap” program operates in this manner to some extent – a senior citizen has choice over all 10 of the Medigap plans for only a short period of time after they turn 65, after which they may be denied based on their health). Imagine a cohort of people turning age 65 and becoming eligible for the Medicare drug benefit. If the decision to enter (or exit) could be made every year, then healthy senior citizens would have a strong incentive to wait until they became unhealthy and needed drugs, and then enter the prescription drug program (presumably resulting in economic losses for the program). Similarly, when people who were collecting the prescription drug benefit became healthy, they would have a strong incentive to “opt-out” of the program. By making the decision opt-in at the beginning or not at all, the healthy younger seniors are likely initially cross-subsidizing the older seniors. Note that this “opt-in at the beginning” works because bad health and older age are positively correlated with each other. If, for example, younger seniors used more drugs (and perhaps older seniors used more inpatient care, etc.), then older seniors could simply stop paying annual premiums and give up their option of being in the program. If this scenario held empirically, this would exacerbate the adverse selection problem and the opt-in scenario would not completely solve the adverse selection problem.
6. The budget constraint initially has units of Medigap on the x-axis, and other goods on the y-axis. Given initial prices of $1 per unit for each good, and $30,000 of income, the budget constraint has a slope of -1, and the intercepts on both axes are at 30,000 units. It is assumed that the initial utility maximizing bundle consumes 5,000 units of Medigap, hence the indifference curve is tangent at (5000,25000). All of this is illustrated in the figure below.
U0
Other Goods
Medigap efficiency units FIGURE 10.6a – Medigap choice without
minimum standards
30,000 30,000
5,000 25,000
After the “minimum Medigap” mandate, the consumer can either choose 0 units of Medigap or 8,000 or more units of Medigap. Thus, part of the budget constraint is eliminated (though the overall shape remains the same as before). After the mandate, the point (0,30000) is available, as well as all of the points to the southeast of the point (8000,22000). Clearly, the person’s utility must fall since the preferred choice, (5000,25000) is no longer available. If the person attains a higher level of utility as (0,30000) compared with (8000,22000), the person chooses to not purchase Medigap. In this case, the marginal rate of substitution is no longer equal to the price ratio. This is illustrated below. U1 U0 Other Goods Medigap efficiency units FIGURE 10.6b – Medigap choice with
minimum standards; no Medigap is purchased 30,000 30,000 5,000 25,000 8,000 22,000
7. a. The gross price of insurance is $2, but since insurance is bought with pre-tax dollars, the effective price of insurance is (1-t)P, where t is the marginal tax rate. Since Connor’s marginal tax rate is 25%, the effective price of insurance is lower, only (1-.25)*$2, or $1.50 per unit. At $1.50 per unit, and using the demand curve of Q=100-8P, this implies that Connor buys Q=100-8($1.50)=88 units of insurance.
b. If insurance is no longer excluded from taxation, the effective price rises to $2 per unit. In this case, Connor buys Q=100-8($2)=84 units of insurance.
c. The exclusion of health insurance from taxation lowers its effective price – as long as the demand for health insurance slopes downward, then lower prices lead to higher demand for insurance. This can be viewed as “over-consumption” if the assumptions of the First Fundamental Welfare Theorem hold, which suggests that the private market allocation without subsidies or taxes yields the Pareto efficient allocation. On the other hand, there may be (weak) reasons based on the Fundamental Welfare theorem, there should be a tax subsidy for health insurance. The main reason would probably be if we thought that health insurance had positive externalities, which might be possible with communicable diseases. There are other reasons why government intervention may be warranted in health insurance markets (e.g., asymmetric information), but it is not obvious that these reasons lead to the tax subsidy we observe in the U.S.
Chapter 11 – Cost Benefit Analysis
1. Yes, one really must ask these questions, although it may seem distasteful. Otherwise, there is no way to determine which safety precautions are sensible.
2. 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 state, and multiply this by the incremental waiting time of 105 minutes.
3. The present value of $25/.10 = $250.
The present value of the perpetual annual benefit = B + B/(1 + r) + B/(1 + r)2 + … = B (r + 1 - r)/r = B/r.
4. a. 1,000=80/ρ
ρ =.08
b. If the money comes from consumer spending, use after-tax rate of interest as the discount rate:
80 - 1,000 = 600 > 0. .05
If the money comes from investment, use before-tax rate of interest as the discount rate:
80 - 1,000 = -200 < 0. .10
The project is not admissible.
In the “mixed case,” for a discount rate, take a weighted average: .6 x 10% + .4 x 5% = 8%.
80 - 1,000 = 0. .08
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. If inflation is fully anticipated, and if market interest rates increase by 10 percentage points, nothing changes in real terms.
5. a. Bill is willing to pay 25 cents to save 5 minutes, so he values 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 to Bill 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 = $20x55,000=$1,100,000. Total costs = $16x55,000 = $880,000. Net benefits = $220,000. c. Costs = $1.25 x 55,000 = $68,750. Benefits =($62,500/1.25) + ($62,500/1.252) = $90,000. Net benefit = $21,250.
d. The subway project has a higher present value. If a dollar to the “poor” is valued the same as a dollar to the “middle class,” choose the subway project.
e. Let λ = distributional weight. set
220,000 = -68,750 + λ [(62,500/1.25) + (62,500/1.252)]
λ = 3.21
This distribution weight means that $1 of income to a poor person must be viewed as more important than $3.21 to the middle class for the legal services to be done. 6. The report for the Czech government that simply computed the savings to the
government for retirees from smoking is inadequate. After all, if one simply counts as “benefits” money saved from transfers, then having all of the retirees die would be
life.” If one computed the value of a life simply based on lost earnings, however, the retirees would suffer no loss. As the textbook mentions on page 255, this method is rejected by most economists. The method that is frequently used by economists is the “value of a statistical life,” which (among other things) compares compensating wage differentials to the probability of death. Viscusi and Aldy (2003) find that the value of statistical life ranges between $4 million and $9 million. One could convert these values from a lifetime into each year of life, to form some estimate of the “cost” of smoking. 7. As discussed on pages 257-8 of the textbook, one of the “games” that cost-benefit
analysts play is viewing the wages paid to labor as a benefit not a cost. This is clearly wrong. The fact that 1,000 people need to be hired to do the recycling in New York is a cost of the program, not a benefit.
8. Currie and Gruber (1996) find the cost of the expansion per life saved was approximately $1.6 million. According to Viscusi and Aldy (2003), the value of a statistical life is between $4 million and $9 million. If all of these calculations are correct, then the Medicaid expansion passes a cost-benefit test.
Chapter 12 – Taxation and Income Distribution
1. The incidence of the subsidy depends on the elasticities of the supply and demand curves. Here the price received by sellers increases from P0 to P1. Buyers also benefit – their price falls from P0 to P2. In evaluating the claims that energy subsidies to low-income families do not benefit industry, the figure below could be modified by shifting the demand curve rather than the supply curve. Nonetheless, what is clear from the diagram is that demand is relatively inelastic, while supply is more elastic. Thus, the subsidies to low-income families do benefit the industry.
2. 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.
3.
4. One expects that those factors that are used intensively in tobacco production will bear the burden of the tax. Assuming, for example, that tobacco production is capital-intensive, one expects owners of all capital (not just those with investments in tobacco) to bear some of the burden.
5. a. Set 2000 – 200P = 200P, so P = $5 and Q = 1000 packs
b. Consumer price = Producer Price + $2. Let P be the producer price. 2000 – 200 (P + 2) = 200 P.
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.
6. The equilibrium price can be calculated by setting the quantity supplied equal to the quantity demanded:
(i) QD = a - bP (ii) QS = c + dP
If QD = QS, then the equilibrium price can be determined as follows:
The equilibrium output can be determined by substituting the equilibrium price into either
d b c a P P d b c a dP c bP a + − = + = − + = − ) (
Substituting into the demand equation:
Substituting into the supply equation:
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:
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:
Next, setting PC = PPT: + − − = − = d b c a b a Q bP a Q + − + = + = d b c a d c Q dP c Q Q b b a PC − = 1 d c Q d PP − = 1 u d c Q d PPT − − = 1 d b dbu bc da Q Q db d b db dbu bc da Q d b u d c b a d c Q d u Q b b a P PCT P + + + = + = + + + = + + − = + − = 1 1 1 1 u Q b b a PCT + − = 1
