instructor s manual publice finance. harvey

7/28/2019 Instructor s Manual Publice Finance. HARVEY

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Part 1 Getting Started

c. The federal budget would decrease if grants-in-aid were reduced. However, if stateand local governments offset this by increasing taxes, the size of the governmentsector 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 beincluded as revenue to the government.

6. The federal government grew by $450 billion. However, because the price level went upby 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 increasein prices of 16 percent in the Rosen text (p. 18) differs from official sources. Accordingto the 2004 Economic Report of the President (Table B-60), the CPI-U was 177.1 in 2001and was 144.5 in 1993, an increase of 22.5 percent, not 16 percent. If one uses thesenumbers, government spending increased in constant 2001 dollars from $1.72 trillion in1993 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 ofgovernment fell and by the other measure, it grew. To get a more complete answer, onewould want data on the population (to compute real spending per capita). Also, it wouldbe useful to add in expenditures by state and local governments, to see if the totalsize ofgovernment fell. Also, although it would be harder to measure, one would want to try togain some sense of how the regulatory burden on the economy grew during this timeperiod.

Chapter 2 Tools of Positive Analysis

1. The reality that astronomers are trying to understand is not influenced by any policiesthat astronomers might implement. That is, planets and stars do act any differently whenthey are being analyzed, whereas people can change their behavior. Moreover, theparameters with which astronomers must deal are constant over time (at least in theshort-run of hundreds of years), while the parameters in economics can quickly changeover time and across geography.

2. A change in the marginal tax rate changes the individuals net wage. This generates bothan income effect and a substitution effect. As long as leisure is a normal good, theseeffects work in opposite directions. Hence, one cannot tell a priori whether labor supplyincreases or decreases. One could ask taxpayers to describe how they would change theirbehavior 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 dataassociated 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 areobserved and others of which are unobserved. Economists often cannot performcontrolled, randomized experiments, which makes it difficult to assess how any singlevariable affects a given outcome. Moreover, even in the cases when experiments are run

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(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 theexperiment for a short amount of time and because of lack of generalizability. In themedical example here, brain impairment may be due to a number of factors that are eitherobserved 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 discountrates, and potentially many other ways. Hence, one cannot definitively conclude whetherbrain 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 causaleffect of Ecstasy. For example, if there were a plausible instrumental variable (perhapsthe punitiveness of the drug laws in a state) that was correlated with the supply of Ecstasybut not otherwise correlated with the outcomes of interest, one may be able to estimatethe causal effect of Ecstasy on long-run developmental problems.

4. The text points out the pitfalls of social experiments: the problem of obtaining a randomsample 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 groupof health care consumers. In addition, the RAND Health Insurance Experiment was oflimited duration, after which the participants would move to some other health plan. Thisdesign could induce certain behavior in the short-run that would not necessarily bepresent if the health insurance coverage were permanent rather than transitory. Further,physicians standard practices are largely determined by the circumstances of thepopulation as a whole, not the relatively small experimental group.

5. First, it is important to note that the numbers on page 32 of Rosens text actually showthe surplus, not the deficit. That is, the negative surplus of $221.2 in 1990 is actually adeficit, while the positive surplus of $236.4 is a surplus. There is a very weak, negativerelationship between surpluses and interest rates (the correlation coefficient is -.043), orput differently, a weak, positive relationship between deficits and interest rates. Howeverit is expressed, it is weak -- by eyeballing the data, it might appear that larger deficitslead to lowerinterest rates (for example, by comparing the data from 1980 with the datafrom 2000). One clearly would need more data to investigate this question. One wouldwant to look at deficits relative to some benchmark, such as GDP. One would want toexpress both interest rates and deficits in real terms, rather than nominal terms. Onewould like to control for other factors that can affect interest rates, such as monetarypolicy and the level of economic activity. Finally, one would want to determine whichway the causality runs do larger deficits cause higher interest rates, or do higher interestrates cause larger deficits (since, by construction, one of the largest items in the federalbudget is interest on the debt).

Chapter 4 Public Goods

1. a. Wilderness area is an impure public good at some point, consumption becomesnonrival; it is, however, nonexcludable.

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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 isrival. The municipality can control who consumes water by shutting off the flowto customers, thus it is excludable. This is a useful question for showing that notall 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 Cheetahs utility does not enter the social welfare function; hence, herallocation 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 anefficient allocation, Cheetah should patrol more.

3. A pure public good is nonrival in consumption, thus it is necessary to determine whetheror not this is the case with the highway. That is, if the additional cost of another personconsuming the highway is zero, then it is a public good. So, as long as the highway isnot congested, then it can be considered to be a public good. However, adding anothermotorist to an already congested roadway can cause traffic jams that cost motorists moretime 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 ornot we could designate it as a public good. Note that we are assuming throughout that thehighway is nonexcludable.

To determine whether or not the privatization of the highway is a sensible idea, it isnecessary to consider the advantages and disadvantages of such an action. First, if themarket structure is such that privatizing the highway would result in a monopolist incontrol of the highway, then this would be inefficient. Also, it would be difficult for thegovernment to write a complete contract for maintaining the highway, which would alsocause inefficiencies that would result from the privatization of the road. However, if thegovernment 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 sensiblesolution.

4. The benefits of maintaining the incomes of the poor accrue largely to the recipients ofwelfare, not to society as a whole. Thus, it is implausible to think of welfare (or theadministration of the welfare system) as a public good. Unless there is a warm-glowfrom income redistribution, there is little basis for thinking that the provision of TANF,Medicaid, public housing, or food stamps offers much in terms of benefit to society as a

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whole. In terms of administration of welfare, it is hard to say whether or not it should bepublicly or privately administered. Private administration might be less costly. On theother hand, private administrators might have an incentive to deprive deservingindividuals of benefits in order to cut costs. It could be difficult to write a contract toprevent this kind of behavior, because one cannot specify in advance every conceivable

set of circumstances under which welfare should be granted. This kind of subjectivitywas present in the 1960s, when caseworkers had a great deal of discretion in terms ofwhich households to offer assistance to. This subjectivity led to accusations ofdiscrimination and, from the 1970s onward, there has been far less subjectivity in termsof defining eligibility. Since that time, eligibility is fairly mechanically related toincome, assets, family structure, and a number of other observable factors. Given thecurrent system, it seems less difficult today to monitor a private firm than it would havebeen in the 1960s.

5. A lower cost is a necessary (but not sufficient) condition to conclude that prisons shouldbe 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 thequality of prisons (e.g., whether the prisoners are treated decently, whether security isadequate, and so on), Hart, Shleifer and Vishny (1997) note that it is sometimesimpossible to write a complete contract because one cannot specify in advance everypossible contingency. The key is whether the administration of prisons is a fairlyroutine activity where complete contracts can be written, or whether there are too manycontingencies.

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. Thoseauthors found that, on average, people contribute a portion of their resources to theprovision of a public good, and there is some free riding. That was the case inManchester, Vermont. Also, Palfrey and Prisbrey found that when the experimentalgame was repeated, people were more likely to free ride. This also happened inManchester -- in the second year, participation was less.

7. There is no compelling reason for museums to be run by the government from the theoryof public goods; thus, it is appropriate to think about privatization. Admissions tomuseums are clearly excludable. And viewing the artwork is also rival, because there iscongestion when too many people are consuming the good. Thus, museums may bethought of as a private good rather than public good. In the United States, many greatmuseums are run privately (not for profit), and they seem to do quite well. In terms ofprivate versus publicproduction, the text points out that this decision should be based onrelative 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 theprivate sector would have higher costs than the public sector. In regards to diversity oftastes, a profit-maximizing private sector museum would likely be more responsive toconsumer tastes than the public sector e.g., adopting new technologies that make themuseum more enjoyable for the typical customer. In regards to distributional issues, it is

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likely that the private sector would be less responsive than the public sector. The notionof commodity egalitarianism, however, is a stretch for museums.

8. If households are allowed to supplement public education with private lessons, then thebudget 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.

6

ep

BA

A

Other Goods

Education

FIGURE 4.8a Supplement publiceducation with private lessons


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If parents pay for the public schooling (rather than perceiving it as being free), and theschooling was paid for with a lump sum tax, then the budget constraint shifts in by anamount that depends on the households share of the tax burden. If the households taxburden exactly equals the cost of public school, the budget constraint is no longer the linesegmentAB but rather the segment CDB, where the segmentDB runs along the original

budget constraint, except that the minimum amount of schooling consumed is eP.

9. In this case, the apartments temperature is a public good because for the society ofRodolfo and Mimi, the temperature is nonrival and nonexcludable. Both get toconsume a warmer house, and neither can exclude the other from this. The marginalbenefit for society is the sum of Rodolfos and Mimis marginal benefit e.g., $20 at 66degrees, $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 temperatureshigher than that, the marginal cost is greater than the marginal benefit for society.

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DC

ep

BA

A

Other Goods

Education

FIGURE 4.8b Parents pay for freeschooling


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10. Thelmas marginal benefit is MBTHELMA=12-Z, and Louises is MBLOUISE=8-2Z. Themarginal benefit for society as a whole is the sum of the two marginal benefits, orMB=20-3Z (for Z4), and is equal to Thelmas marginal benefit schedule afterwards (forZ>4). The marginal cost is constant at MC=16. Setting MB=MC along the first segmentgives 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 wouldoccur since the marginal cost of $16 exceeds either of their individual marginal benefitsfrom the first unit ($12 or $8). Thus, this is clearly a situation when the private marketdoes not work very well. Also note, however, that if the marginal cost were somewhatlower, (e.g., MC8), then it is possible that Louise could credibly free ride, and Thelmawould provide the efficient allocation. This occurs because if Thelma believes thatLouise will free ride, Thelma provides her optimal allocation, which occurs on the secondsegment of societys MB curve, which is identical to Thelmas MB curve (note thatLouise gets zero marginal benefit for Z>4). Since Louise is completely satiated with thisgood at Z=4, her threat to free ride is credit if Thelma provides Z>4.

Chapter 5 - Externalities

1. Classical economics explicitly requires that allcosts and benefits be taken into accountwhen assessing the desirability of a given set of resources, so Gores statement is false.The notion that rescuing the environment should be the central organizing principle forcivilization provides no practical basis for deciding what to do about automobileemissions (or any other environmental problem), because it provides no framework forevaluating the tradeoffs that inevitably must be made.

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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 subsidycan be raised without any efficiency costs. (Cassanovas friends gain gchd;Cassanova loses chdbut gains abcd, which is a subsidy cost to government.)

3. a. If you know who was cooking, the externality is easy to identify, and dependingon how many students are involved, the costs of negotiation should be fairlysmall.

b. It is unlikely that property rights could be enforced in terms of catching tropicalfish 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 weregiven to the divers, it is not clear who is actually harmed (perhaps society as awhole) by the depletion of exotic fish. Given the large number of people who areharmed (in a small amount), and the large number of people who are engaging inthis 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 outhow to transfer bribes.

4. a. The price of imported oil does not reflect the increased political risk byeffectively subsidizing authoritarian regimes like those in Saudi Arabia.

b. The tax would estimate the marginal damage (e.g., the increased instability in theMiddle East, etc.) by importing oil from Saudi Arabia.

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c. The supply of vouchers is vertical at 140 billion. The demand curve is downwardsloping. For every gallon of gasoline, you either have to buy a voucher or use upone 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 marginalexternal cost of $1.19 per ounce. Although the deadweight loss is smaller than with notax at all, the allocation is still far from the socially efficient level. The current allocationproduces too much alcohol at too low of a price.

6. By establishing a market for air pollution rights, the Chicago Board of Trade has appliedthe Coase Theorem. The potential efficiency of the outcome may be laudable, but thedistributional 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 thejoint profit maximization problem, not the profit maximization problem at eitherfirm alone. Thus, the LP farm produces 2 units, the socially efficient amount.

10

$0.75

140 billion

D

S

PVOUCHER

QVOUCHER

FIGURE 5.4c Tradeable vouchers for oil


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d. Before the merger, the LP farm produced 4 units. By cutting back to 2 units, itloses marginal profit of $3. On the other hand, the Tipsy Vineyards profitsincrease 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 socialmarginal cost. Hence, the efficiency gain is (5 - 3)(7 - 5) = 2.

A Pigouvian tax adds to the private marginal cost the amount of the external cost at thesocially optimal level of production. Here a simple tax of $2 per unit will lead toefficient production. This tax would raise ($2) (3 units) = $6 in revenue.

9. In the absence of persuasive evidence on positive externalities for higher education, thereis no reason for the government to provide free tuition. True, taxes on wages may distorteducation 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 impliesthat 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 $3in costs.

Chapter 6 Political Economy

1. a. Below, the preferences for Person 1 and Person 2 are drawn. Same procedure isused for the other three people.

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b. C wins in every pairwise vote. Thus, there is a stable majority outcome, despite thefact that persons 1, 2, and 3 have double-peaked preferences. This demonstrates thatalthough multi-peaked preferences may lead to voting inconsistencies, this is notnecessarily the case.

2. The votes by the Senators from the northeast and south to subsidize each others interestsare consistent with the logrolling model. The senators from the affected states made thedeal 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 publicgood increases by three percent a year.

c. The size of government increases. For further discussion of this phenomenon, see thepaper by W. J. Baumol, Macroeconomics of Unbalanced Growth: The Anatomyof Urban Crises,American Economic Review, 1967.

4. Yes, it is consistent, because the theory says that when unanimity is required, nodecisions are likely to be made. A majority system might be more suitable, although it issubject 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 themedian participatingvoter. The reason for this is because of the different turnout rates

for individuals in different income categories. Consider this simple example: supposethat voters have single-peaked preferences, and they are trying to determine how muchshould be spent on national defense. Their preferences are listed as follows:

Andrew: $500 Bob: $700 Charlie: $850

Allison: $600 Bill: $750 Cathy: $900

Anne: $650 Beth: $800 Cheryl: $1,000

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The median voter theorem predicts that a majority vote will result in $750 being spent ondefense (which is reflective of Bills preferences, since he is the median voter).However, if there are different participation rates by different groups (in this case, thegroups are determined by the first letter in the persons name), then the preferences of themedian voter (Bill) are no longer reflected in the majority vote. Suppose that Andrew

and Anne dont 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 issplit between four relatively preferred options, and the fifth option wins. The winningoption may have been voted down if it had been a two-way vote with any of the otheroptions. Further, if preferences are not single-peaked, cycling and inconsistent publicdecisions may emerge.

7. Given the U.S. experience with the Budget Enforcement Act of 1990, we would expectthe EU deficit limits to be ineffective. We would expect accounting tricks to mask thesize of the deficits (such as itemizing various budget items as unexpected

emergencies), and if that didnt work, we would expect the deficit rules to be ignored.This is apparently what is happening. When Germany exceeded the deficit target, nomoves were taken to levy the required fines.

8. Since rents, by definition, are the returns above a normal return, then when the licensesare put on the market, their price will be the value of the rents. Hence, the owner of thepeanut license, whoever he or she is, only makes a normal return. Put another way, thelicense is an asset that earns a normal rate of return. If the peanut license system wereeliminated, 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 thatwhen 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 notunfair 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 cartelwould ideally produce a quantity where MR=MC, or 10-(1/5)Q=2, or Q=40. Theprice 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 unitand the number of units produced. The marginal profit per unit of milk is $4 (=$6price - $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 fulleconomic rent of $160. The cartel situation, the quantity of milk produced is toolow from societys point of view. The deadweight loss triangle is computed using

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the difference between the cartel output and competitive output as the base ofthe triangle, and the difference between the cartel price and competitive price asthe 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 $160rents + $80 DWL = $240. This is because, as noted on page 131, rent-seekingcan use up resources lobbyists spend their time influencing legislators,consultants testify before regulatory panels, and advertisers conduct publicrelations campaigns. Such resources, which could have been used to produce newgoods and services, are instead consumed in a struggle over the distribution ofexisting goods and services. Hence, the rents do not represent a mere lump-sumtransfer; it is a measure of real resources used up to maintain a position of marketpower.

10. Niskanens model of bureaucracy is illustrated in Figure 6.4 of the textbook. In the

aftermath of September 11

th

, the new concerns over food safety would likely shift the Vcurve upward (that is, the value placed on each level ofQ). Assuming that Ccurve (costsper unit of Q) does not change, then this shift increases the actual number of foodinspectors hired. It is also likely that the slope of the V curve changes, with eachmarginal unit ofQ becoming more valuable. Thus, the Vcurve not only shifts upward,but becomes steeper as well. Both of these effects the shifting of the Vcurve and thechange in the slope lead to greater values of Q under the bureaucracy model. Thechange in the slope leads to a greater value ofQ*, the efficient level of output. Thus, theoptimal number of FDA employees and the actual number of FDA employees are likelyto 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. Whetherthe rich are vulgar is irrelevant, so this part of the statement is inconsistent withutilitarianism. On the other hand, Steins assertion that inequalityper se is unimportant isinconsistent 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 themoney in the economy is exhausted first).So,400-6 Ic = 0; hence, Ic = 66.67.

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Giving any more money to Charity causes her marginal utility to become negative,which is not optimal. Note that we dont care if the remaining money ($33.33) isgiven 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 alldistributions of income.

3. The main conceptual problem with the poverty gap is that it doesnt account for theincome effect on labor force participation rates. The poverty gap is calculated assumingthere are no behavioral responses; e.g., that labor income would remain unchanged evenafter the income was transferred to the poor population, but economic theory predicts thatthis 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 ofreceiving this transfer. This complicates the analysis, of course, because once thehousehold works less, then it will generate less labor income, thus lowering its overallincome. This means that the poverty gap actually understates the amount of moneynecessary to alleviate poverty in the United States. In addition, the poverty gap is basedon the official poverty line, which is thought to be an ad-hoc measure of the true needsof a family.

4. A day care center is an example of an in-kind compensation. The figure below is similarto 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 centermay not be $5,000 better off. The employee consumes at point A, but would be better offat point B, which represents consumption after a cash transfer of $5,000.

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5. a. This would increase the incomes of the providers of computer equipment and theindividuals who maintain the equipment. In the long run, this might also increasethe incomes of the students who use the equipment. Moreover, giving a laptop toall seventh graders (rather than poor seventh graders) may simply crowd-outcomputer transfers from parents to children. One could imagine that nowadays

many children do have a computer at home, paid for by the parents. Thisgovernment transfer may simply result in less parental transfer to the child.

b. Providing free after-school programs for children in impoverished families largelyacts as an in-kind transfer for poor, working households. The program is of littlevalue for unemployed households, as the alternative would be childcare at home.For those who are employed, and paying for childcare, this program provides analternative and effectively changes the after-tax, after-working-cost wage. Thisalso may affect work behavior on the extensive margin. The likely losers fromsuch a program are childcare providers, who see a reduction in demand for theirservices. In principle, this reduction in demand could lower the hourly childcare

cost forallworkers with children, though this effect is likely to be modest becausemost 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 eachindividual. Imagine that UL=I and UJ=2I. Then each dollar given to Jonathanraises welfare more than the same dollar given to Lynne.

b. True. The social welfare function assumes a cardinal interpretation of utility sothat comparisons across people are valid.

c. False. Departures from complete equality raise social welfare to the extent thatthey raise the welfare of the person with the minimum level of utility. Forexample, with the utility functions UL=I and UJ=2I, the social welfare functionW=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 marketfor food stamps changes the price of food sold to $1. In Figure 7.2 of the textbook, asone moves to the northwest from point F, the segment will now have a slope (inabsolute value) of 1 rather than 2. The black market may make the individual better off ifthe 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 thatthe black market does not always make the recipient better off. If the (absolute value) ofthe marginal rate of substitution (MRS) were between 1 and 2, the indifference curvewould not cut into the new part of the budget constraint with the black market.

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17

U0

FA

FoodStamp

Allotment

D

Other Goods

Food

FIGURE 7.7a Black market where foodstamps are sold for fifty cents on the dollar,no better off

Sell food stamps for othergoods on black market


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If the MRS were less than (or equal to) 1 in absolute value, the person would be madebetter off and would reduce food consumption by selling the food stamps on the blackmarket.

8. Pareto efficient redistribution is a reallocation of income that increases (or does notdecrease) the utility of all consumers. With these two consumers, Marshas utilityincreases as Sherrys utility increases. Thus, it may be possible to reallocate income fromMarsha to Sherry and raise both of their utility. With Sherrys initial utility function ofUS=100YS

1/2, her utility with $100 of income is US=100($100)1/2, or US=1,000. With

Marshas 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 toSherry, then Sherrys income is now $136 and Marshas is now $64. With Sherrysutility function, her utility with $136 of income is US=100($136)

1/2, or US=1,166.190.

With Marshas utility function, her utility with $64 of income isUM=100($64)1/2+0.8(1,166.190), or UM=800+932.952=1,732.952. In this case, Sherrys

utility increases from 1,000 to 1,166.190, while Marshas utility falls from 1,800 to1,732.952. Social welfare increases with this redistribution, going from 2,800 to2,899.142. Thus, this redistribution increases social welfare, but is not Pareto efficientredistribution.

Chapter 8 Expenditure Programs for the Poor

18

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 othergoods on black market

F


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1. a. Note that the figure below shows the correct shape of the budget constraint, butthe numbers themselves are outdated. With a wage rate of $10 per hour,Elizabeth earns $100. Because the deduction in California is $225, none of herearnings 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), whereB=actual benefits, G=welfare grant, t=tax rate on earned income, and D=standarddeduction. Thus, (Earnings-D) is the net earnings that are taxed away in the formof reduced benefits. When benefits equal zero (B=0), the expression becomes0=G-t(Earnings-D), which collapses to: Earnings=G/t+D. This is known as thebreakeven formula. In the California context here, the expression becomesEarnings=$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 figureshould 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 workingand 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 datafrom nonparticipants. Regress the earnings variable on demographic variables and otherfactors that determine earnings (such as education and experience), and a variable thatindicates whether the individual participated in the training program. Factors that affectlocal employment conditions, such as unemployment levels, may help explain earnings,but they may also explain participation in the program. The econometric strategy shouldbe chosen carefully to account for this.

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3. If the quantity of leisure consumed by X appears as an argument in the utility function ofY, then Xs 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 efficientnumber 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 laborsupply is determined less through market incentives now, workfare would be lessefficient.

4. He participates in the public housing program as long asP1P2ca>cef.

5. As illustrated below, the budget constraint with food stamps has a notch in it, similar tothe analysis of Medicaid in Figure 8.9 of the textbook. At the notch, the marginal tax rateis greater than 100%. One key difference from the figure in the textbook is that themarginal tax rate on earned income for Medicaid is 0% until the Medicaid notch, whilethe marginal tax rate on earned income for food stamps is 24% until the food stampnotch. The reason the food stamp notch exists at all is that there is a gross incometest, where a recipient is ineligible if income is higher than the limit. Thecharacterization in the Rosen textbook on page 189 that at some point near the povertyline, food stamps worth about $1,250 are suddenly lost implicitly assumes that childcarecosts are quite high. This is likely to be true for many households. In the year 2004, thismonthly (annual) gross income limit was $1,994 per month ($23,928 per year) for afamily of four, while the monthly guarantee was $471 ($5,652 per year). Assuming thefamily had earnings at the limit of $1,994 of earnings during the month, and afterapplying a 20% earnings deduction and a $134 monthly standard deduction, thehousehold would receive a monthly (annual) benefit of $32 ($384). We arrive at thisnumber 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 benefitsreceived, G=food stamp guarantee, t=tax rate, E=earnings, and D=standard deduction.

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Increasing annual earnings by $1 from $23,928 to $23,929 would reduce food stampbenefits from $384 to $0; hence the food stamp notch. This notch would be evenhigher if the household qualified for a childcare deduction, child support deduction, orshelter deduction. The childcare deduction ranges between $175 and $200 per child permonth. 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 modificationhere is that C=childcare costs. This amount corresponds to an annual food stamp benefitof $2,280. Figure 8.5 below draws the budget constraint using annual levels for the foodstamp program, using 2004 rules and assumes no childcare expenses.

6. For an individual who is not working while on welfare, in this case the highestindifference curve touches the budget constraint on the right vertical axis. Note that themarginal 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 moreleisure than the time endowment but is obviously constrained from doing so.

21

Statutory food stampmaximum = $5,652

Food stamp notch; eligibilitydetermined separately from

benefits. Notch = $384

Other Goods orAnnual Income

Leisure

FIGURE 8.5 The food stamp notchwith 24% tax rate on earned income

$23,928


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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.

23

Q0

D0

S

PHOUSING

QHOUSING

FIGURE 8.7a Demand curve shiftsoutward, perfectly inelastic supply

P0

D1

P1


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b. If there is no increase in the price of housing, but there is an increase in the stockof housing, then the supply curve is perfectly elastic, e.g., horizontal.

24

Q0

D0

S

PHOUSING

QHOUSING

FIGURE 8.7b Demand curve shiftsoutward, perfectly elastic supply

P0

D1

Q1


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c. If there is an increase in both the price andquantity of housing, then the supplycurve 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 theshort-run, the number of rental homes can be more elastic as (potential) landlords convertvacation homes or vacant homes into rental units.

8. a. When Eleanors hours (earnings) go from 0 to 1,000 ($0 to $8,000), she qualifiesfor 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 thedistinction between earnings and income may cause confusion in the studentsanswers.

b. When Eleanors 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). Shereceives the full EITC when her earnings exceed $10,510, at which time the creditequals $4,204 (=0.4*$10,510). The earnings between $10,510 and $12,000 faceneither a subsidy nor phase-out from the EITC. Thus, her income goes up from$11,200 to $16,204.

c. When Eleanors 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

25

Q0

D0

S

PHOUSING

QHOUSING

FIGURE 8.7c Demand curve shifts outward,upward sloping supply curve

P0

D1

Q1

P1


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6. Equation (9.1) relates taxes paid into the Social Security system to the dependency ratioand the replacement ratio, that is, t=(Nb/ Nw)*(B/w). If the goal of public policy is tomaintain 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), thenit 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 inwage 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 governmentbond 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 newsaving and no new capacity to take care of future retirees.

8. Diamond and Grubers calculations suggest that the additional year of work (and delayedretirement) lowers the present discounted value of expected Social Security wealth by

$4,833. If the adjustment were actuarially fair, Social Security wealth would neither risenor fall. Since wealth falls, the adjustment is actuarially unfair.

9. For those who argue that the scheme for financing Social Security is unfair becausepeople with low earnings are taxed at a higher rate than those with high earnings, the keyissue is that the cumulative payroll tax of 12.4 percent is capped for each person, afterwhich 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 taxesas a share of earnings fall after the ceiling is passed thus, the Social Security payroll taxmay be thought of as regressive. The opponents to this view note that the above analysisonly focuses on taxes paid, not benefits received. As shown in Table 9.3, Social Securityredistributes from high earners to low earners, and the formula for the primary insuranceamount offers extremely high replacement rates to very low earners, and much lowerreplacement rates to high earners. Thus, the net tax payment (taxes minus benefits) islikely to be progressive, not regressive. One critical assumption in this kind of analysis ishow one computes lifetime benefits e.g., do we assume that low earners and highearners live the same number of years?

10. Let G stand for the individuals gross earnings. The question assumes that the personfaces a marginal tax rate of 15% and a payroll tax of 7.45%. Thus, the persons after-taxearnings (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 taxes, so B=(1-tearn)U=(1-tearn)0.5G=(1-0.15)0.5G=0.425G. The percentage of the individuals after-taxincome that is replaced by UI is therefore equal to B/N, or 0.425G/0.7755G, which isapproximately 54.8%. Unemployment benefits are about 55% of the individualsprevious after-tax income. The effects of unemployment insurance on unemployment area matter of considerable debate. While the high replacement rates from UI may increasethe duration of unemployment, the longer search time may reduce recurrence ofunemployment by allowing time for a worker to find a better job match. Empirical

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studies seem to show that the hazard rate into employment spikes up around the time thatbenefits 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 doesnot mean that health care is not a good. Economists do not care about the cost ofhealth care per se. Rather, the issue is whether there are distortions in the market thatlead to more than an efficient amount being consumed. Second, it makes a lot ofdifference how money is spent. One can create employment by hiring people to digditches and then fill them up, but this produces nothing useful in the way of goods andservices. Thus, employment in the health care sector is not desirable in itself. It isdesirable to the extent that it is associated with the production of an efficient quantity ofhealth care services.

2. a. Those who have a relatively high probability of needing the insurance are the oneswho are most likely to buy it. This raises the premium, which in turn, leads toselection by people who have an even higher probability of using it. The cyclecontinues 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 tothe employee.

c. Because of the tax subsidy, individuals may purchase more than the efficient amountof health insurance. That is, they over-insure. An interesting example of howthe 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 twodifferent California Blue Cross health plans identical in all respects except forthe deductible and annual premiums. The low-deductible plan (the generousplan) has a deductible of $500 per family member, up to a maximum of two andan 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 thepremium savings of $4,524 actually exceeds the maximum incremental deductiblepayment of $4,000 (which would only occur if the family had very high healthexpenses). In principle, the high deductible plan is unambiguously better. But thetraditional 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 taxablesalary, the individuals net income would only rise by $2,488. Thus, families withhigh expected medical expenses do better with the generous plan, even though itis more costly in terms of premiums.

3. a. Dd=4.22(0.044)(50)=2 visits per year.Total expenditure =(2)(50)=$100

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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) = $180Total expenditure = $200, double its previous level.

4. Examining Figure 10.1, we can see why health care costs increased for the state ofTennessee. As insurance coverage increases, this lowers the cost of medical expenses forthose who were previously did not have insurance, which increases the overall amount ofmedical services they consume. Before receiving insurance, these people demand Mounits of medical services, and the amount they pay is represented by the area OP oaMo.But after receiving insurance coverage, they demand M1 amounts of medical services,paying only OjhM1, while their insurance pays jPobh. The increase in insurancepayments is sizable for two reasons first, by providing coverage, it pays for the majorityof the already sizable medical expenses incurred by this group, and second, theintroduction of insurance makes the group consume even more medical services. Inshort, 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 atthe consequences of their program.

To explain why HMOs have been unable to contain long-run health care costs, it isnecessary to consider the effect of technology on health care costs in the long-term. Theinherent problem is that the market for medical care places a large premium on using thelatest and most-developed medicines and machinery for treating patients. Thesetechnologies tend to be expensive. Hence, while introducing HMOs can lead to a onceand for all decrease in the rate of change in health care costs, there is nothing that anHMO 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, permanentdecision is to reduce the adverse selection problem (note: the current Medigapprogram operates in this manner to some extent a senior citizen has choice over all 10of the Medigap plans for only a short period of time after they turn 65, after which theymay be denied based on their health). Imagine a cohort of people turning age 65 andbecoming eligible for the Medicare drug benefit. If the decision to enter (or exit) couldbe made every year, then healthy senior citizens would have a strong incentive to waituntil they became unhealthy and needed drugs, and then enter the prescription drugprogram (presumably resulting in economic losses for the program). Similarly, whenpeople who were collecting the prescription drug benefit became healthy, they wouldhave a strong incentive to opt-out of the program. By making the decision opt-in at thebeginning or not at all, the healthy younger seniors are likely initially cross-subsidizingthe older seniors. Note that this opt-in at the beginning works because bad health andolder age are positively correlated with each other. If, for example,youngerseniors usedmore drugs (and perhaps older seniors used more inpatient care, etc.), then older seniorscould simply stop paying annual premiums and give up their option of being in theprogram. If this scenario held empirically, this would exacerbate the adverse selectionproblem and the opt-in scenario would not completely solve the adverse selectionproblem.

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30


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6. The budget constraint initially has units of Medigap on the x-axis, and other goods on they-axis. Given initial prices of $1 per unit for each good, and $30,000 of income, thebudget constraint has a slope of -1, and the intercepts on both axes are at 30,000 units. Itis 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.

31

U0

Other Goods

Medigapefficiency units

FIGURE 10.6a Medigap choice withoutminimum standards

30,000

30,000

5,000

25,000


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If the money comes from investment, use before-tax rate of interest as the discountrate:

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 x5% = 8%.

80 - 1,000 = 0..08There 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 percentagepoints, 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 perminute. The subway saves him 10 minutes per trip, or 50 cents. The value of 10trips per year is $5. The cost of each trip is 40 cents, or $4 per year. The annualnet 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 valuedthe same as a dollar to the middle class, choose the subway project.

e. Let = distributional weight. set

220,000 = -68,750 + [(62,500/1.25) + (62,500/1.252)]

= 3.21This distribution weight means that $1 of income to a poor person must be viewedas 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 thegovernment for retirees from smoking is inadequate. After all, if one simply counts asbenefits money saved from transfers, then having all of the retirees die would beconsidered an enormous benefit. What this analysis obviously missed is the value of

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life. If one computed the value of a life simply based on lost earnings, however, theretirees would suffer no loss. As the textbook mentions on page 255, this method isrejected by most economists. The method that is frequently used by economists is thevalue of a statistical life, which (among other things) compares compensating wagedifferentials 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 valuesfrom 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-benefitanalysts play is viewing the wages paid to labor as a benefit not a cost. This is clearlywrong. The fact that 1,000 people need to be hired to do the recycling in New York is acost 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 isbetween $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 theirprice falls from P0 to P2. In evaluating the claims that energy subsidies to low-incomefamilies do not benefit industry, the figure below could be modified by shifting thedemand curve rather than the supply curve. Nonetheless, what is clear from the diagramis that demand is relatively inelastic, while supply is more elastic. Thus, the subsidies tolow-income families do benefit the industry.

2. These reports about demand sensitivity suggest that there is a very elastic demand curvefor goods sold over the Internet. Because of this high elasticity, the incidence of a taxlevied on Internet sales is primarily borne by producers, not consumers.

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3.

4. One expects that those factors that are used intensively in tobacco production will bearthe 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) tobear 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 thequantity 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 eitherthe supply or demand equation.

36

db

caP

Pdbca

dPcbPa

+

=

+=

+=

)(


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Substituting into the demand equation:

Substituting into the supply equation:

If a unit tax ofu dollars is imposed on the commodity, then it doesnt matter which partyit 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 consumerpays is u higher than the price received by the supplier. The consumers price withoutthe tax, PC, and price that includes the tax, PCT, are:

Similarly, the price received by the producer in the absence of the tax, P P, is u lower thanthe 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 canderive the solution setting PCT = PP:

Next, setting PC = PPT:

37

+

=

=

db

cabaQ

bPaQ

+

+=

+=

db

cadcQ

dPcQ

Qbb

aPC

= 1

d

c

QdP

P

=

1

ud

c

QdP

PT

=

1

db

dbubcdaQ

Qdb

db

db

dbubcda

Q

db

u

d

c

b

a

d

cQ

duQ

bb

a

PP PCT

+++=

+=++

+=++

=+

=

11

11

uQbb

aPCT +

= 1


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Therefore, both approaches lead to the same outcome.

7. Equation (12.1) relates progressiveness, v1, to average tax rates. Assume throughout that

I1>I0>0. Then progressivity is measured by v1=[(T1/I1)- (T0/I0)]/(I1-I0). With a $300 lumpsum tax refund for all earners, the progressivity changes to v1=[((T1-300)/I1)- ((T0-

300)/I0)]/(I1-I0). Rearranging, we have v1= v1+[(300/I0)-(300/I1)]/(I1-I0). Thus, the

progressivity differs only by the second term, [(300/I0)-(300/I1)]/(I1-I0). This second termis positive because (300/I0)>(300/I1). Thus, v1

>v1, and average tax rates increase withincome by more when a $300 lump sum tax refund is given. Intuitively, the average taxrate falls by more for a low-income person from a lump sum tax reduction. Equation(12.2) relates progressiveness, v2, to the elasticity of tax revenue with respect to income.Then progressivity is measured by v2=[(T1-T0)/T0]/[(I1-I0)/I0]. With a $300 lump sum taxrefund for all earners, the progressivity changes to v2

=[(T1-300-T0+300)/(T0-300)]/[(I1-I0)/I0]= [(T1-T0)/(T0-300)]/[(I1-I0)/I0]. Note that v2

differs from v2 only by the term (T0-

300). Thus, the numerator ofv2

is larger than v2, while the denominator is the same.Thus, v2>v2, and the tax system is more progressive under the second measure as well

when the lump sum tax refund is given.

8. The equation T=-4000+.2Iis somewhat similar to the exercise in Table 12.1 on page 277of the textbook. If we follow the text and define progressivity with respect to average taxrates rather than marginal tax rates, then the average tax rate equal ATR=(-4000/I)+.2 forany income level. Clearly this average tax rate converges to ATR=20% as income getslarge, and is lower for lower income levels. Replicating Table 12.1 for the tax systemgiven here, we get:

Income Tax Liability Average Tax Rate Marginal Tax Rate$2,000 $-3,600 -1.80 0.2

3,000 $-3,400 -1.13 0.2

5,000 $-3,000 -0.60 0.2

10,000 $-2,000 -0.20 0.2

30,000 $2,000 0.066 0.2

38

db

dbubcdaQ

Qdb

db

db

dbubcda

Qdbud

c

b

a

ud

cQ

dQ

bb

a

PP PTC

+++=

+=

++

+=++

=

=

11

11


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9. With the schedule T=a+tI, the average tax rate as a function of income isATR=T/I=(a+tI)/I=(a/I)+t. Aprogressive tax system, using equation (12.1), means thatthe average tax rate goes up with income, ordATR/dI>0. Taking derivatives, dATR/dI=-a/I2>0, which implies a>0 or a1 orD


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Chapter 13 Taxation and Efficiency

1. a. Since land is fixed in supply, we expect no excess burden when it is taxed. Thesupply curve is inelastic.

b. There are fairly good substitute for cell phones. Therefore, their demand is quiteelastic, and a tax on them will have a substantial excess burden, relative to the sizeof revenues collected.

c. Without knowing exactly what high-tech means, it is likely that many companiescould relabel themselves as high-tech in order to receive the subsidy. Thus, thesupply is quite elastic, and there will be substantial excess burden.

d. A tax on economic profits does not affect behavior, and hence has no excess burden.

e. & f. A tax on all computer software will have a smaller excess burden (relative torevenues collected) than a tax on one particular type of software like the Excelspreadsheet. This is because it is easier to substitute away from one type ofsoftware than software in general.

2. Equation (13.4) computes the excess burden of a tax on labor, which equals wL1t2.

Thus, when taxes are lowered from 39.9% to 34%, the ratio of the excess burden trianglesdiffers only by the last term, the square of the tax rate. Thus, (34/39.9)2 =.726. So, under

40

Q0

D0

S

wFOREIGN

QFOREIGN

FIGURE 12.11 Economic incidence of tax onHong Kong foreign workers

w0

D1

Q1

wn

wg

tax=$51


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the new regime, excess burden is only 72.6 percent of the excess burden under the oldregime.

3. The quote is misleading. The way in which the presence of the t-squared makes the taxmore important is that when the tax increases, the excess burden increases with its

square. Thus, when the tax doubles, the excess burden quadruples.

4. Figure 13.9 shows how a tax on market activity leads to "too much" nonmarket activity.More generally, the model shows that when different sectors are taxed at different rates,the allocation of resources is distorted, and real income falls as a result. The morepervasive distortionary taxes are in an economy, the more severe the misallocation ofresources, and the lower is real income. Hence, it is no surprise that economies with a lotof distortionary taxes tend to grow relatively slowly.

5. It is likely that the elasticity of demand for television is quite inelastic. It follows that theexcess burden from a $160 per year television tax is small relative to the revenues that are

collected.

6. Figure 13.6 from the textbook is reproduced below, with a perfectly elastic supply curveand a downward sloping demand curve. The market price of corn is $2.25 a bushel,while the subsidy is 50 cents; thus the cost of corn is $2.75 a bushel. The excess burdenis given by ovu in the figure.

41

Q0

D

S0

PCORN

QCORN

FIGURE 13.6 Incidence of a corn subsidywith perfectly elastic supply

P0=$2.75

Q1

S1

P1=$2.25

Excess burden from subsidy

o v

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7. a. The value of the marginal product of capital in the corporate sector is given byVMPc=100-Kc, and the value of the marginal product of capital in thenoncorporate sector is given by VMPn=80-2Kn. With 50 units of capitalaltogether in society (Kc+Kn=50), and no taxation, capital should be allocatedso that the values of the marginal products in each sector are equalized. Thus,setting VMPc=VMPn gives 100-Kc=80-2Kn and substituting in the constraint of50 units gives 100-50+Kn=80-2Kn orKn=10. This implies thatKc=40. This isillustrated below:

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 byVMPc

=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 orKn=12. This

implies thatKc=38. This is illustrated below:

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VMPC=100-K

C

VMPCORPORATE

QNONCORPORATE

FIGURE 13.7a Allocation of capital tothe corporate and non-corporate sectors

100

VMPNONCORPORATE

80

VMPN

=80-2KN

QCORPORATE

KC=40

KN

=10


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Thus,K=2 and the tax wedge is t=$6, so the excess burden is (2)($6)=$6.

8. With a conventional supply and demand model, where the supply curve slopes upward

and the demand curve slopes downward, the excess burden of a unit tax (in this case,imposed on demanders) is similar to Figure 12.2 (page 280) of the textbook. The shadedyellow area in the figure below (corresponding to fgh in the textbook) is the excessburden, and shaded pink area below (corresponding to kfhn in the textbook) is the taxrevenue.

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VMPC=94-K

C

VMPCORPORATE

QNONCORPORATE

FIGURE 13.7b Reallocation after per-unit tax on corporate capital

100

VMPNONCORPORATE

80

VMPN

=80-2KN

QCORPORATE

KC=38

KN

=12

94

Excess burden from$6 per unit tax


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Chapter 14 Efficient and Equitable Taxation

1. Assuming that all other commodities (except for cable and satellite television) wereuntaxed, then optimal tax policy suggests the commodities should be taxed according to

the inverse elasticity rule. Goolsbee and Petrin (2001) find that the elasticity of demandfor basic cable service is -0.51, and the demand for direct broadcast satellites is -7.40.Applying the inverse elasticity rule would imply that(tBASIC/tSATELLITE)=(SATELLITE/BASIC)=(7.40/0.51)=14.5. Thus, tax rates on basic cable shouldbe 14.5 times higher than tax rates on satellite television because basic cable isinelastically demanded, while demand for satellite television is highly elastic. Among theassumptions that go into the inverse elasticity rule are that goods are neither complementsnor substitutes, and that the elasticities are the Hicksian compensated elasticities ratherthan the Marshallian uncompensated elasticities. In this case, it is likely that the first ofthese assumptions is false basic cable and satellite television are likely substitutes foreach 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.

2. Although the tax schedule is progressive, the incidence is not clear at all. This isdetermined by the relative demand and supply elasticities for expensive cars. One mayargue that behavior will be distorted only at the margin, and hence demanders largelybear the burden. However, administration of this tax would not be straightforward: Onecould imagine methods of evasion such as misrepresenting invoices or selling the car inparts!

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Q0

D0

S

P

Q

FIGURE 13.8 Excess burden of a unit taximposed on demanders

P0

D1

Q1

Pn

Pg

unit tax

excess burden

tax revenue


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3. The beard tax was progressive because it was a function of social position. Its hard toknow about the efficiency consequences unless one knows more about the price elasticityof demand for the privilege of having a beard. If the elasticity was small, then it wouldbe an efficient tax. However, conventional notions of horizontal equity suggest that the

tax was unfair.

4. If the nut fee is truly collected whether or not the farmer collects nuts, then it isindependent of the farmer's behavior. Hence, it is a lump-sum tax, and perfectly efficient(unless it drives some individuals out of farming). However, optimal tax theory tells usthat we must consider equity as well as efficiency considerations. If the fee is the samefor all households, regardless of their incomes, then it is regressive. With a conventionalutilitarian welfare function, this is unlikely to be optimal. Because farmers who are notalike in relevant aspects (e.g., income) pay the same tax, the nut tax would seem toviolate horizontal equity. Things become even worse when we bring city-dwellers, whodon't have to pay the nut tax at all, into the picture.

Moral: An efficient tax need not be optimal or horizontally equitable.

5. One could use Figure 14.5 on page 351, on tax evasion, to understand this phenomenon.The horizontal axis now represents the amount of underreporting of the value ofcommodities, and the vertical axis represents the cost in dollars. Fisman and Wei (2001)find that in the case of China, a 1 percent increase in the tax rate results in a 3 percentincrease in evasion (by reclassifying a commodity as a lower-taxed commodity). The1 percent increase shifts up theMB curve, which leads to a new intersection between MBandMC, and a higherR*, which was found to be 3 percent higher.

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6. Figure 14.5 equates the marginal benefit of underreporting $1s worth of income to themarginal cost. The marginal benefit is equal to the taxes saved, which is simply thepersons marginal tax rate, orMB=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 dollarof underreporting, orMC=*Marginal Penalty. As shown in Figures 14.5 and 14.6, theoptimal amount of underreporting, R* equals zero ifMCMB. Thus, if*MarginalPenaltyt, then there will be no underreporting. With=0.02 and t=0.36, the inequalitybecomes 0.02*Marginal Penalty0.36, orMarginal Penalty$18. With a fine of $18 (ormore), Sharlene would not cheat on her taxes. The figure below illustrates this case.

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R*

MC

MB0=t

$ savings

Amount ofunderreporting

FIGURE 14.5 Underreporting ofcommodities in China due to tariffs

MB1=t+.01

1.03R*


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a tax on commodities leads to a budget constraint of (1-)pCC+(1-)pFF+wL=I,which does change the relative price of leisure compared with food orconsumption goods. Thus, it is not a lump sum tax. Instead, the inverse elasticityrule given in equation (14.9) on page 333 of the textbook would suggest that theratio 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)=(F/C).

c. It is true that average cost pricing for a natural monopoly allows the enterprise tobreak even, but the outcome is inefficient. Figure 14.3 in the textbook onpage 338 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 isalways declining, but above the marginal cost curve. SettingP=ACresults in anoutput level ofZA and zero economic profits. The figure illustrates, however, thatthe marginal benefit of more output exceeds the marginal cost, so the efficientlevel of production occurs at P=MC, or an output level Z*>ZA. The deadweightloss is the area between the demand curveDZ and marginal cost curve, going from

ZA to Z

*

. If output were at the efficient level, however, there would be economiclosses rather than zero profits.

d. One notion of horizontal equity is that people in equal positions should be treatedequally by the tax system. Under this traditional notion of horizontal equity, thefact that Toms workplace provides free access to a fitness room suggests thiskind of compensation should be taxed; Jerry pays full taxes on hiscompensation while Tom does not. Another notion of horizontal equity relies onthe utility definition of horizontal equity. This concept says that if two individualshave 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 utilitydefinition is that any existing tax structure does not violate the notion ofhorizontal equity if individuals are free to choose their activities and expenditures.If Tom and Jerry have free choice between the two different jobs (and identicalpreferences), then the net after-tax rewards (including amenities) must be thesame at both jobs; otherwise there would be migration. In this case, the before-tax wage on Toms job adjusts for the fact that there is a fringe benefit.

Chapter 15 The Personal Income Tax

1. The Haig-Simons definition of income is the net change in the individuals power toconsume during a given period. This criterion suggests the inclusion of all sources of

potential increases in consumption and also implies that any decreases in an individualspower to consume should be subtracted in determining income. Overall, it reflects thebroadest possible base of income. Allowing capital losses of $5,000 to be deductibleagainst other forms of income, rather than the current $3,000, would move the tax systemmore in the direction of the Haig-Simons criterion.

2. From a Haig-Simons point of view, the McCain proposal makes sense. According toHaig-Simons, all income should be taxed at the same rate, regardless of the use to which

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it is to be put. Under the status quo, income (in the form of capital gains) is taxed at alower rate if it is donated to charity. Note that wage income that is to be donated tocharity does notenjoy the same benefit.

Under the status quo, the tax price of a gift of appreciated property is 1 - t - tk*g, where t

is the marginal tax rate on ordinary income, tk is the tax rate on capital gains, and g is theproportion of the gift that is appreciated property. With the McCain proposal, the taxprice would be 1 - t. Thus, the tax price goes up. We expect charitable contributions togo down by an amount that depends on the elasticity of charitable contributions withrespect to their tax price.

3. Suppose Jones buys the oil stock for $1,000 at the start of period 0. At the start ofperiod 1, he has two options.

a. Hold the oil stock one more period, then sell.

b. Sell the oil stock, buy the gold 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 ofperiod 2. What are the returns to option a)? At a 10 percent rate of appreciation,the oil stock is worth $1,210 after period 2, the capital gain is $210 and assuminga 29 percent rate applies to capital gains, the capital gains tax is 28 percent of$210 or $58.80. Thus, Jones is left with $1,210 - $58.80 or $1,151.20 after tax.

If Jones follows strategy b), the value of the oil stock at the start of period 1 is$1,000, the capital gain is $100, and the tax $28. Thus Jones has $1,672 left overto proceeds (V) from selling the gold stock at the end of period 1.

V = Value of gold stock taxes

= (1+r)($1,072) (.28)[(1+r)($1,072)-($1,072)]

= (1+r)($1,072) (.28)r($1,072)

= $1,072 + .72r($1,072)

Setting V = $1,151.20 (same as oil stock):

$1,151.20 = $1,072 + .72r($1.072) r=10.26%

Thus the gold stock must pay a premium of 0.26% (10.26% - 10%) over the oilstock in order to overcome the tax cost of realizing the capital gain.

4. Dear Newsweek: Your Wall Street editor does not understand the tax code. The bracket

widths, exemptions, and deductions are all indexed and have been since the early 1980s.In effect, this indexes wage income against inflation.

5. For an itemizer, a $500 tax deduction lowers the tax bill by t*deduction. Thus, for anitemizer with a 30% marginal tax rate, the tax bill is lowered by 30%*$500, or $150. A(refundable) tax credit, on the other hand, directly lowers the tax bill by that amount, inthis case, $500.

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ii. Ignoring other features like the exemption phaseout, an increase in incomeof $2,500 leads to an increase in taxes of $750 with a marginal tax rate of30% ($750=$2,500*30%).

iii. Personal exemptions are reduced by 2 percentage points for each $2,500

increase in AGI. Thus, the exemption falls from $12,200 to98%*$12,200, and taxable income goes up by 2%*$12,200, or $244.

iv. The additional increase in taxable income of $244 increases the taxliability by 30%*$244, or $73.20.

v. The total change in tax liability, the effective tax rate, is ($750+$73.20)/$2,500, or 32.928%.

b. i. With $100 of income initially, the family would owe 30%*$100, or $30 intaxes.

ii. According to the textbook (page 377), the phaseout on itemizeddeductions is at a rate of 3% for AGI above a certain threshold. Theitemized deduction falls by 3%, or $3, for the $100 increase in income.Taxable income goes up by $3.

iii. The $3 change in taxable income increase the tax liability by $0.90(=30%*$3).

iv. The effective tax rate is ($30+$0.90)/$100=30.9%.

10. Of the $4,000 of earnings that Sam has, he is able to invest (1-tI)*earnings in the market,or (1-0.25)*$4,000=$3,000. Assume that when he saves the money in a taxable account,he has to pay taxes each year on the capital gains, and that those capital gains are treatedas ordinary income and taxed at 25%. In this case, his 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 thetaxable savings account is $3,000*(1.06)10=$5,372.54. If he invests the money in a RothIRA, the money accrues at the before-tax rate of return, and there is no tax liability at theend. Thus, the amount in the Roth IRA is $3,000*(1.08)10=$6,476.77. It turns out thatthe key difference between a traditional IRA and a Roth IRA is whether the income taxrate today differs from the income tax rate in retirement. Thus, the amount in the RothIRA would be identical to that of a traditional IRA if tax rates 10 years from now werethe same 25%.

Chapter 16 Personal Taxation and Behavior

1. The supply of labor (and other factors) in and out of a state is more elastic than the supplyof factors to the nation as a whole. Therefore, an income tax reduction at the state level islikely to lose less revenue than such a reduction at the federal level, ceteris paribus. Justas one can think of welfare-induced migration for poor households, one can think of

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tax-induced migration for businesses and possibly workers. If the state lowers tax rates(and other states do not respond accordingly), then one imagines that a number ofbusinesses will enter that state and spur economic activity.

2.

If individuals view their loss in the labor income taxes as offset by the benefits of public

services, labor supply falls by AB hours. This is the compensated change in hours withrespect to a change in the net wage rate.

3.

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4. The effect of the change in the highest marginal tax rate on the individuals budgetconstraint is demonstrated below:

Income

Leisure

The resulting change in the tax rate moves part of the budget line out to the new, dotted

budget constraint. This policy has an effect on labor supply analogous to the effect of anincrease in an individuals wage rate on labor supply: it is theoretically ambiguous. Thereason for this ambiguity is that there are two competing effects -- a substitution effectwhich acts to decrease leisure, and an income effect which increases leisure. Thedecrease in the tax rate makes leisure more expensive, so the substitution effect dictatesthat less of it is to be consumed. However, there is extra income provided by this tax cut,and the income effect makes the individual want to consume more leisure. These twocompeting effects make the overall change in labor supply ambiguous. Existingempirical work suggests that for prime age males, the income and substitution effectsmore or less cancel each other out. For working wives, the substitution effect dominates,meaning that the reduction in marginal tax rates would tend to increase their labor supply.

The effect on savings can be demonstrated using a diagram illustrating the change in theintertemporal budget constraint that results from this tax change:

FutureConsumption

E ECurrent Consumption

The policy moves the endowment point from point E to E, and it changes the slope ofthe intertemporal budget const

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