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There is no compelling reason to think the private sector would have higher costs than the public sector.. The marginal benefit for society equals the marginal cost at 67 degrees; for te

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

Individuals and their goals are less important than the state

b Rehnquist makes a clear statement of the mechanistic view of the state

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

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

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

fact that inflation reduces the real debt obligation means that this figure should be

included as revenue to the government

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

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

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

observed and others of which are unobserved Economists often cannot perform

controlled, randomized experiments, which makes it difficult to assess how any single

variable affects a given outcome Moreover, even in the cases when experiments are run

(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

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

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

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)

allocation of labor supply across activities does not matter

a The public good is patrol; the private good is fruit

efficient allocation, Cheetah should patrol more

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

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,

Medicaid, public housing, or food stamps offers much in terms of benefit to society as a

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

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

(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

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

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

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

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

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

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

c P* Give a per-unit subsidy of $b per party

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.)

on how many students are involved, the costs of negotiation should be fairly small

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.”

how to transfer bribes

effectively subsidizing authoritarian regimes like those in Saudi Arabia

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

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

the Coase Theorem The potential efficiency of the outcome may be laudable, but the

distributional impact may be unpalatable to some

equal to marginal cost This occurs at 4 units

which is the sum of MC and MD At 2 units, MB=MSC=13

joint profit maximization problem, not the profit maximization problem at either firm alone Thus, the LP farm produces 2 units, the socially efficient amount

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

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

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

that 50=100-10P, or P=$5

($8 versus a market price of $5), ACME buys the permit By doing so, it saves $3

in costs

Chapter 6 – Political Economy

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

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

b Assuming that the public sector uses only labor as an input, the price of the public

good increases by three percent a year

paper by W J Baumol, “Macroeconomics of Unbalanced Growth: The Anatomy

of Urban Crises,” American Economic Review, 1967.

decisions are likely to be made A majority system might be more suitable, although it is

subject to cycling and other problems

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:

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

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

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

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

then the milk is sold at a price of $2, and a quantity of 80 units is sold

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

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

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.

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.”

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

optimal number of FDA employees and the actual number of FDA employees are likely

to rise

is basically a description of the median voter rule

Chapter 7 – Income Redistribution: Conceptual Issues

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

So,

money in the economy is exhausted first)

So,

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.

all the money to Simon is optimal (In fact, we would like to give him up to

$200.)

distributions of income

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

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

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

raises welfare more than the same dollar given to Lynne

that comparisons across people are valid

they raise the welfare of the person with the minimum level of utility For

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

U 0

F A

Food Stamp Allotment

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

Sherry, then Sherry’s income is now $136 and Marsha’s is now $64 With Sherry’s

With Marsha’s utility function, her utility with $64 of income is

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

Sell food stamps for other goods on black market

F

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

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

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

received, G=food stamp guarantee, t=tax rate, E=earnings, and D=standard deduction

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

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

$23,928

Statutory TANF benefit

7 In all cases, the demand curve for housing slopes downward.

of housing, then the supply curve is perfectly inelastic, e.g., vertical

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

D 0 S

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

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.

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

she moves into the range where the EITC is phased out According to Figure 8.8

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

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

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

Call 1990 year 1 and 2050 year 2 Then

would have to increase by 71 percent Similarly, to keep the initial tax rate constant, we

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

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

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

wage rates (the second term) offset increases in the dependency ratio (the third term)

Thus, constant benefits do not necessarily imply higher tax rates

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

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

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?

faces a marginal tax rate of 15% and a payroll tax of 7.45% Thus, the person’s after-tax

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

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

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

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

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

Total expenditure =(2)(50)=$100

b Now the individual pays only $5 per visit.

Insurance company pays ($45)(4) = $180Total expenditure = $200, double its previous level

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

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

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

www.elsolucionario.net

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

U 0

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

FIGURE 10.6b – Medigap choice with minimum standards; no Medigap is purchased

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

unit In this case, Connor buys Q=100-8($2)=84 units of insurance

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

there is no way to determine which safety precautions are sensible

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

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

.10The 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

.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 percentage

points, nothing changes in real terms

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

the same as a dollar to the “middle class,” choose the subway project

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

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

considered an enormous benefit What this analysis obviously missed is the “value of

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

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

$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

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

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

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

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

quantity demanded:

The equilibrium output can be determined by substituting the equilibrium price into either

the supply or demand equation

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

c a b a Q

bP a Q

− +

=

+

=

d b

c a d c Q

dP c Q

Q b 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

+

+ +

1 1

u Q b b

Therefore, both approaches lead to the same outcome.

-300)/I 0 )]/(I 1 -I 0 ) Rearranging, we have v 1 ’ = v 1 +[(300/I 0 )-(300/I 1 )]/(I 1 -I 0 ) Thus, the

income by more when a $300 lump sum tax refund is given Intuitively, the average tax

rate falls by more for a low-income person from a lump sum tax reduction Equation

-I 0 )/I 0 ]= [(T 1 -T 0 )/(T 0 -300)]/[(I 1 -I 0 )/I 0 ] Note that v 2 ’ differs from v 2 only by the term (T 0

-300) Thus, the numerator of v 2 ’ is larger than v 2, while the denominator is the same

when the lump sum tax refund is given

of the textbook If we follow the text and define progressivity with respect to average tax

rates rather than marginal tax rates, then the average tax rate equal ATR=(-4000/I)+.2 for

any income level Clearly this average tax rate converges to ATR=20% as income gets

large, and is lower for lower income levels Replicating Table 12.1 for the tax system

given here, we get:

Income Tax Liability Average Tax Rate Marginal Tax Rate

dbu bc da Q

Q db

d b db

dbu bc da

Q d b

u d

c b a

u d

c Q d

Q b b a

P

+

+ +

1 1

9 With the schedule T=a+tI, the average tax rate as a function of income is

ATR=T/I=(a+tI)/I=(a/I)+t A progressive tax system, using equation (12.1), means that

the average tax rate goes up with income, or dATR/dI>0 Taking derivatives,

dATR/dI=-a/I 2 >0, which implies –a>0 or a<0 Thus, with a linear tax schedule, a negative

intercept, a, implies progressivity Similarly, a regressive tax system implies dATR/dI<0

positive intercept, a, implies regressivity.

which is of second order importance Then dTR=QdP-PdQ If this change in

ε D <1 Thus, the absolute value of the elasticity of demand is less than 1, or

demand must be inelastic in this case

enacted As more time passes and consumers are able to adjust (e.g., by quitting smoking, substituting to other forms of tobacco that are not taxed in the same way, etc.), it is expected that the long-run elasticity of demand for cigarettes will

be larger in absolute value (e.g., become relatively more elastic), and revenues will likely fall

employers, the tax may very well be borne primarily by the foreign domestic-help

workers This could happen if the demand for the foreign domestic-help workers is

relatively elastic and/or the supply of foreign domestic-help workers is relatively

inelastic One might imagine, for example, that native domestic-help is a good substitute

for foreign domestic-help, and thus, demand for foreign domestic-help is quite elastic

Thus, wages of foreign workers are likely to fall, assuming there is no minimum wage in

Hong Kong (if there was a minimum wage, it is likely that employment would fall)

Thus, the Philippine president was correct to be disturbed, because the economic

incidence falls on his countrymen The figure below illustrates the likely situation with