Part 1 – Getting Started
Instructor’s Manual to accompany
Public Finance, Tenth Edition, by Harvey S. Rosen and Ted Gayer
Chapter 1 – Introduction
Brief Outline
1. Public Finance and Ideology
a. The Organic View of Government
b. The Mechanistic View of Government
c. The Viewpoint of This Book
2. Government at a Glance
a. Legal Framework
i. Federal Government
ii. State and Local Governments
b. Size of Government
c. Expenditures
d. Revenues
e. Our Agenda
Suggested Answers to End-of-Chapter Discussion Questions
1.
a. McCain’s statement is consistent with an organic conception of government.
Individuals and their goals are less important than the state.
b. Locke makes a clear statement of the mechanistic view of the state in which
individual liberty is of paramount importance.
c. Chavez’s statement is consistent with an organic view of government.
individual has significance only as part of society as a whole.
The
2. Libertarians believe in a very limited government and are skeptical about the ability of
government to improve social welfare. Social democrats believe that substantial
government intervention is required for the good of individuals. Someone with an
organic conception of the state believes that the goals of society are set by the state and
individuals are valued only by their contribution to the realization of social goals.
a. A law prohibiting receiving compensation for organ donation would be opposed
by libertarians, as they would want the market to decide who buys and who sells
organs and at what price the organs would be sold. Social democrats also might
oppose the law if they consider that such a law would prevent organ donation
from happening as frequently. However, they are likely to support the law on the
grounds that paying for organ donation would coerce financially desperate people
to sell their organs. The law would protect the individual from making a poor
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Chapter 1 - Introduction
decision. The organic view might also oppose the law because the society might
become healthier if more individuals received transplants, although they would
believe that individuals should donate for the good of society, rather than for
compensation.
b. Libertarians oppose the law mandating helmet use for motorcyclists, arguing that
individuals can best decide whether or not to use helmets without government
coercion. Social democrats take the position that the mandate saves lives and
ultimately benefits individuals. The organic view would probably lead to
favoring the mandate on the grounds that reduced health care costs caused by
fewer injuries benefit society.
c. Libertarians oppose the law mandating child safety seats, arguing that individuals
can best decide whether or not to use child safety seats without government
coercion. Social democrats take the position that the mandate saves lives and
ultimately benefits individuals. The organic view would probably lead to
favoring the mandate on the grounds that reduced health care costs caused by
fewer accidents benefit society.
d. Libertarians would probably oppose a law prohibiting prostitution, while social
democrats would likely favor such a law. The organic view depends on the type
of society policymakers are attempting to achieve. The law would probably be
favored on moral grounds.
e. Libertarians would probably oppose a law prohibiting polygamy, while social
democrats would likely favor such a law. The organic view depends on the type
of society policymakers are attempting to achieve. The law would probably be
favored on moral grounds.
f. Libertarians would likely oppose the ban on trans fats in restaurants, believing
that consumers will demand restaurants remove trans fats if they believe that is
important. Social democrats would probably support the ban because consumers
might not understand how bad trans fats are for their health. Those with an
organic view would probably favor the ban because the scientific literature
suggests that people who avoid trans fats are healthier, therefore the ban would
reduce health care costs.
3. The mechanistic view of government says that the government is a contrivance created by
individuals to better achieve their individual goals. Within the mechanistic tradition,
people could disagree on the tax on saturated fats to reduce obesity. Libertarians would
say that people can decide what is best for themselves - whether to consume saturated
fats - 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.
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Part 1 – Getting Started
4.
a. If the size of government is measured by direct expenditures, the mandate does
not directly increase it. Costs of compliance, however, may be high and would
appear as an increase in a “regulatory budget.”
b. This ban would not increase government expenditures, but the high costs of
compliance would increase the regulatory budget.
c. 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.
d. The federal budget would decrease if grants-in-aid were reduced. However, if
state and local governments offset this by increasing taxes, the size of the
government sector as a whole would not go down as much as one would have
guessed.
5. The inflation erodes the real value of the debt by 0.036 x £904 billion or £32.54 billion.
The fact that inflation reduces the real debt obligation means that this figure should be
included as revenue to the government.
6. If you consider the size of government as the extent to which society’s resources are
subject to control by the government, the both Policy 1 and Policy 2 would increase the
size of government by the same amount. While it seems Policy 1 has no effect of the size
of the government because it only mandates private spending, it causes resources to be
under the control of the government. Policy 2 seems to affect the size of the government
because it changes revenues and transfers, but the cost to each household is the same as
in Policy 1, a $5000 expenditure on health insurance or in additional taxes.
7. Relative to GDP, defense spending grew from 5.0 percent of GDP in 1981 to 6.0 percent
of GDP in 1985 and then grew from 3.9 percent of GDP in 2007 to 4.7 percent of GDP
in 20011. The increase from 2007 to 2011 was proportionally larger, but both increases
were the same in terms of the percentage point increase.
8.
a. For the years 1997 to 2001, the absolute change in federal expenditures was
$261.7 billion [$1862.8 - $1,601.2 billion],
the change in federal expenditures in real terms (2001 dollars) was $146.26
billion [inflation rate = (90.727-84.628)/84.628=7.21%, $1,862 billion –
$1,601(1+0.0721)=$146.26 billion],
the change in real government expenditures per capita was $241.26 [real
government
expenditures
per
capita
in
1997
(2001
dollars):
$1,601.1*(1+1.0721)/0.227912 = $6,289.72; real government expenditures per
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Chapter 1 - Introduction
capita in 2001 (2001 dollars): $1862.8/0.285225 billion = $6,530.98; $6,530.98$6,289.72=$241.26],
and the change in expenditures per GDP is -$0.01106 billion [$601.1/$8,332.4 –
$1,862.8/$10,286.2].
For the years 2007 to 2011, the absolute change in federal expenditures was
$874.4 billion [$3,603.1 billion - $2,728.7 billion],
the change in federal expenditures in real terms (2011 dollars) was $691.9 billion
[inflation rate = (113.338-106.231)/106.231=6.69%, $3,603.1 billion –
$2728.7(1+0.10669) = $691.9 billion],
the change in real government expenditures per capita was $1,899.78 [real
government
expenditures
per
capita
in
2007
(2011
dollars):
$2,728*(1+1.10669)/0.3017 = $9,647.14;
real government expenditures per capita in 2011 (2011 dollars): [$3,603/0.3120
billion = $11,546.92; $11,546.92$9,647.14=$1,899.78],
and the change in expenditures per GDP is -$0.0442 billion [$2,728.7 /$14,028 –
$3,603.1/$15,094].
b. The health spending and “other” categories had the largest relative increases
changes from 1997 to 2001 and 2007 to 2011. Net interest had the only decrease
in spending.
Defense
Health
Medicare
Income secruity
Social Security
Net Interest
Other
1997
285.7
123.8
190.0
235.0
365.3
244.0
157.3
2001
321.2
172.2
217.4
269.8
433.0
206.2
243.1
relative
change from
1997 to 2001
12.426%
39.095%
14.421%
14.809%
18.533%
-15.492%
54.545%
2007
579.8
266.4
375.4
366.0
586.2
237.1
317.9
2011
751.3
372.5
485.7
597.4
730.8
230.0
435.5
relative
change from
2007 to 2011
29.579%
39.827%
29.382%
63.224%
24.667%
-2.995%
36.993%
9.
a. The 1997 to 2001 absolute change in federal tax revenues was $411.9 billion
(=$1991.1 - $1579.5), while from 2007 to 2011 the same change was -$264.5
billion (=$2303.5-$2568.0).
In real terms, the 1997 to 2001 change in federal tax revenues was $298.04
(inflation over period 7.21%, real change =$1991.1-($1579.2*1.0721). For 2007
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Part 1 – Getting Started
to 2011, the change in federal tax revenues was $-436.30 (inflation over period
6.69%, real change = $2303.5-$2568.0*1.0669).
The change in real tax revenues per capita for 1997 to 2001 was $778.16
(=($1991.1/.285225-$1579.2*(1.0721)/0.272958)) and for 2007 to 2011 was $1699.26 (=($2303.5/.312040-$2568.0*(1.0669)/0.301696)).
The change in the tax revenues per GDP from 1997 to 2001 was 0.004
(=$1991.1/10286.2-$1579.5/8332.4) and from 2007 to 2011 was 0.0530
($2303.5/15094-$2568.0/14028).
b. From 1997 to 2001, social insurance taxes had the largest relative increase. From
2007 to 2011, the excise tax had the largest relative increase. From 1997 to 2001
and 2007 to 2011, social corporate taxes revenue had the largest relative decrease.
Individual Income Tax
Corporate Tax
Social Insurance
Excise Tax
1997
737.5
182.3
539.4
120.1
2001
994.3
151.1
694.0
151.7
relative
change from
1997 to 2001
34.820%
-17.115%
28.661%
26.311%
2007
1163.5
370.2
869.6
164.7
2011
1091.5
181.1
818.8
212.1
relative change
from 2007 to
2011
-6.188%
-51.080%
-5.842%
28.780%
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Part 1 - Getting Started
Chapter 2 – Tools of Positive Analysis
Brief Outline
1. The Role of Theory
2. Causation versus Correlation
3. Experimental Studies
a. Conducting an Experimental Study
b. Pitfalls of Experimental Studies
4. Observational Studies
a. Conducting an Observational Study
b. Pitfalls of Observational Studies
5. Quasi-Experimental Studies
a. Conducting a Quasi-Experimental Study
b. Pitfalls of Quasi-Experimental Studies
6. Conclusions
Answers to End-of-Chapter Questions
1. A change in the marginal tax rate changes the individual’s net wage. This generates both
an income effect and a substitution effect. As long as leisure is a normal good, these
effects work in opposite directions. Hence, one cannot tell a priori whether labor supply
increases or decreases. If there were no political or legal impediments, an experimental
study could be conducted in which a control group confronts the status quo, and an
experimental group faces the new tax regime. Other things that affect work effort would
impact both the control group and the experimental group, so any difference in work
effort between the two groups could be attributed to the change in marginal tax rates.
2. This is a valid criticism of the study of New York Homelessness. It reflects the problem
of causality. Two things may be correlated, but it can be difficult to determine which
causes the other. The remedy would be to set up a study in which individuals are
randomly assigned to groups. In an experimental study, the group offered job training,
counseling services, and emergency money would not necessarily be more motivated
than a group not signed up for those services, so if they do not become homeless, it could
be attributed to the programs.
3. The workers who spend time on a computer probably have other skills and abilities that
contribute to higher wages, so training children to use computers would not necessarily
cause their earnings potential to improve. This study illustrates the difficulty of
determining cause and effect based on correlations. The data do not reveal whether using
a computer causes higher earnings, or whether other factors cause workers to use
computers and to earn higher wages.
4. The text points out the pitfalls of social experiments: the problem of obtaining a random
sample and the problems of extending results beyond the scope of the experiment.
Participants in the study had found it to their advantage to be a part of the experiment,
which may have resulted in a self-selected population unrepresentative of the wider group
of health care consumers. In addition, the RAND Health Insurance Experiment was of
limited duration, after which the participants would move to some other health plan. This
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Chapter 2 - Tools of Positive Analysis
design could induce certain behavior in the short-run that would not necessarily be
present if the health insurance coverage were permanent rather than transitory. Further,
physicians’ “standard practices” are largely determined by the circumstances of the
population as a whole, not the relatively small experimental group.
5. The scenario set up by the change in unemployment lends itself to a difference in
difference approach, in which the first difference is across time and the second difference
is across income level. The researcher would measure the change in unemployment
duration for high earners between the period of lower benefits and the period of higher
benefits, and then compare this change to the change for the low earners. The treatment
group would be the high earners and the control group would be the low earners. The
assumption that must hold for unbiased estimates is that in the absence of the policy
change, both the treatment and control groups would have experienced the same change
in unemployment duration across the periods preceding and following the policy change.
6. Since only five states reduced income taxes, we could examine what happened in a
control group of states (those with an income tax but with no change in the tax rates) and
compare savings rates between the two. This is important because other factors affect
savings rates, but if other factors affected both the control group and the treatment group,
then we can conclude that the treatment (lower taxes) caused the change in savings. If,
for example, the saving rate for the five states with lower taxes (the treatment group)
increased by two percent, while the savings rate for the other states (the control group)
increased by one percent, then we could conclude that lower taxes caused the saving rate
to increase by one percent—the difference between the two percent increase in the
treatment group and the one percent increase in the control group. The assumption that
must hold for this difference in difference approach to be valid is that in the absence of
the income tax cut, the savings rates of the treatment rates would have increased by the
same percentage as the savings rates of the control states.
7. Correlation does not, in general, reveal anything about causation. Spitzer is assuming that
because there is no correlation between higher marginal tax rates and slowing economic
activity in the data, that marginal tax rates can be raised without harming economic
growth. The assumption ignores that other factors could be playing in the economy that
would mitigate the effect of higher marginal tax rates. Further, current higher marginal
tax rates could imply lower future economic growth, which may not be reflected in the
data to which he was referring.
8. There is a weak, positive relationship between deficits and interest rates, implying that
larger deficits lead to lower interest rates. Inferences based on these data along would be
problematic because there are only a few data points and because it would be more
informative to look at deficits relative to some benchmark, such as GDP, and to express
both interest rates and deficits in real terms, rather than nominal terms. It would also be
useful to control for other factors that can affect interest rates, such as monetary policy
and the level of economic activity. Most importantly, the correlation found here does not
necessarily indicate a causal relationship.
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Part 1 - Getting Started
Chapter 3 – Tools of Normative Analysis
Brief Outline
1. Welfare Economics
a. Pure Economy Exchange
b. Production Economy
2. The First Fundamental Theorem of Welfare Economics
3. Fairness and the Second Fundamental Theorem of Welfare Economics
4. Market Failure
a. Market Power
b. Nonexistence of Markets
c. Overview
5. Buying into Welfare Economics
Answers to End-of-Chapter Questions
1.
a. In this particular insurance market, one would not expect asymmetric information
to be much of a problem – the probability of a hurricane is common knowledge.
Moral hazard could be an issue – people are more likely to build near a beach if
they have hurricane insurance. Still, one would expect the market for hurricane
insurance to operate fairly efficiently.
b. There is substantial asymmetric information in the markets for medical insurance
for consumers and also malpractice insurance for physicians. For efficient
consumption, the price must be equal to the marginal cost, and the effect of
insurance may be to reduce the perceived price of medical care consumption.
That would lead to consumption above the efficient level. Because of the roles of
regulation, insurance, taxes, and the shifting of costs from the uninsured to the
insured, there is little reason to expect the market to be efficient.
c. In the stock market, there is good information and thousands of buyers and sellers.
We expect, in general, efficient outcomes.
d. From a national standpoint, there is a good deal of competition and information
with regards to MP3 players and music. The outcome will likely be efficient for
MP3 players and music. However, some firms might exercise some market
power through high brand awareness and proprietary downloading systems.
e. The private market allocation is likely inefficient without government
intervention. Student loan markets may suffer from asymmetric information – the
student knows better than the lender whether he will repay the loan or default on
it, a form of adverse selection. Government intervention does not “solve” the
adverse selection problem in this case (because participation in the student loan
program is not compulsory), but it may create a market that would not exist
without intervention.
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Chapter 3 - Tools of Normative Analysis
f. The market for housing is likely to be relatively efficient. Some inefficiencies
may exist, such as asymmetric information—the seller knows more about the
house than the buyer—and differentiated products. But, the market has developed
to mitigate these inefficiencies. For example, a buyer can employ a home
inspector to help him understand more about the quality of the home. Also, a
large number of homes on the market increases competition.
2. The social welfare function of W=f(U a , U b ) implies that the welfare of society depends
on the utility of the individuals. It does not imply that the utility of the individual
depends on the welfare of society as then-Senator Obama’s comment suggests.
3. The First Theorem of Welfare Economics says that market transactions only occur when
the transactions would be in the best interest of both parties. In contrast, the psychologist
seems to view the kidney market as hurting one or both parties involved.
4. If insurers in California could no longer use location to determine automobile insurance
rates, some of the higher costs incurred by urban residents would be shifted to rural and
suburban residents. This change would reduce efficiency, but the purpose of the policy is
to improve equity, based on an argument that it is unfair that urban residents should have
to pay more for insurance because they are more likely to be involved in accidents.
Social welfare increases if the additional utility enjoyed by urban residents offsets the
loss in utility to rural and suburban residents.
5.
Tickets
Seller
A
Other goods
Other goods
B
Buyer
Tickets
a. Point A is the initial allocation.
b. Given the initial allocation in the Edgeworth Box above, one can see that both the
seller and buyer can reach a higher indifference curve at point B by trading tickets
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Part 1 - Getting Started
and other goods without either person being worse off. Therefore, the current
allocation is inefficient.
c. A situation in which the original allocation is efficient and the trading does not
affect efficiency is shown below at point A.
Tickets
Other goods
Buyer
Seller
Other goods
A
Tickets
6.
a. Social indifference curves are straight lines with slope of –1. As far as society is
concerned, the “util” to Augustus is equivalent to the “util” to Livia.
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Chapter 3 - Tools of Normative Analysis
b. Social indifference curves are straight lines with slope of –2. This reflects the fact
that society values a “util” to Augustus twice as much as a “util” to Livia.
c.
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Part 1 - Getting Started
7. Musgrave (1959) developed the concept of merit goods to describe commodities that
ought to be provided even if the members of society do not demand them. “Sin taxes”
work the opposite way and apply to commodities that members of society might demand,
but ought not to have.
8.
a. There is no obvious reason why there is a market failure with burglar alarm calls;
the Los Angeles police could set a response fee equal to the marginal cost.
b. There is no obvious reason that the production of a documentary film about rock
music and the fall of the Soviet Union would improve welfare in the United States.
c. There is no economic reason why cherry pies should be regulated, especially
since there are no such regulations for apple, blueberry, or peach frozen pies.
d. It is hard to imagine a basis in welfare economics for this guarantee to the
domestic sugar producers, unless the utilities of sugar producers are given great
weight in the social welfare function.
e. This is not an efficient policy. If the problem is that too much water is being
consumed, then the answer is to increase the price of water. On that basis, people
can decide whether or not they want to buy toilets that require less water. Water,
like most other resources, is a private good.
f. There is no obvious reason that the preservation of video game history would
improve welfare.
9. In this case, the “Edgeworth Box” is actually a line because there is only one good on the
island. The set of possible allocations is a straight line, 100 units long. Every allocation
is Pareto efficient, because the only way to make one person better off is to make another
person worse off. There is no theory in the text to help us decide whether an allocation is
fair. Although splitting the peanuts even between the people may be fair, it may not be
fair if the calorie “needs” of the people are different. With a social welfare function, we
can make assessments on whether redistribution for society as a whole is a good thing.
10. Social welfare is maximized when Mark’s marginal utility of income is equal to Judy’s
marginal utility of income. Taking the derivative of Mark’s utility function to find his
marginal utility function yields MU M = 50/(I M 1/2) and taking the derivative of Judy’s
utility function yields MU J = 100/(I J 1/2). If we set MU M equal to MU J , the condition for
maximization becomes I J = 4I M and, since the fixed amount of income is $300, this
means that Mark should have $60 and Judy should have $240 if the goal is to maximize
social welfare = U M + U J .
11.
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Chapter 3 - Tools of Normative Analysis
a. If the food is evenly distributed between Tang and Wilson, Tang will have 14.14
units of utility and Wilson will have 7.07 units of utility.
b. If the social welfare function is U T +U W , then the marginal utilities of both should
be equal to maximize social welfare. Equate MU T =1/(2F T 1/2) to MU W =1/(4F W 1/2)
and substitute F T =400-F W . Therefore, F T =320 and F W =80.
c. If the utility of both Tang and Wilson must be equal, then set U T =U W and
substitute F T =400-F W and solve. Therefore, F T =80 and F W =320.
12. Although Victoria’s marginal rate of substitution is equal to Albert’s, these are not equal
to the marginal rate of transformation and the allocation is, therefore, Pareto inefficient.
Both people would give up 2 cups of tea for 1 crumpet but, according to the production
function, could actually get 6 crumpets by giving up 2 cups of tea. By giving up tea and
getting crumpets through the production function, both utilities are raised.
13.
a. The marginal rates of substitution for coffee and for tea are constant for both
Hannah and Jose. Hannah would trade ¼ pound of coffee for 1/3 pound of tea to
remain equally satisfied. Similarly, Jose would trade ¼ pound of tea for 1/3
pound of coffee to remain equally satisfied. The constant MRS means linear
indifference curves
b. Green indifference curves are Jose’s and red indifference curves are Hannah’s.
Coffee
13
Jose
Tea
11
10
Tea
Hannah
15
Coffee
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Part 1 - Getting Started
c. The contract curve follows the bottom and right borders of the Edgeworth Box. At
any interior point in the box, the parties will find it in their interest to trade until
they reach these borders. This is because Hannah would only choose to consume
tea once she has consumed all the coffee in the economy. Likewise, Jose would
only choose to consume coffee once he has consumed all the tea in the economy.
d. The initial allocation is not Pareto efficient. It is possible to make one better off
without making the other worse off.
14.
a. False. As shown in the text, equality of the marginal rates of substitution is a
necessary, but not sufficient, condition. The MRS for each individual must also
equal the MRT.
b. Uncertain. As long as the allocation is an interior solution in the Edgeworth box,
the marginal rates of substitution must be equal across individuals. This need not
be true, however, at the corners where one consumer has all the goods in the
economy.
c. False. A policy that leads to a Pareto improvement results in greater efficiency,
but social welfare depends on equity as well as efficiency. A policy that improves
efficiency but creates a loss in equity might reduce social welfare.
d. False. Moving to a point on the utility possibilities curve may not result in a
Pareto improvement because one party may receive less utility on the curve than
they received at the interior point.
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Part 2 – Public Expenditure: Public Goods and Externalities
Chapter 4 – Public Goods
Brief Outline
1. Public Goods Defined
2. Efficient Provision of Public Goods
a. Deriving the Efficiency Condition
b. Problems in Achieving Efficiency
c. The Free Rider Problem
3. Privatization
a. Public versus Private Provision
b. Public versus Private Production
4. Public Goods and Public Choice
Answers to End-of-Chapter Questions
1.
a. Wilderness area is an impure public good – at some point, consumption becomes
nonrival; it is, however, nonexcludable.
b. Satellite television is nonrival in consumption, although it is excludable; therefore
it is an impure public good.
c. Medical school education is a private good.
d. Television signals are nonrival in consumption and not excludable (when
broadcast over the air). Therefore, they are a public good.
e. An automatic teller machine is rival in consumption, at least at peak times. It is
also excludable as only those patrons with ATM cards that are accepted by the
machine can use the machine. Therefore the ATM is a private good.
2.
a. False. Efficient provision of a public good occurs at the level where total
willingness to pay for an additional unit equals the marginal cost of producing the
additional unit.
b. False. Due to the free rider problem, it is unlikely that a private business firm
could profitably sell a product that is non-excludable. However, recent research
reveals that the free rider problem is an empirical question and that we should not
take the answer for granted. Public goods may be privately supported through
volunteerism, such as when people who attend a fireworks display voluntarily
contribute enough to pay for the show.
c. Uncertain. This statement is true if the road is not congested, but when there is
heavy traffic, adding another vehicle can interfere with the drivers already using
the road.
d. False. There will be more users in larger communities, but all users have access
to the quantity that has been provided since the good is nonrival, so there is no
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Chapter 4 – Public Goods
reasons larger communities would necessarily have to provide a larger quantity of
the nonrival good.
3. We assume that Cheetah’s utility does not enter the social welfare function; hence, her
allocation of labor supply across activities does not matter.
a. The public good is patrol; the private good is fruit.
b. Recall that efficiency requires MRSTARZAN + MRSJANE = MRT. MRSTARZAN =
MRSJANE = 2. But MRT = 3. Therefore, MRSTARZAN + MRSJANE > MRT. To
achieve an efficient allocation, Cheetah should patrol more.
4. The Search for Extra-Terrestrial Intelligence is a public good because it is nonrival and
presumably non-excludable. The government should pay for the research only if the
SMB is greater than the SMC.
5. Wine and liquor are both rival and excludable goods, so public sector production is not
justified on the basis of public goods. Therefore, it makes no economic sense to have
public production.
6. It is unlikely that if Pemex were privatized that the situation would lead to a monopoly
situation. Comparing oil production to telephone service is not a correct comparison. In
the case of the telephone company, there was only one provider of telephone service. In
the case of oil production, there would be only one producer in Mexico, but many
competitors providing oil from which Mexico could buy. The newly privatized company
would have to compete to sell its goods. It would likely become more efficient than the
state run company because of this competition.
7. These amenities being present in private airports alone would not be enough to
recommend that airports be privately run. If fliers desire such amenities, it is not clear
that they cannot be provided in public airports via renting space. One would also need
information on the cost of running the airports and distributional issues that might exist
for publicly run airports versus privately run airports before recommending that airports
be privately run.
8. The experimental results on free-riding suggest that members of the community might
voluntarily contribute about half of the required amount. The reason these citizens
wanted to use private fundraising was because the state government redistributed tax
dollars from wealthy districts to poor districts (the so-called Robin Hood plan), so using
private donations was a way to avoid losing tax dollars to other districts.
9. Books are not a public good. They are both rival (two people cannot read a book at the
same time) and excludable (you can keep a person from reading a book). But if the goods
libraries provide are a sense of community or a better educated populace, these would
qualify as public goods. If the public good aspect of the library is to produce a better
educated populace, then perhaps the classic books are a better choice.
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Part 2 – Public Expenditure: Public Goods and Externalities
10. Hiring private military firms to provide military support in Afghanistan, Iraq, or Darfur
would be similar to the example of airport security in the text. One might argue that a
private firm would not provide adequate training, use unethical or especially aggressive
methods to shorten the conflict, thus lowering costs to increase profits. Proponents
would argue that such things could be stipulated in a well-written contract. However, no
contract can specify every possible contingency. In high conflict situations this may be
especially true as the opposing side will not be predictable.
11.
a. Zach’s marginal benefit schedule shows that the marginal benefit of a lighthouse
starts at $90 and declines, and Jacob’s marginal benefit starts at $40 and declines.
Neither person values the first lighthouse at its marginal cost of $100, so neither
person would be willing to pay for a lighthouse acting alone.
b. Zach’s marginal benefit is MB ZACH =90-Q, and Jacob’s is MB JACOB =40-Q. The
marginal benefit for society as a whole is the sum of the two marginal benefits, or
MB=130-2Q (for Q≤40), and is equal to Zach’s marginal benefit schedule
afterwards (for Q>40). The marginal cost is constant at MC=100, so the
intersection of aggregate marginal benefit and marginal cost occurs at a quantity
less than 40. Setting MB=MC gives 130-2Q=100, or Q=15. Net benefit can be
measured as the area between the demand curve and the marginal benefit of the
15th unit. The net benefit is $112.5 for each person, for a total of $225.
12. Each day the private decision of each shepherd would equate private cost with private
benefit. Therefore, 7 would show up because then each shepherd would graze four sheep.
If the shepherds graze less than four sheep, then they will stay home. The net benefits to
society are 0 sheep (the benefit to the seven shepherds is 4 sheep (7x4=28) and the cost to
society is 4 sheep per shepherd (7x4=28)). The efficient number of shepherds to show up
at the meadow is the number that will maximize social net benefits, which happens where
the social marginal benefit equals the social marginal cost. This occurs at four shepherds,
where the net social benefits equal 12 sheep (4x7 – 4x4). Access to the meadow is an
impure public good. It is rival – if one shepherd has access to the meadow, the others
have less access. It is, however, non-excludable because it is difficult to keep shepherd
from grazing the meadow.
13. Britney’s marginal benefit is MB BRITNEY =12-Z, and Paris’s is MB PARIS =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 Britney’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 Britney or Paris 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 Paris could credibly free ride, and Britney would
provide the efficient allocation. This occurs because if Britney believes that Paris will
free ride, Britney provides her optimal allocation, which occurs on the second segment of
society’s MB curve, which is identical to Britney’s MB curve (note that Paris gets zero
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Chapter 4 – Public Goods
marginal benefit for Z>4). Since Paris is completely satiated with this good at Z=4, her
threat to free ride is credit if Britney provides Z>4. See the graph below.
MBParis
MBBritney
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Part 2 – Public Expenditure: Public Goods and Externalities
Chapter 5 – Externalities
Brief Outline
1. The Nature of Externalities
2. Graphical Analysis
a. Implications
b. Conclusion
3. Private Responses
a. Bargaining and the Coase Theorem
b. Mergers
c. Social Conventions
4. Public Responses to Externalities: Taxes and Subsidies
a. Taxes
b. Subsidies
5. Public Responses to Externalities: Emissions Fees and Cap-and-Trade Programs
a. Emissions Fee
b. Cap-and-Trade
c. Emissions Fee versus Cap-and-Trade
d. Command-and-Control Regulation
6. The US Response
a. Progress with Incentive-Based Approaches
7. Implications for Income Distributions
a. Who Benefits?
b. Who Bears the Cost?
8. Positive Externalities
a. A Cautionary Note
Answers to End-of-Chapter Questions
1. Before passengers were charged for checked bags, they would choose whether to check
bags or carry them on based on whether they were willing to trade time for the hassle of
dealing with carry-on bags. That is, passengers who valued saving time by not having to
deal with baggage claim more than the cost of dealing with carry-on baggage will choose
to carry on. The fact that passengers are now charged for checked baggage but not for
baggage carried onto the plane will inefficiently allocate overhead space. Passengers will
carry on more and bigger bags to save the fee charged, resulting in full overhead luggage
containers. Overhead space will go to the first passengers on the plane, rather than being
distributed more evenly. Bags checked (without a charge) at the gate forces some who
would choose to carry on even without the fee to have to check, which is a loss in
efficiency. Those who elect to carry on to avoid the fee, but would rather check their
bags, also result in an inefficiency.
2. The Coase theorem suggests that the church and the comedy club could negotiate. If the
church possessed the right to the “noise” in the building, the comedy club could pay the
church to be quiet. If the comedy club possessed the right to quiet in the building, the
church could compensate the club for the noise.
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Chapter 5 - Externalities
3. It is the case that a carbon tax would be passed on to the consumer. The tax raises costs
to the producer for producing the final good. These increased costs would decrease
supply, which will increase the price of that final good. In a cap and trade system,
businesses must purchase permits in order to emit carbon. If the cost of purchasing and
using abatement equipment is less than the cost of buying a permit, the business will use
abatement equipment. In either case (buying a permit or using abatement equipment)
costs for the producer increase, decreasing supply and increasing the price of the final
good. If the carbon tax and the number of permits issued in the cap and trade system
were set appropriately, the outlays for both programs would be the same.
4.
a. The number of parties per month that would be provided privately is P.
b. See schedule MSB p.
c. P*. Give a per-unit subsidy of $b per party to induce the correct number of parties.
d. The optimal subsidy is $b. The total subsidy=abcd. “Society” comes out ahead by
ghc, assuming the subsidy can be raised without any efficiency costs.
(Cassanova’s friends gain gchd; Cassanova loses chd but gains abcd, which is a
subsidy cost to government.)
5. The payment for signing a waiver is a negotiation as suggested by the Coase Theorem. If
residents accept the payment and sign the waiver, they are signaling that the noise cost to
them is less than the payment. If the residents choose not to accept the payment and sign
the waiver, the payment is not great enough to cover the cost of the noise. The Coase
Theorem suggest in this case that further negotiation could occur.
6. On the surface, the tax on saturated fat seems like a Pigouvian tax, if you assume that the
$3 is equivalent to the level of the damage from the saturated fats. The commentator is
not correct in his criticism that the tax is levied on an input rather an outcome. If the tax
is properly set and is the direct cause of unhealthy consumers, the efficient level of
saturated fat will be consumed. However, this tax suffers from the problem of assuming
that the saturated fat leads directly to poor health outcomes and is the only source of
unhealthy outcomes. Some consumers are healthy no matter the level of consumption of
saturated fats. Others are unhealthy even with no consumption of the saturated fats. And
many consumers will simply reallocate their consumption to nontaxed unhealthy foods.
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Part 2 – Public Expenditure: Public Goods and Externalities
7.
a. It is very likely that the farmer could negotiate with the neighbors, provided
property rights are clearly defined. The Coase Theorem is therefore applicable.
b. It is unlikely that negotiation could result in an efficient outcome in this case. It is
likely that there are a great number of farmers involved in both harvesting ants
and growing trees, making negotiation very difficult.
c. Property rights are not being enforced, making negotiation through the Coase
Theorem impossible.
d. There are too many people involved for private negotiation.
8.
a.
The price of imported oil does not reflect the increased political risk by
effectively subsidizing authoritarian regimes like those in Saudi Arabia.
b. The tax would estimate the marginal damage (e.g., the increased instability in the
Middle East, etc.) by importing oil from Saudi Arabia.
c. The supply of TGRs is vertical at 104.5 billion if government seeks to reduce
consumption of gasoline to 104.5 billion. Consumers must have one TGR in
order to buy one gallon of gasoline, plus they must pay the price at the pump.
Limiting TGRs effectively limits the demand for gasoline, so the price per gallon
will fall, but consumers must have TGRs in order to purchase gasoline. If the
market price of one TGR is $0.75, this means that supply and demand intersect at
$0.75, as shown in the graph. This kind of program curbs consumption without
giving government more revenue because consumers are purchasing the TGRs
from each other. However, the total amount of TGRs is limited by government.
Those consumers seeking to purchase more gasoline than allowed by the initial
allocation of TGRs can purchase additional TGRs from other consumers at the
market price of $0.75. By choosing to use a TGR to purchase gasoline, a
consumer incurs an opportunity cost equal to $0.75 since they cannot sell the
TGR once it has been used.
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Chapter 5 - Externalities
$
Supply of TGRs
$0.75
Demand for TGRs
104.5 billion
TGRs
9. The use of the drug to treat sick cows leads to a positive externality (the benefit enjoyed
by air travelers) as well as a negative externality (the costs created by a larger number of
rats and feral dogs). Banning the drug might raise or lower efficiency, depending on
whether the positive externality is larger or whether the negative externality is larger.
There are many ways to design incentive-based regulations. Policymakers could
determine the efficient level of drug usage and then either allocate or sell the right to use
the drug for sick cows.
10. The program matches prices to changes in demand, fluctuating as demand changes. This
results in higher efficiency. Drivers will respond efficiently by choosing to park based on
their willingness to pay.
11.
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=1600.
c. The efficient number of hogs sets marginal benefit equal to marginal social costs.
At 3 hogs, MB=MSC=1600.
12. Private Marginal Benefit = 10 - X
Private Marginal Cost = $5
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Part 2 – Public Expenditure: Public Goods and Externalities
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.
13.
a. The total cost of emissions reduction is minimized only when the marginal costs
are equal across all polluters, therefore a cost-effective solution requires that MC 1
= MC 2 or that 300e 1 = 100e 2 . Substituting 3e 1 for e 2 in the formula e 1 + e 2 = 40
(since the policy goal is to reduce emissions by 40 units) yields the solution. It is
cost-effective for Firm 1 to reduce emissions by 10 units and for Firm 2 to reduce
emissions by 30 units.
b. In order to achieve cost-effective emission reductions, the emissions fee should
beset equal to $3,000. With this emissions fee, Firm 1 reduces 10 units and Firm
2 reduces 30 units, but Firm 1 has to pay $3,000 for each unit of pollution they
continue to produce, which gives them a tax burden of $3,000 x 90 (Firm 1
generated 100 units in the absence of government intervention) or $270,000.
Firm 2 has a lower tax burden because it is reducing emissions from 80 units to
50units. Firm 2 pays $3,000 x 50 = $150,000. As the text concludes, the firm
that cuts back pollution less isn’t really getting away with anything because it has
a larger tax liability than if it were to cut back more.
c. From an efficiency standpoint, the initial allocation of permits does not matter. If
the two firms could not trade permits, then Firm 2 would have to undertake all of
the emissions reduction. Initially, Firm 1’s MC is zero, while Firm 2’s MC is
$4,000, so there is a strong incentive for Firm 2 to purchase permits from Firm 1.
Trading should continue until MC 1 = MC 2 , which is the cost-effective solution.
This means that the market price for permits will equal $3,000, the same as the
emissions fee. At this price, Firm 2 will purchase 10 permits from Firm 2,
allowing Firm 2 to reduce emissions by 30 rather than 40 and requiring Firm 1 to
reduce emissions by 10. This solution is the same as the solution achieved with
the emissions fee. However, Firm 1 is better off because instead of having to pay
taxes, it will receive a payment of $30,000 for its permits. Firm 2 must pay
$30,000 for the extra permits, but it also avoids the payment of taxes. The
government lost $420,000 in tax revenue. The firms must still pay the cost of
emissions reduction, plus Firm 2 must pay for the permits purchased from Firm 1.
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Chapter 5 - Externalities
14. If marginal costs turn out to be lower than anticipated, cap-and-trade achieves too little
pollution reduction and an emissions fee achieves too much pollution reduction. With an
inelastic marginal social benefit function, cap-and-trade is not too bad from an efficiency
standpoint, while an emissions fee causes pollution reduction to be much greater than the
efficient level when marginal cost is lower than anticipated. When marginal social
benefits are elastic, the opposite is true.
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Part 2 – Public Expenditure: Public Goods and Externalities
Chapter 6 – Political Economy
Brief Outline
1. Direct democracy
a. Unanimity Rules
b. Majority Voting Rules
c. Logrolling
d. Arrow’s Impossibility Theorem
2. Representative Democracy
a. Elected Politicians
b. Public Employees
c. Special Interests
d. Other Actors
3. Explaining Government Growth
a. Conclusion
Answers to End-of-Chapter Questions
1.
a. Below, the preferences for each person.
Person 4
Person 5
1
Person 3
2
Person 1
3
4
Person 2
A
B
C
D
b. C wins in every pair wise vote. Thus, there is a stable majority outcome, despite
the fact that persons 1, 2, and 3 have double-peaked preferences. This
demonstrates that although multi-peaked preferences may lead to voting
inconsistencies, this is not necessarily the case.
2. The passage of the agriculture bill in 2007 is consistent with the logrolling model.
Because the members of rural areas were able to trade votes with those in urban areas
3.
a. Neither issue would pass with majority voting as in both cases, two voters of the
three would vote against the each issue because they receive negative net benefits.
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Chapter 6 – Political Economy
This is not efficient because issue X has a positive total net benefit and should be
funded.
b. With logrolling, voters A and B can trade votes. A will vote for issue Y if B votes
for issue X, but C will not vote for either project. Both issues will pass with two
votes for and one against. This is not efficient because issue Y has a negative
total net benefit.
c. If side payments were allowed A could pay B to vote for issue X (A would not
pay C because C would require a higher payment than B), and B could pay A or C
to vote for issue Y. This would result in the same inefficient outcome as in b.
d. If side payments were allowed A would have to pay B at least 1 to vote for issue
X. A would only be willing to pay less than 6. B would have to pay A or C at
least 3, but no more than 4 to entice him to vote for issue Y.
4. Yes, it is consistent, because the theory says that when unanimity is required, no
decisions are likely to be made. A majority system might be more suitable, although it is
subject to cycling and other problems.
5. When the policy changed to allow and encourage female voting, female voters became
the majority, so it is sensible that the median voter is now a woman. Given this, the
median voter theorem suggests that politicians should shift their positions to more closely
align with the views of women.
6. When there is a vote over five options, there is the chance that a potential majority vote is
split between four relatively preferred options, and the fifth option wins. The winning
option may have been voted down if it had been a two-way vote with any of the other
options. Further, if preferences are not single-peaked, cycling and inconsistent public
decisions may emerge.
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Part 2 – Public Expenditure: Public Goods and Externalities
7. On the graph below, the price of taxi rides would increase from P C to P Med and the
number of taxi rides would decline from Q C to Q Med . This would result in a deadweight
loss to society of triangle dce.
$
f
b
c
a
d
PMed
e
S=MC
PC
D
Qmed
8.
QC
MR
Number of taxi rides
a. With the demand curve of Q=100-10P and a perfectly elastic supply curve at P=2,
the milk is sold at a price of $2, and a quantity of 80 units is sold.
b. The marginal revenue curve associated with the inverse demand curve P=10(1/10)Q is MR=10-(1/5)Q, while the marginal cost curve is MC=2. The cartel
would ideally produce a quantity where MR=MC, or 10-(1/5)Q=2, or Q=40. The
price associated with a cartel quantity of 40 units is P=10-(1/10)*40, or P=6.
c. The rent associated with the cartel is the product of the marginal profit per unit
and the number of units produced. The marginal profit per unit of milk is $4 (=$6
price - $2 marginal cost), while 40 units are produced. Thus, the rents equal $160.
d. The most the cartel would be willing to contribute to politicians is the full
economic rent of $160. The cartel situation, the quantity of milk produced is too
low from society’s point of view. The deadweight loss triangle is computed using
the difference between the cartel output and competitive output as the “base” of
the triangle, and the difference between the cartel price and competitive price as
the “height.” Thus, the triangle is equal to (1/2)*(80-40)*($6-$2)=$40.
e. As Figure 6.5 in the textbook shows, the deadweight loss could now go as high as
the sum of the conventional deadweight loss and the rents, or $160 rents + $80
DWL = $240. This is because, as noted in the text, “rent-seeking can use up
resources – lobbyists spend their time influencing legislators, consultants testify
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Chapter 6 – Political Economy
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.”
9. This is an example of possible rent-seeking. If Philip Morris supports limited cigarette
advertising, it is unlikely that there will be new entrants in the cigarette market because
establishing business would be more difficult with reduced advertising. Philip Morris
will maintain or develop market power.
10.
a. The outcome of the first election (M vs. H) is M. The outcome of the second
election (H vs. L) is L. The outcome of the third election (L vs. M) is M.
Majority rule leads to a stable outcome since M defeats both H and L. Giving one
person the ability to set the agenda would not affect the outcome in this case.
b. With the change in Eleanor’s preference ordering, majority rule no longer
generates a stable outcome. In a vote between M and H, the outcome is H. In a
vote between H and L, the outcome is L. In a vote between L and M, the outcome
is M. So, giving one person the ability to set the agenda affects the outcome. For
example, Abigail prefers H, so she might pit L against M first in order to
eliminate L and avoid having L defeat H.
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Part 2 – Public Expenditure: Public Goods and Externalities
Chapter 7 – Education
Brief Outline
1. Justifying Government Intervention in Education
a. Is Education a Public Good?
b. Does Education Generate Positive Externalities?
c. Is the Education Market Inequitable?
2. What Can Government Intervention in Education Accomplish?
a. Does Government intervention Crowd Out Private Education?
b. Does Government Spending Improve Educational Outcomes?
c. Public Spending and the Quality of Education
d. Does Education Increase Earnings?
3. New Directions for Public Education
a. Charter Schools
b. Vouchers
c. School Accountability
Answers to End-of-Chapter Questions
1. There are numerous rationales given for government provision of education. Even
though education is primarily a private good, many argue that educating a child provides
external benefits. However, the existence of a positive externality implies that
government should subsidize education rather than making it free and mandatory. Other
rationales are based on equity, including a belief in commodity egalitarianism. The
rationales do imply a lower level of provision of higher education versus primary and
secondary. Higher education has higher private benefits and fewer externalities,
therefore requires a lower level of provision.
2. It may be that national income is increased purely though private returns to education
summed up across the economy. If this is the case, one could not use an externality-based
argument to justify subsidization. However, if education quality increases the growth rate
of national income outside of the returns that accrue to individuals who consume the
education, then private decisions will yield a lower than efficient level of education
quality. This reasoning would allow for government subsidization that would improve the
quality of education.
3. If students are required to pay “a lifelong tithe on all earnings” there might be a distortion
in choices of careers among students. Under the tithe system, some students would
choose a lower paid (and less productive) career path, compared to the situation in which
they faced a standard bank loan. The tithe system would create inefficiencies by partially
removing incentives for students to pursue the highest-paying jobs.
4. If households are allowed to supplement public education with private lessons, then the
budget constraint in Figure 7.1 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.
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Chapter 7 – Education
Parents can supplement public
education with private lessons
Other Goods
A
B
A
ep
Education
If parents pay for the public schooling (rather than perceiving it as being free), and the
schooling was paid for with a lump sum tax, then the budget constraint shifts in by an
amount that depends on the household’s share of the tax burden. If the household’s tax
burden exactly equals the cost of public school, the budget constraint is no longer the line
segment AB but rather the segment CDB, where the segment DB runs along the original
budget constraint, except that the minimum amount of schooling consumed is e P .
Other Goods
A
C
Public School is financed by taxes levied
on parents
D
BA
ep
Education
5. Making wealthy students pay more tuition only increases efficiency if it is reasonable to
assume that wealthy students will be paid more than less wealthy students at the end of
the education. If there are few externalities, then the demand for education should come
from the private benefits of the education, which is the present value of future earnings.
If wealthy students are paid better after college, their demand would be higher and they
would be willing to pay more for the education. In terms of equity, this policy seems to
be fair in that it gives less wealthy students a better chance at an education.
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Part 2 – Public Expenditure: Public Goods and Externalities
6.
a. If income is $50,000 per year, the budget constraint is a straight line, as shown
below.
Other Goods
$50,000
$50,000
Education
b. With $8,000 worth of free public education, the family can consumer up to $8,000
worth of education without reducing the consumption of other goods.
Other Goods
$50,000
$8,000
$50,000
7-3
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Chapter 7 – Education
c. The family maximized utility at point A before the introduction of free public
education, and maximizes utility at point B after free public education is
introduced, so the optimal consumption of education fell.
Other Goods
$50,000
.
B
.
A
$8,000
$50,000
Education
d. With an $8,000 education voucher, the family can spend some of its income on
education to purchase more education if it desires. If the optimal point moves
from A to B, as shown in the graph below, then the introduction of vouchers
causes the family to purchase more education.
Other Goods
$50,000
.
B
.
A
$8,000
$50,000
7-4
$58,000
Education
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Part 2 – Public Expenditure: Public Goods and Externalities
7.
a. The results might be biased because the teachers with master’s degrees may have
abilities or interests that encourage them to get an advanced degree and also make
them better teachers. If this is the case, when other teachers got higher degrees
just because they were required to do so, they likely would not show the
improvement in test scores. The student characteristics are also not being taken
into account.
b. This experiment doesn’t address the concern raised in part a because the Master’s
degrees were not “randomly assigned” to teachers. In other words, the same bias
in the estimates persists because the teachers with Master’s degrees may still have
abilities that both caused them to pursue advanced degrees and caused them to be
better teachers. Randomizing students does not solve this problem.
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Part 2 – Public Expenditure: Public Goods and Externalities
Chapter 8 – Cost-Benefit Analysis
Brief Outline
1. Present Value
a. Projecting Present Dollars into the Future
b. Projecting Future Dollars into the Present
c. Inflation
2. Private Sector Project Evaluation
a. Internal Rate of Return
b. Benefit-Cost Ratio
3. Discount Rate for Government Projects
a. Rates Based on Returns in the Private Sector
b. Social Discount Rate
c. Discounting and the Economics of Climate Change
d. Government Discounting in Practice
4. Valuing Public Benefits and Costs
a. Market Prices
b. Adjusted Market Prices
c. Consumer Surplus
d. Inferences from Economic Behavior
e. Valuing Intangibles
5. Games Cost-Benefit Analysts Play
a. The Chain-Reaction Game
b. The Labor Game
c. The Double-Counting Game
6. Distributional Considerations
7. Uncertainty
8. An Application: Are Reductions in Class Size Worth It?
a. Discount Rate
b. Costs
c. Benefits
d. The Bottom Line and Evaluation
9. Use (and Nonuse) by Government
Answers to End-of-Chapter Questions
1. Yes, one really must ask these questions, although it may seem distasteful. Otherwise,
there is no way to determine which safety precautions are sensible.
2. The decreased time spent at the inspection must be counted as a benefit of the program.
One reasonable way to estimate the value of the time would be to use the average wage
rate in the state, and multiply this by the decreased waiting time of 54 minutes.
3. The present value of $25/.10 = $250.
The present value of the perpetual annual benefit = B + B/(1 + r) + B/(1 + r)2 + … = B (r
+ 1 - r)/r = B/r.
8-1
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Chapter 8 – Cost-Benefit Analysis
4.
a. The internal rate of return is the discount rate that would make the project’s net
present value (NPV) equal zero. To solve for the internal rate of return, ρ, set the
present value of benefits minus the present value of costs equal to zero. If we
assume the benefit of using the bicycle is immediate (and worth $170), there is
also the benefit of re-selling the bicycle for $350, but it can’t be re-sold until next
year, so must be discounted. Therefore, NPV is 170 + [350/(1+ρ)] – 500 = 0.
Solving this expression for ρ yields ρ = 6 percent. If we assume that the benefits
of the vacation will not be enjoyed for one year, then NPV is [(170+350)/(1+ρ)] –
500 and setting this expression equal to zero and solving for ρ yields ρ = 4
percent.
b. If the discount rate is 5 percent, purchasing the bicycle is a good idea if ρ is 6
percent, but a bad idea if ρ is 4 percent.
5.
a. Bill is willing to pay 25 cents to save 5 minutes, so he values time at 5 cents per
minute. The subway saves him 10 minutes per trip, or 50 cents. The value of 10
trips per year is $5. The cost of each trip is 40 cents, or $4 per year. The annual
net benefit to Bill is therefore $1. The present value of the benefits = $5/.25 =
$20; the present value of the costs is $4/.25 = $16.
b. Total benefits = $20x55,000=$1,100,000.
Total costs = $16x55,000 = $880,000.
Net benefits = $220,000.
c. Costs = $1.25 x 55,000 = $68,750.
Benefits =($62,500/1.25) + ($62,500/1.252) = $90,000.
Net benefit = $21,250.
d. The subway project has a higher present value. If a dollar to the “poor” is valued
the same as a dollar to the “middle class,” choose the subway project.
e. Let λ = distributional weight. set
220,000 = -68,750 + λ[(62,500/1.25) + (62,500/1.252)]
λ = 3.21
This distribution weight means that $1 of income to a poor person must be viewed
as more important than $3.21 to the middle class for the legal services to be done.
6. $100 billion invested for 100 years at 5 percent per year would generate over $13 trillion,
a little more than twice the $700 billion in damage caused by the climate change. There
might be other considerations offered when evaluating this proposal, but the critic is
correct from a financial standpoint.
7. Considering the money that has already been spent on the space station is considering
sunk costs that are not in the present value of operating the space station. To determine
whether the space station should continue to operate, one must consider the present value
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Part 2 – Public Expenditure: Public Goods and Externalities
of the future costs of operating versus the present value of the future benefits of operating.
If the PV of benefits is greater than the PV of costs, the station should remain online.
8. The “labor game” suggests that jobs and the wages paid to people in those jobs are
considered by some to be one benefit of a public project. In fact, the wages are a cost and
this cost can only be partially offset if the people were truly unemployed before the
project. The “green” jobs plays the “chain-reaction” game, because they are secondary
profits.
9. Viscusi (2006) finds the value of a life between $4 and $10 million. Therefore, the
passive restraints in vehicles passes cost benefit analysis, but the asbestos removal does
not. This implies that resources could be shifted from asbestos removal to vehicle
restraints to reduce costs or save lives.
8-3
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Chapter 9 – The Health Care Market
Brief Outline
1. What’s Special about Health Care?
a. The Role of Insurance
b. The Role of Risk Pooling
c. Adverse Selection in the Health Insurance Market
d. Insurance and Moral Hazard
e. Other Information Problems in the Health Care Market
f. Externalities of Health Care
2. Do We Want Efficient Provision of Health Care?
a. Paternalism
b. The Problem of the Uninsured
c. High Health Care Costs
Answers to End-of-Chapter Questions
1.
a. Concern with health care costs does not mean that health care is not “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.
b. It makes a lot of difference how money is spent. One can create employment by
hiring people to dig ditches and then fill them up, but this produces nothing useful
in the way of goods and services. Thus, employment in the health care sector is
not desirable in itself. It is desirable to the extent that it is associated with the
production of an efficient quantity of health care services.
2. Those employees who leave a job and choose to maintain the health insurance even in the
presence of the high premiums are likely individuals who need health insurance because
of poor health. This adverse selection violates risk pooling by eliminating low risk
people from the insurance, leading to losses by the insurance companies.
3. This situation can be explained by the concept of moral hazard. The traffic lights created
dangerous behavior, like speeding up to make it through a light, which made accidents
more likely. Removing the lights forced drivers to be more cautious at intersections to
avoid accidents.
4. If the elasticity of demand for medical care is -2.3, a 20 percent coinsurance should
decrease the demand for care by 46 percent. This should increase efficiency, because a
zero price leads to overuse – use of care where the benefit of the care is less than the cost
to provide the care.
5. The Tennessee plan is not consistent with the theory of efficient insurance. Efficient
insurance requires that patients pay high out of pocket payments for health care with low
expenditures and low out of pocket payments for health care with high expenditures. Here,
patients seem to pay nothing in out of pocket costs for relatively low levels of expenditure
(<$25,000), and high expenditure care is not covered.
9-1
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Chapter 9 – The Health Care Market
6.
a. P=100-25Q=$50, so Q=2 visits per year. Total cost is ($50)(2) = $100.
b. With 50 percent coinsurance, the individual pays $25 per visit and the quantity
demanded is 3 visits per year. The individual’s out-of-pocket costs are $75 and
the insurance company pays $75 ($25 per visit, 3 visits per year).
c. The introduction of insurance caused the quantity demanded to increase from 2 to
3 because the individual’s effective price fell from $50 to $25, but the marginal
cost is still $50 per visit. The individual consumes medical services past the point
where the marginal benefit to the individual equals the marginal cost, leading to
inefficiency or deadweight loss. The marginal cost of the third visit is $50, but the
marginal benefit is $25, so the deadweight loss is equal to this difference, or $25.
If the method presented in Figure 9.4 is applied, the deadweight triangle will
have an area equal to $12.50.
d. If the marginal benefit of visiting the doctor is $50, there is no deadweight loss
because marginal benefit equals marginal cost.
7.
a. There is a 95 percent chance of no illness, in which case income is $30,000, and a
5 percent chance of illness, in which case income is $10,000 because of the
$20,000 loss. Thus, expected income is (0.95)(30,000) + (0.05)(10,000) = 29,000.
The utility of having income of $29,000 with certainty is 11.66, but the expected
utility is only (0.95)U(30,000) + (0.05)U(10,000) = (0.95)(11.695) +
(0.05)(10.597) = 11.64.
b. An actuarially fair premium would be $1,000 since there is a one in twenty chance
that the insurance company will have to cover losses of $20,000. If the individual
buys insurance for $1,000, then they have certain income of $29,000 and the
utility of $29,000 is 11.66.
c. Setting the expected utility equal to 11.64 and solving for income yields
approximately $28,388, indicating that the individual is indifferent between
bearing the risk and having expected income of $29,000 or purchasing insurance
with a certain income of $28,388. If the insurance costs $30,000 - $28,388 =
$1,612, the individual is indifferent between having insurance and not having
insurance, so $1,612 is the most they’d be willing to pay (allow some difference
for rounding).
8. If the probability of being caught is 0.2 and the fine is $100, the expected cost is $20. If
the probability of being caught is 0.1 and the fine is $200, the expected cost is again $20.
With the first option, the expected value of littering is 0.8(B) + 0.2(B - $100), whereas the
expected value of littering with the second option is 0.9(B) + 0.1(B - $200), where B is
the benefit of littering. The expected utility of the first option is 0.8U(B) + 0.2U(B $100), and the expected utility for the second option is 0.9U(B) + 0.1U(B - $200). Since
expected utility is higher for the first option, assuming diminishing marginal utility, the
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
second option would have a stronger deterrent effect and lead to a larger reduction in
littering. In addition, setting higher fines is cheaper than employing more police officers.
If litterers are risk lovers, then the reverse is true. Expected utility is higher for the
second outcome, so employing more police officers would have a stronger deterrent
effect.
9. Several of the reasons why health care spending for individuals is growing are also
reasons why spending on health care for pets is growing at the same rate. There is
increased technology and the owners have increased incomes.
9-3
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Chapter 10 – Government and the Market for Health Care
Brief Outline
1. Private Health Insurance
a. The Implicit Subsidy for Employer-Provided Insurance
b. The Advantages of Employer-Provided Health Insurance
c. Employer Provided Health Insurance and Job Lock
d. Cost Control and Private Insurance
2. Government Provision of Health Insurance: Medicare and Medicaid
a. Medicare: Overview
b. Cost Control under Medicare
c. Medicare: Impacts on Spending and Health
d. Medicaid: Overview
e. Medicaid: Impacts on Health
3. Affordable Care Act of 2010
a. Alternative Paths to Health Care Reform
b. Single Payer Approach
c. Market-Oriented Approach
d. Final Thoughts
Answers to End-of-Chapter Questions
1. One explanation discussed in the chapter is that the shift toward managed care led to a
one-time decrease in expenditures, but advances in medical technology continued,
resulting in concomitant growth in expenditures. This explanation implies that HMOs
helped prevent rising health care costs during the 1990s, but have been unable to keep
costs low due to rapid advances in technology. The structure of HMOs creates incentives
for health care providers to skimp on the quality of care. HMOs used “gag rules” that
prohibited physicians from discussing treatment options that were not covered by the plan,
but government regulation has since banned these gag rules, allowing patients greater
access to information. Medical technology creates new, and often more expensive,
treatment options, which many patients believe they should have. It has become
increasingly difficult for HMOs to keep costs down by denying more expensive treatment
options, especially since they can no longer prevent physicians from informing patients
of these options.
2. Increasing the price of medical care should improve the efficiency of health care slightly.
Once people begin to pay for the care they receive, they will reduce their use of care,
increasing efficiency. The cost to the consumer will come closer, by a small amount, to
the actual cost of the care, making their decisions more efficient.
3. Medicare covers nearly the entire population aged 65 and older and is not means tested.
About 99 percent of the eligible population chooses to enroll in supplementary medical
insurance (SMI), or Part B of Medicare, which pays for physicians and services rendered
outside the hospital. Patients pay a monthly premium, a small annual deductible, and a
20 percent coinsurance rate. Because out of pocket costs are low for a doctor visit, the
10-1
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Chapter 10 – Government and the Market for Health Care
service is over-utilized. The Medicare program has not improved the health status of the
elderly very much, but is has led to significant benefits in the form of reducing the risk of
facing major reductions in consumption due to medical expenses.
4. Allowing individuals to join the Medicare prescription drug benefit plan at any time
would like lead to an adverse selection problem. As individuals age and their health
deteriorates, the likelihood that they will need expensive prescription drugs increases. If
individuals wait until several years after becoming eligible for Medicare to add the
prescription drug benefit plan, they pay less in premiums, which adds to the already
enormous expense of the Medicare drug benefit. Requiring individuals to stick with their
decisions will improve the risk pool for two reasons. First, if a person chooses to
purchase the plan even though they do not use it early on, they will help to pay for those
who use the plan frequently. Second, if a person opts out of the program, they will not be
able to enter the risk pool when they are using prescriptions frequently, thereby avoiding
paying when they don’t use the plan.
5. 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.
Medigap choice without minimum
standards
Other Goods
30,000
25,000
U0
5,000
30,000
Medigap
efficiency units
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
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
point (0, 30000) is available, as well as all of the points to the southeast of the point
(8000, 22000). Clearly, the person’s utility must fall since the preferred choice, (5000,
25000) is no longer available. If the person attains a higher level of utility as (0, 30000)
compared with (8000, 22000), the person chooses to not purchase Medigap. In this case,
the marginal rate of substitution is no longer equal to the price ratio. This is illustrated
below.
Medigap choice with minimum standards;
no Medigap is purchased
Other Goods
30,000
25,000
U0
U1
22,000
5,000
8,000
30,000
10-3
Medigap
efficiency units
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Education.
Chapter 10 – Government and the Market for Health Care
6. If individuals are allowed to purchase supplemental private insurance, then the budget
constraint in Figure 10.5 of the textbook is modified by drawing a line starting at point B
that runs to the southeast and is parallel to AC.
Individuals can purchase supplemental
private insurance
Other Goods
A
B
C
M
Health Insurance
If individuals pay for health insurance (rather than perceiving it as being free), and the
insurance 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 health insurance, the budget constraint is no longer the
line segment AD but rather the segment BCD, where the segment CD runs along the
original budget constraint, except that the minimum amount of health insurance
consumed is M.
10-4
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Other Goods
Government health insurance is financed by taxes
A
B
C
D
M
Health Insurance
7. Below is a set of indifference curves that represent a situation in which the introduction
of a government plan reduces the purchase of health insurance. F is the possible
combination of other goods and C is the choice of health insurance in the absence of the
government option.
Other Goods
F
G
HIG
HIS
Health Insurance
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Chapter 11 – Social Security
Brief Outline
1. Why Have Social Security?
a. Consumption Smoothing and the Annuity Market
b. Adverse Selection and the Annuity Market
c. Other Justifications
2. Structure of Social Security
a. Basic Components
b. Distributional Issues
c. The Trust Fund
3. Effect of Social Security on Economic Behavior
a. Saving Behavior
b. Retirement Decisions
c. Implications
4. Long-term Stresses on Social Security
5. Social Security Reform
a. Maintain the Current System
b. Privatize the System
6. Conclusions
Answers
1. With adverse selection, insurance contracts with more comprehensive coverage are
chosen by people with higher unobserved accident probabilities. To make up for the fact
that a benefit is more likely to be paid to such individuals, the insurer charges a higher
premium per unit of insurance coverage.
2. Individuals who do not save enough for their retirement years may believe that the
government will feel obliged to come to their aid if they are in a sufficiently desperate
situation. With this belief, younger individuals may purposely neglect to save adequately.
One justification for the compulsory nature of Social Security is to address the
inefficiently low saving caused by moral hazard.
3. Use the basic formula for balance in a pay-as-you-go social security system:
t =(N b /N w )*(B/w).
Call 1990 year 1 and 2050 year 2. Then
t 1 = .267*(B/w) 1
t 2 = .458*(B/w) 2
It follows that to keep (B/w) 1 =(B/w) 2 we require t 2 /t 1 =.458/.267=1.71. That is, tax rates
would have to increase by 71 percent. Similarly, to keep the initial tax rate constant, we
would require (B/w) 2 /(B/w) 1 =.267/.458=0.58. Benefits would have to fall almost by half.
11-1
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Chapter 11 – Social Security
4. The sharp increase in the number of elderly men who marry young women affects the
solvency of the Brazilian system because, after the earner dies, the non-earning spouse
can continue to receive pension benefits. The young women collect for many more years
than an older non-earning spouses, resulting in higher-than-expected payouts.
5. Austen’s quote seems like it could relate adverse selection, but perhaps more likely, to
moral hazard. The quote “If you observe, people always live forever when there is any
annuity to be paid them” in a sense sounds like they act differently (e.g., better diet, more
exercise, etc.) when an annuity is to be paid – the idea of moral hazard. In contrast,
adverse selection suggests that people who expect to live a long time to be the ones who
purchase annuities. A recent paper by Finkelstein and Poterba (NBER working paper,
December 2000) found that “mortality patterns are consistent with models of asymmetric
information” and that annuity “insurance markets may be characterized by adverse
selection.”
6. Equation (11.1) relates taxes paid into the Social Security system to the dependency ratio
and the replacement ratio, that is, t=(N b / N w )*(B/w). If the goal of public policy is to
maintain a constant level of benefits, B, rather than a constant replacement ratio, (B/w),
then taxes may not need to be raised. If there is wage growth (through productivity), then
it is possible to maintain B at a constant level, even if the dependency ratio is growing.
By rearranging the equation, we can see that B=t*w*(N b / N w )-1. That is, increases in
wage rates (the second term) offset increases in the dependency ratio (the third term).
Thus, constant benefits do not necessarily imply higher tax rates.
7. The statement about how the different rates of return in the stock market and government
bond market affect the solvency of the trust fund is false. If the trust fund buys stocks,
someone else has to buy the government bonds that it was holding. So, there is no new
saving and no new capacity to take care of future retirees.
8.
a. The problem does not provide information about the utility function, so the
optimal point is where the indifference curve is drawn tangent to the budget line,
which can occur at different values depending on how the curve is drawn. In the
diagram below, the optimal point involves saving $8,000 and future consumption
consists of period 2 income ($5,000) plus savings with interest ($8,800).
11-2
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Future
Consumption
$27,000
$13,800
.
Optimal Point
Endowment
Point
.
$5,000
$12,000
$20,000
$25,545
Present
Consumption
b. If Social Security takes $3,000 from the individual in the first period and pays
him this amount with interest in the second period, then private savings falls from
$8,000 to $5,000. There would be no change in optimal consumption values.
9. If the implicit rate of return from Social Security is lower than the private return, the
endowment point shifts from A to B as present consumption falls from $20,000 to
$17,000 when $3,000 is taken for social security. The arrow connecting the old
endowment point A to the new endowment B is flatter than the budget line, reflecting the
lower rate of return on Social Security compared to private saving. For savings beyond
the $3,000 taken for Social Security, the private rate of return is available, so the new
budget line is parallel to the original line. This would cause the optimal point to change
and put the individual on a lower indifference curve. In the graph below, the effect is to
increase private saving slightly.
11-3
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Chapter 11 – Social Security
$27,000
$13,800
..
First Optimal
Point
New Optimal
Point
B
.
A
$5,000
$12,000 $17,000 $20,000
Endowment
Point
$25,545
Present
Consumption
10. Moving the financing of Social Security from a pay-roll tax financing to income-tax
financing makes sense from the perspective of the fact that the system is pay-as-you-go.
The payroll-tax system implies that workers are “saving” for their retirement through the
payroll tax. But, this is not accurate. This financing would also broaden the base for the
tax to be paid on. The change may be politically difficult, because benefits are calculated
based on earned income, while income taxes can be based on more than earned income.
11. If the expected present value of the benefit reduction just equals the decrease in taxes,
then the solvency of the system is unaffected. The pay-as-you-go formula shows that the
system is solvent if taxes collected equal benefits paid, or twN w = BN b . Dividing both
sides by the number of covered workers yields tw = B(N b /N w ). If a worker diverts
$1,000 from payroll taxes to a private account, then the left-hand side of this expression
falls by $1,000. To maintain solvency, the right-hand side must also fall by $1,000, so
benefits must fall by 1,000 times the ratio N w /N b . If, for example, there are three
covered workers for every retired worker, so that N w /N b is equal to 3, then the necessary
reduction in the expected value of benefits is $3,000. If a worker invests $1,000 for 40
years at about 3 percent
per year, that worker will have enough in his private
account to compensate for the lost benefits. If the offset rate is lower than the rate of
return workers can earn on private accounts, workers will gain, and vice versa.
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Chapter 12 – Income Redistribution: Conceptual Issues
Brief Outline
1. Distribution of Income
a. Interpreting the Distributional Data
2. Rationales for Income Redistribution
a. Simple Utilitarianism
b. The Maximin Criterion
c. Pareto Efficient Income Redistribution
d. Nonindividualistic Views
e. Other Considerations
3. Expenditure Incidence
a. Relative Price Effects
b. Public Goods
c. Valuing In-Kind Transfers
d. Reasons for In-Kind Transfers
4. Conclusion
Suggested Answers to End-of-Chapter Questions
1. Utilitarianism suggests that social welfare is a function of individuals’ utilities. Whether
the rich are vulgar is irrelevant, so this part of the statement is inconsistent with
utilitarianism. On the other hand, Stein’s assertion that inequality per se is unimportant is
consistent with utilitarianism.
2.
a. To maximize W, set marginal utilities equal; the constraint is I s + I c = 100. So,
400 - 2I s = 400 - 6I c , substituting I c = 100 - I s gives us 2I s = 6 (100 – Is).
Therefore, I s = 75, I c = 25.
b. If only Charity matters, then give money to Charity until MU c = 0 (unless all the
money in the economy is exhausted first). So,400-6 I c = 0; hence, I c = 66.67.
Giving any more money to Charity causes her marginal utility to become negative,
which is not optimal. Note that we don’t care if the remaining money ($33.33) is
given to Simon or not.
If only Simon matters, then, proceeding as above, MU s. 0 if I s = 100; hence,
giving all the money to Simon is optimal. (In fact, we would like to give him up
to $200.)
c. MU s = MU c for all levels of income. Hence, society is indifferent among all
distributions of income.
3. Suppose the government is initially providing an in-kind benefit of 10 units of free public
transportation, worth $2 each, so the cost of the subsidy is $20. Without the subsidy,
income is $40. With no subsidy, the consumer maximizes utility at point A, and with an
in-kind benefit of 10 units of free public transportation, the consumer maximizes utility at
point B. A cash subsidy equal to $20 would allow the consumer to reach point B as well,
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Chapter 12 – Income Redistribution: Conceptual Issues
so the government could convert an in-kind subsidy valued at $20 to a cash subsidy of
$20 and leave people equally well off.
Other goods
B
A
10
30
20
Public Transportation
Another possibility is that the utility-maximizing point for a cash subsidy differs from the
utility-maximizing point for an in-kind subsidy, as illustrated in the next graph.
In this case, an in-kind subsidy, costing $20, would allow the consumer to move from
point A’ to point C’, while a cash subsidy of $20 would make the consumer better off at
point B’. In order to make the consumer equally well off, the cash subsidy should be a
little less than $20.
Other goods
B’
C’
A’
10
20
30
Public Transportation
4. If the poverty measure was fixed at the level of the supplemental poverty measure and if
the actual level of consumption of food, clothing, shelter, and utilities doubled because
prices doubled, the new poverty measure will drastically understate the level of poverty
12-2
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Education.
Part 3 – Public Expenditure: Social Insurance and Income Maintenance
in America. The families in poverty as determined by the new measure before the
income and price changes would still be in poverty after, but the fixed level of the
measure would not have changed.
5. The influx of low-income immigrants would increase the percent of income held by the
upper fifth of income earners and decrease those in the lower fifths (the distribution
would be skewed downward). The influx would also increase the percent of the
population whose incomes fall below the poverty line.
6. According to the maximin criterion, social welfare depends on the utility of the individual
who has the minimum utility in the society. A peculiar implication of this criterion, as
noted by Feldstein, is that if society has the opportunity to raise the welfare of the least
advantaged by a slight amount, but make almost everyone else substantially worse off
except for a few individuals who would become extremely wealthy, then society should
pursue this opportunity. Transferring large sums of income from the middle class to both
the poor and the rich would achieve this end, and so would be supported by someone
with the maximin social welfare function.
7.
a. False. Society is indifferent between a util to each individual, not a dollar to each
individual. Imagine that U L =I and U J =2I. Then each dollar given to Jonathan
raises welfare more than the same dollar given to Lynne.
b. True. The social welfare function assumes a cardinal interpretation of utility so
that comparisons across people are valid.
c. False. Departures from complete equality raise social welfare to the extent that
they raise the welfare of the person with the minimum level of utility. For
example, with the utility functions U L =I and U J =2I, the social welfare function
W=min[U L ,U J ] would allocate twice as much income to Lynne than Jonathan.
12-3
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Education.
Chapter 12 – Income Redistribution: Conceptual Issues
8. Initially the price of food was $2 and the price of other goods was $1. The black market
for food stamps changes the price of food sold to $1. In Figure 12.3 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. See
graph below.
Black market where food stamps are sold
for fifty cents on the dollar, no better off
Other Goods
Sell food stamps for other
goods on black market
A
F
U0
D
Food
Stamp
Allotment
Food
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.
12-4
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
FIGURE 7.7b – Black market where food
stamps are sold for fifty cents on the dollar,
higher utility
Other Goods
Sell food stamps for other
goods on black market
A
F
U1
U0
D
Food Stamp
Guarantee
Food
9. 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
U S =100Y S 1/2, her utility with $100 of income is U S =100($100)1/2, or U S =1,000. With
Marsha’s initial utility function of U M =100Y M 1/2+0.8U S , her utility with $100 of income
is U M =100($100)1/2+0.8(1,000), or U M =1,800. If the social welfare function is additive,
then initial welfare is W=U S +U M =1,000+1,800=2,800. If $36 is reallocated from
Marsha to Sherry, then Sherry’s income is now $136 and Marsha’s is now $64. With
Sherry’s utility function, her utility with $136 of income is U S =100($136)1/2, or
U S =1,166.190. With Marsha’s utility function, her utility with $64 of income is
U M =100($64)1/2+0.8(1,166.190), or U M =800+932.952=1,732.952. In this case, Sherry’s
utility increases from 1,000 to 1,166.190, while Marsha’s utility falls from 1,800 to
1,732.952. Social welfare increases with this redistribution, going from 2,800 to
2,899.142. Thus, this redistribution increases social welfare, but is not Pareto efficient
redistribution.
12-5
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
Chapter 13 – Expenditure Programs for the Poor
Brief Outline
1. A Quick Look at Welfare Spending
2. TANF
3. Income Maintenance and Work Incentives
a. The Basic Trade-Offs
b. Analysis of Work Incentives
c. Work Requirements
d. Time Limits
e. Family Structure
f. National versus State Administration
4. The Earned income Tax Credit
5. Supplemental Security Income
6. Medicaid
7. Unemployment Insurance
a. Benefits
b. Financing
c. Effects on Unemployment
8. Supplemental Nutrition Assistance Program (SNAP)
9. Housing Assistance
10. Programs to Enhance Earnings
a. Education
b. Employment and Job Training
11. Overview
Suggested Answers to End of Chapter Questions
1.
a. 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.
13-1
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Chapter 13 – Expenditure Programs for the Poor
c.
645
22.5
d. See graph above. The diagram shows one possibility – in this case, Elizabeth is
both working and on welfare – but she collects a reduced welfare benefit in this
case.
2. This method would not provide accurate results because it does not adequately control for
the reason why children with similar economic and demographic characteristics did not
choose to participate, thereby including selectivity bias. One might choose instead to
compare areas that implemented head start with areas that did not and complete a
difference-in-difference method or randomize which Head Start applicants were admitted
to the program, comparing the admitted children to those who applied but were denied.
3. This proposal would not clearly increase the incentive to work because the basic income
grant would have to be phased out as income increased. The phaseout would be an
implicit tax on the income earned from working, reducing the incentive for the work.
13-2
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
4. He participates in the public housing program as long as P 1 P 2 ca>cef, where P 1 P 2 ca is
the consumer surplus Philip receives by his optimal square feet at P 2 and cef is the lost
consumer surplus by paying a price higher than desired for H 2 .
5. As illustrated below, the budget constraint with SNAP benefits has a “notch” in it, similar
to the analysis of Medicaid in Figure 13.9 of the textbook. At the notch, the marginal tax
rate is greater than 100%.
Annual Income
Food Stamp notch
Statutory Food
Stamp Maximum
Maximum
Income
Leisure
13-3
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Chapter 13 – Expenditure Programs for the Poor
6. For an individual who is not working while on welfare, in this case the highest
indifference curve touches the budget constraint on the right vertical axis. Note that the
marginal rate of substitution (MRS) does not necessarily equal the after-tax wage rate at
the time endowment – rather, it is possible that the person would want to consume more
leisure than the time endowment but is obviously constrained from doing so.
Individual is on welfare and does not work
at all
Other Goods
Statutory TANF
benefit
U0
MRS>(1-t)w
Leisure
13-4
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
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. See graph
below.
Demand curve shifts outward, perfectly
inelastic supply
PHOUSING
S
P1
P0
D1
D0
Q0
QHOUSING
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. See graph
below.
13-5
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Education.
Chapter 13 – Expenditure Programs for the Poor
FIGURE 8.7b – Demand curve shifts
outward, perfectly elastic supply
PHOUSING
P0
S
D1
D0
Q0
Q1
QHOUSING
c. If there is an increase in both the price and quantity of housing, then the supply
curve slopes upward. See graph below.
FIGURE 8.7c – Demand curve shifts outward,
upward sloping supply curve
PHOUSING
S
P1
P0
D1
D0
Q0
Q1
QHOUSING
13-6
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Education.
Part 3 – Public Expenditure: Social Insurance and Income Maintenance
According to Sinai and Waldfogel, there is partial crowding out, consistent with case c
above. Although the underlying housing stock itself is probably quite inelastic in the
short-run, the number of rental homes can be more elastic as (potential) landlords convert
vacation homes or vacant homes into rental units.
8.
a. When Eleanor’s hours (earnings) go from 0 to 1,000 ($0 to $8,000), she qualifies
for an additional earned income tax credit (EITC) worth $3,200 (=0.4*8,000).
Thus, her income goes up from $0 to $11,200. The implicit tax rate is -40% (or a
subsidy). Note to instructors – the distinction between earnings and income may
cause confusion in the students’ answers.
b. When Eleanor’s hours (earnings) go from 1,000 to 1,500 ($8,000 to $12,000), she
still does not qualify for the maximum EITC (according to Figure 13.8 in the
textbook). She receives $4,800 ($12,000 x 0.4). The earnings between $0 and
$12,060 face a subsidy, thus her hourly wage faces a subsidy of 40 percent. Her
income goes up from $11,200 to $16,800. The implicit tax rate is -40% (or a
subsidy).
c. When Eleanor’s hours (earnings) go from 1,500 to 2,000 ($12,000 to $16,000),
she moves into the range where the EITC is at its maximum of $4,824 ($12,060 x
0.4). Her income goes up from $16,800 to $20,824. The implicit tax rate is 0%
because her EITC is neither increasing nor decreasing.
9.
a. Since Wang does not have to pay Social Security and Medicare payroll taxes on
unemployment benefits, approximately 55 percent (=(1-.15)(.5)/(1-.2245)) of his
after-tax income is replaced by unemployment insurance. After the legislation,
the replacement rate increases to 64 percent (=.5/(1-.2245)). The existence of UI
may make workers more likely to accept employment in industries where the
probability of future layoffs is great. UI may also induce the unemployed to spend
more time looking for work than they would have otherwise. These moral hazard
problems are likely to be more serious as the after-tax replacement rate rises.
13-7
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Education.
Chapter 13 – Expenditure Programs for the Poor
b. Line AE gives Wang’s budget constraint in the absence of UI. ACDE gives
Wang’s budget constraint when UI is benefits are granted. Extending UI benefits
past the two-week limit has the potential to increase the length of the
unemployment spell by making leisure (or more extensive job search) less costly.
Weekly Income
A
B
IB
C
D
0.55 * IB
Leisure
E
13-8
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Part 3 – Public Expenditure: Social Insurance and Income Maintenance
10. In the graph below, the budget constraint between consumption of $31,389 and
$93,699 is higher than the original budget constraint (in red). The increase in
consumption possibilities at $93,699 will decrease the incentive to work to receive
the 93,700th dollar. However, there may be an incentive for a person who is earning
$31, 388 to work for the additional dollar that would make him or her eligible for the
subsidy (depending on the value of the health benefits provided on incomes less than
those for which the subsidy is paid).
Consumption
$108,489
$93,699
$54,129
$31,389
Leisure
13-9
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Education.
Part 4 – A Framework for Tax Analysis
Chapter 14 – Taxation and Income Distribution
Brief Outline
1. Tax Incidence: General Remarks
a. Only People Can Bear Taxes
b. Both Sources and Uses of Income Should Be Considered
c. Incidence Depends on How Prices are Determined
d. Incidence Depends on the Disposition of Tax Revenues
e. Tax Progressiveness Can Be Measured in Several Ways
2. Partial Equilibrium Models
a. Unit Taxes on Commodities
b. Ad Valorem Taxes
c. Taxes on Factors
d. Commodity Taxation without Competition
e. Profits Taxes
f. Tax Incidence and Capitalization
3. General Equilibrium Models
a. Tax Equivalence Relations
b. The Harberger Model
c. Analysis of Various Taxes
d. Some Qualifications
e. An Applied Incidence Study
4. Conclusions
14-1
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Chapter 14 – Taxation and Income Distribution
Suggested Answers to End of Chapter Questions
1. The market initially is at P 1 Q 1 . Adding a per-customer tax on strip clubs would be a tax
on a commodity. Because the producer would be paying the tax, the effective supply
curve for suppliers would be S 1 . The producers are happy and the market clears only
when P S is paid by the customers for quantity Q 2 . Of this price, P S -P C is the tax paid,
where customers pay P S -P 1 of the tax and the suppliers pay P 1 -P C . The incidence
depends on the relative elasticities of supply and demand. Here, the curves are drawn
such that the consumers and suppliers face roughly the same incidence. However, if one
believed that the supply was relatively more inelastic, then the strip clubs would face a
higher incidence.
S1
Price
S
PS
P1
PC
D
Q2
Q1
Brothel Transactions
2. No, it does not follow that the tax will be progressive. If both lose the same amount of
utility, the rich person will pay more because of diminishing marginal utility of income.
But, a progressive tax requires that a higher proportion of income (the average tax rate)
be taken from the rich person. This tax plan only requires that the absolute amount be
higher, not the proportional amount. For instance, if the marginal utility were decreasing,
but very close to constant, then the rich and poor would pay very close to the same
amount in taxes. This amount would be a much larger share of the poor person’s income.
14-2
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Part 4 – A Framework for Tax Analysis
3. In the competitive case, the full tax is paid by the consumer because the supply curve,
given by MC, is perfectly elastic. With a monopoly, the tax is shared between the
consumer and the producer depending on the elasticity of demand. (If the tax is imposed
on the consumer, the demand curve falls by $u, and the result is the same in both cases).
Perfectly Competitive Market
Price
P+u
MC+u=AC+u
P
MC= AC
D
Q1
Price
Q
Quantity
Monopoly Market
P1
P
P1-u
MC+u=AC+u
MC= AC
D
Quantity
MR
Q1 Q
14-3
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Chapter 14 – Taxation and Income Distribution
4.
a. The assumption is that firs will pay the full tax from its profits rather than passing
some of the cost to consumers.
Profits before tax
b.
Price
Profits after tax
P2
P1=AR1
AR2
MC = AC
AR1
AR2
MR1
MR2
Quantity
c. With the tax, profits for the companies do decline, but the price paid by the
consumer before the tax is P 1 while it is P 2 after the tax, with the difference
between the two the amount of the tax that the consumer pays.
5.
a. Before-tax equilibrium: P = $10 and Q = 300,000
Q D =Q S
500,000-20,000P=30,000P
500,000=50,000P
P=10
Q=30,000*10=300,000
After-tax equilibrium: P = $10.60 and Q = 288,000, producers receive $9.60
500,000-20,000P=30,000(P-1)
530,000=50,000P
P=10.6
Q=30,000*(10.6-1)=288,000
14-4
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Part 4 – A Framework for Tax Analysis
b. Revenue = $288,000. Consumers bear 60 percent of the tax burden and producers
bear 40 percent. So, $172,800 comes from consumers and $115,200 from
producers.
c. With a more elastic demand curve, quantity consumed will decrease even more as
a result of the tax, so the liquor tax will be more effective at reducing
consumption among young drinkers.
6. The equilibrium price can be calculated by setting the quantity supplied equal to the
quantity demanded:
(i)
(ii)
QD = a - bP
QS = c + dP
If QD = QS, then the equilibrium price can be determined as follows:
a − bP = c + dP
a − c = (b + d ) P
a−c
P=
b+d
The equilibrium output can be determined by substituting the equilibrium price into either
the supply or demand equation.
Substituting into the demand equation:
Q = a − bP
 a−c
Q = a − b

b+d 
Substituting into the supply equation:
Q = c + dP
 a−c
Q = c + d

b+d 
If a unit tax of u dollars is imposed on the commodity, then it doesn’t matter which party
it is imposed upon (the consumer or producer); the new equilibrium will be the same in
either case. If the unit tax is imposed upon the consumer, then the price the consumer
pays is u higher than the price received by the supplier. The consumer’s price without
the tax, PC, and price that includes the tax, PCT, are:
PC =
a 1
−  Q
b b
P CT =
14-5
a 1
−  Q + u
b b
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Education.
Chapter 14 – Taxation and Income Distribution
Similarly, the price received by the producer in the absence of the tax, PP, is u lower than
the price received with the imposition of the tax, PPT. These prices are expressed below:
c
1
P P =  Q −
d
d
c
1
P PT =  Q − − u
d
d
The equilibrium that prevails after the imposition of the tax can be found by setting PCT =
PP or PC = PPT -- in the end, both approaches will yield the same answer. First, we can
derive the solution setting PCT = PP:
P CT = P P
c
a 1
1
−  Q + u =  Q −
d
b b
d
a c
1 1
+ + u =  + Q
b d
b d 
da + bc + dbu  b + d 
=
Q
db
 db 
da + bc + dbu
Q=
b+d
Next, setting PC = PPT:
P C = P PT
a 1
c
1
−  Q =  Q − − u
b b
d
d
a c
1 1
+ + u =  + Q
b d
b d 
da + bc + dbu  b + d 
=
Q
db
 db 
da + bc + dbu
Q=
b+d
Therefore, both approaches lead to the same outcome.
7.
a. A part-time worker with annual income of $9,000 pays no taxes since everyone
gets a $10,000 deduction. Her marginal tax rate is 0% and her average tax rate is
0%.
b. A retail salesperson with annual income of $45,000 has taxable income of
$35,000 and pays $1750 in taxes (5 percent of taxable income). As a percentage
14-6
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Education.
Part 4 – A Framework for Tax Analysis
of income, the average tax rate is 3.89% ($1750 is 3.89% of $45,000). Her
marginal tax rate is 5%.
c. An advertising executive with annual income of $600,000 pays $2,500 in taxes
since no tax is levied above $50,000 in taxable income. As a percentage of
income, the average tax rate is 0.42%. Her marginal tax rate is 0%.
The tax is initially progressive, but because of the cap on taxable income, becomes
regressive.
8. The equation T=-4000+.2I is somewhat similar to the exercise in Table 14.1. If we
follow the text and define progressivity with respect to average tax rates rather than
marginal tax rates, then the average tax rate equals 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. The tax system is regressive. Replicating Table 14.1 for
the tax system given here, we get:
Income
$2,000
3,000
5,000
10,000
30,000
Tax Liability
$-3,600
$-3,400
$-3,000
$-2,000
$2,000
Average Tax Rate
-1.80
-1.13
-0.60
-0.20
0.066
Marginal Tax Rate
0.2
0.2
0.2
0.2
0.2
To show that the tax system is progressive if a is negative, write ATR as:
ATR = T/I = (a + TI)/I = a/I + t
Then take the derivative of ATR with respect to I in order to check whether ATR goes up
or down as I increases: d(ATR)/dI = d(a/I + t)/dI = -a/I2. The change in average tax rate is
increasing in income (which implies a progressive tax schedule) as long as a is negative.
9. Current residents of Vancouver will bear the future taxes. If the city increases property
taxes to pay the debt over time, the present value of property owned will decline and
therefore the current price.
10. In the graph below, before the taxes on real estate buyers and sellers imposed, the market
clearing price is P 0 at quantity Q 0 . When the tax is imposed the effective demand curve
becomes D with tax and the effective supply curve is S with tax. The new equilibrium is
P 1 and Q 1 . However, the buyer pays P P while the seller receives P R, with the full tax paid
P P -P R . The amount of the tax paid by the buyer is P P -P 1 . The amount of the tax paid by
the seller is P 1 -P R. It is highly unlikely that the actual percentage paid by both the buyer
and the seller will be equal. The relative amounts paid will depend on the elasticities of
demand and supply. The graph below shows different payments for both the buyer and
seller.
14-7
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Chapter 14 – Taxation and Income Distribution
Price
D without tax
S with tax
S without tax
D with tax
PP
P0
P1
PR
Q1
Q0
Quantity
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Part 4 – A Framework for Tax Analysis
11. This finding implies that the labor supply of European soccer players is highly elastic.
These soccer players will pay little in taxes.
12. The producer would gain the entire reduction in the gas tax (P T -P S ) because the supply
curve is perfectly inelastic, causing the full tax to be paid by the producer. When the tax
is removed, the payment does not have to be made.
D with tax
Price
S
D
PT
PS
Quantity
13. Using equation 14.1, the progressivity of the old tax system is: 0.00111 [=(50/200 –
1/20)/(200-20)], and the progressivity of the new tax system is exactly the same
[=(48/200 – .8/20)/(200-20)].
Using equation 14.2, the progressivity of the old tax system is: 5.44 [=((50-1)/1)/((20020)/20)], and the progressivity of the new tax system is: 6. [=((48-.8)/.8)/((200-20)/20)].
Thus, under this measure of progressivity, the new tax system is more progressive.
14-9
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Part 4 – A Framework for Tax Analysis
Chapter 15 – Taxation and Efficiency
Brief Outline
1. Excess Burden Defined
a. Questions and Answers
2. Excess Burden Measurement with Demand Curves
a. Preexisting Distortions
b. The Excess Burden of a Subsidy
c. The Excess Burden of Income Taxation
3. Differential Taxation of Inputs
4. Does Efficient Taxation Matter
Suggested Answers to End of Chapter Questions
1.
a. The supply of land is fixed, or perfectly inelastic, so there is no excess burden
because the lower price that sellers receive does not cause quantity supplied to fall.
b. The use of cell phones is probably fairly price-elastic, which implies that the
excess burden could be large.
c. It is possible that companies could identify themselves as high-tech in order to
receive the subsidy. Thus, the supply is quite elastic, and there will be substantial
excess burden.
d. Consumers and sellers will likely agree to avoid cups and glasses in order to avoid
the tax. A tax that is easily avoided does not have much of an impact, except to
create some inconvenience, and does not raise revenue.
e. Card companies can easily increase or decrease the number of cards in a pack,
avoiding the tax and reducing the excess burden.
f. There are many good substitutes for blueberries. Therefore, their demand is quite
elastic, and a tax on them will have a substantial excess burden, relative to the
size of revenues collected.
2. Prior to the tax, you and your neighbor are both made better off by the trade. After the
introduction of the tax, the work does not get done even though you would be willing to
accept the wage that your neighbor is willing to pay. This loss of a potentially beneficial
trade that is not compensated by an increase in tax revenue (in fact, no tax is collected) is
exactly the idea of excess burden.
3. Equation 15.3 relates excess burden to elasticity, price, quantity, and the tax rate. Excess
burden is positively related to the (absolute value of) elasticity of the product, the revenue
on the product before the tax is imposed, and the tax rate. If you assume that the
elasticity and the revenues of both Botox and breast implant procedures are the same,
then the tax would impose a larger excess burden on the market for breast implants.
However, it is unlikely that either the elasticity for these procedures or the revenues from
the procedures is the same, making the excess burden from each difficult to determine.
For example, if the elasticities are the same, but the revenue from Botox injections is
higher, then the excess burden from the tax would be higher on Botox injections.
15-1
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Chapter 15 – Taxation and Efficiency
4. The quote is misleading. The way in which the presence of the t-squared makes the tax
more “important” is that when the tax increases, the excess burden increases with its
square. Thus, when the tax doubles, the excess burden quadruples.
5. Using equation 15.4, which says that the excess burden of an income tax is a function of
the compensated elasticity, the wage, and the square of the tax rate, the excess burden of
the tax increase would go up by 7.11 percent.
6. The tax credit might have the effect of increasing the number of children a family has
because it decreases the cost of having kids, creating excess burden. Families are making
decisions based on a distorted price for children, and they might make different decisions
absent the tax credit. The tax credit would make sense only if social policy desired more
children.
7. The cap and trade program would likely cause the cost of producing many consumer
goods to increase. By changing prices in this way, the program may induce an excess
burden. However, if the program succeeds in addressing a significant externality, the
distortion in status-quo prices may actually succeed in bringing consumption closer to the
efficient level. As to the cap and trade revenues, distributing the revenues via a lump sum
transfer would have no impact on excess burden. If one wants to reduce excess burden,
the revenues should be redistributed via reduction in marginal tax rates, for instance, in
the payroll and income taxes.
8. If Nigeria subsidizes gasoline, the price of gasoline goes to (1-s)P G in the graph below.
Rectangle ovur is the subsidy paid by the government, while osur is the increase in
consumer surplus from the subsidy. The excess burden is svu, the amount of the subsidy
that is paid but does not translate into consumer surplus. Because excess burden is
created with a subsidy, the subsidy was wisely removed.
Price
D
PG
(1-s)PG
o
s
v
r
u
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Part 4 – A Framework for Tax Analysis
9. It is likely that the demand for owning at least one television is quite inelastic. It follows
that the excess burden from a $233 per year television tax is small relative to the revenues
that are collected.
10. The horizontal distance OO’ measures the total amount of capital available in society.
Any point along OO’ represents some allocation of capital between the manufacturing
sector and the non-manufacturing sector. Assume that firms allocate capital between the
two sectors to maximize total incomes. It follows that the taxed value of the marginal
product of capital is the same in both sectors. In the graph below, equilibrium occurs
where OK* units of capital are devoted to the non-manufacturing sector and O’K* units
of capital are devoted to the manufacturing sector.
Now assume that the corporate tax is removed in the manufacturing sector, but not in the
non-manufacturing sector. The tax removal increases the rate of return on capital in the
manufacturing sector to VMP MANU and causes an increase in the allocation of capital to
the manufacturing sector to O’K S , along with a decrease in the allocation of capital to the
non-manufacturing sector to OK S . The lost income to the non-manufacturing sector is
aced, while the income gained by the manufacturing sector is abde. The excess burden is
triangle abc, the amount of the tax that comes from lost income in the non-manufacturing
sector.
$
$
a
VMP2
(1-t)VMP1
b
c
(1-t)VMP2
VMPMANU
(1-t)VMPMANU
(1-t)VMPNON-MANU
e
d
O
KS
Capital used in the nonmanufacturing sector
O’
K*
Capital used in the
manufacturing sector
11.
a. The value of the marginal product of capital in the corporate sector is given by
VMP c =100-K c , and the value of the marginal product of capital in the
noncorporate sector is given by VMP n =80-2K n . With 50 units of capital
altogether in society (K c +K n =50), and no taxation, capital should be allocated so
that the values of the marginal products in each sector are equalized. Thus,
setting VMP c =VMP n gives 100-K c =80-2K n and substituting in the constraint of
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Chapter 15 – Taxation and Efficiency
50 units gives 100-50+K n =80-2K n or K n =10. This implies that K c =40. This is
illustrated below.
VMPCORPORATE
100
VMPNONCORPORATE
Allocation of capital to the corporate
and non-corporate sectors
80
VMPN=80-2KN
VMPC=100-KC
KC=40
KN=10
QCORPORATE
QNONCORPORATE
b. If a unit tax of $6 is leveled on capital employed in the corporate sector, the aftertax value of the marginal product in the corporate sector falls. It is now given by
VMP c ’=100-K c -6=94-K c . Now setting VMP c ’=VMP n gives 94-K c =80-2K n and
substituting in the constraint of 50 units gives 94-50+K n =80-2K n or K n =12. This
implies that K c =38. This is illustrated below.
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Part 4 – A Framework for Tax Analysis
VMPCORPORATE
100
VMPNONCORPORATE
FIGURE 13.7b – Reallocation after perunit tax on corporate capital
94
80
Excess burden from
$6 per unit tax
VMPN=80-2KN
VMPC=94-KC
KC=38
KN=12
QCORPORATE
QNONCORPORATE
Thus, ΔK=2 and the tax wedge is t=$6, so the excess burden is ½(2)($6)=$6.
12.
a. Before-tax equilibrium: P = $10 and Q = 300,000
After-tax equilibrium: P = $10.60 and Q = 288,000
Consumers pay $10.60 and producers receive $9.60.
Excess Burden = ½(12,000)($0.60) + ½(12,000)($0.40) = $6,000.
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Chapter 15 – Taxation and Efficiency
P
Tax revenue
S
$10.60
Excess burden
$10
unit tax
$9.60
D0
D1
288,000
300,000
Q
b. If the negative external cost were equal to $1 per gallon, then a $1 tax would
achieve an efficient allocation and would create no excess burden. With a
negative external cost of $0.50 per gallon, there is still an excess burden
associated with a $1 per gallon tax, but it is smaller since the efficient level of
output in this market would be between 288,000 and 300,000.
15-6
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Part 4 – A Framework for Tax Analysis
Chapter 16 – Efficient and Equitable Taxation
Brief Outline
1. Optimal Commodity Taxation
a. The Ramsey Rule
b. Equity Considerations
c. Summary
d. Application: Taxation of the Family
2. Optimal User Fees
a. Overview
3. Optimal Income Taxation
a. Edgeworth’s Model
b. Modern Studies
4. Politics and the Time Inconsistency Problem
5. Other Criteria for Tax Design
a. Horizontal Equity
b. Costs of Running the Tax System
c. Tax Evasion
6. Overview
Suggested Answers to End of Chapter Questions
1. Assuming that all other commodities (except for cable and satellite television) were
untaxed, then optimal tax policy suggests the commodities should be taxed according to
the inverse elasticity rule. Goolsbee and Petrin (2004) find that the elasticity of demand
for basic cable service is -0.51, and the demand for direct broadcast satellites is -7.40.
Applying the inverse elasticity rule would imply that:
(t BASIC /t SATELLITE )=(η SATELLITE /η BASIC )=(7.40/0.51)=14.5
Thus, tax rates on basic cable should be 14.5 times higher than tax rates on satellite
television because basic cable is inelastically demanded, while demand for satellite
television is highly elastic. Among the assumptions that go into the inverse elasticity rule
are that goods are neither complements nor substitutes, and that the elasticities are the
Hicksian compensated elasticities rather than the Marshallian uncompensated elasticities.
In this case, it is likely that the first of these assumptions is false – basic cable and
satellite television are likely substitutes for each other. The Hicksian and Marshallian
demand elasticities are likely to be close to each other because the income effects are
likely to be small for this commodity.
2. Luxury cars have a higher demand elasticity than basic transportation, so this tax would
be less efficient (have a larger excess burden) compared, for example, to a tax on the first
$10,000 of any car purchase. Although the tax schedule is progressive, the incidence is
not clear at all. This is determined by the relative demand and supply elasticities for
expensive cars. Administration of this tax would not be straightforward: One could
imagine methods of evasion such as misrepresenting invoices or selling the car in parts!
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Chapter 16 – Efficient and Equitable Taxation
3. The beard tax was progressive because it was a function of social position, which was
probably a good proxy for income. Because the tax attempted to treat people with the
same income similarly, it satisfied some level of horizontal equity, even though it
penalized those with a preference for facial hair. It’s hard to know about the efficiency
consequences unless one knows more about the price elasticity of demand for the
privilege of having a beard. If the elasticity was small, then it would be an efficient tax.
4. Given the reduced ability to avoid the tax because of the captive tax base, the increased
sales tax appears to be tax efficient, although the tax may result in lower purchases of
non-necessities. The tax might, however, be unfair because individuals with lower
incomes because they tend to spend more of their income resulting in higher taxation.
5. Efficiency generally requires setting price equal to MC, but doing so here would result in
a price lower than the average cost, which would be unsustainable. In this case, the
problem of paying for fixed costs could be solved by charging a price equal to MC and
levying a lump sum tax to pay for the fixed costs associated with the pipes.
6. If the tax increases, the model implies that the number of smuggled cigarettes will
increase because the marginal benefit of doing so (tax avoided) has increased.
$
MC = p*MP
t2
t1
C1
C2
Smuggled cigarettes
7. The problem with a one-time tax on profits is that the government has an incentive to
renege on its promise. The time inconsistency of optimal policy occurs when the
government cannot implement an optimal tax policy because the stated policy is
inconsistent with the government’s incentives over time. Since pharmaceutical
companies know that government has an incentive to impose a tax on profits more than
once, their behavior will be affected by the tax, creating an excess burden.
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Part 4 – A Framework for Tax Analysis
8.
a. It is true that a proportional tax on all commodities (including leisure) is
equivalent to a lump sum tax. To illustrate, consider the simplest example where
there are only two goods: consumption goods and leisure. The budget constraint
is equal to: p C C+wL=I, where p C and w are the prices of consumption goods and
leisure, C and L are the quantities of consumption and leisure, and I is income.
Then a proportional tax on all goods changes the budget constraint to: (1τ)p C C+(1-τ)wL=I, or rearranging, p C C+wL=I’, where I’=I/(1-τ)<I. Thus, a
proportional tax on all goods does not change relative prices and is equivalent to
taking away income. So it is equivalent to a lump sum tax.
b. It is (usually) false that efficiency is maximized when all commodities are taxed
at the same rate; this will not be true if leisure is untaxed. Imagine a more
complicated budget constraint: p C C+p F F+wL=I. If leisure cannot be taxed, then
a tax on commodities leads to a budget constraint of (1-τ)p C C+(1-τ)p F F+wL=I,
which does change the relative price of leisure compared with food or
consumption goods. Thus, it is not a lump sum tax. Instead, the inverse elasticity
rule given in equation (16.9) would suggest that the ratio of the tax rates are
inversely related to the ratio of the compensated demand elasticities for all
commodities that can be taxed. That is, (t C /t F )=(η F /η C ).
c. It is true that average cost pricing for a natural monopoly allows the enterprise to
break even, but the outcome is inefficient. Figure 16.3 in the textbook shows the
typical natural monopoly problem, with an initial fixed cost, and an everdeclining marginal cost curve. In this case, the average cost curve is always
declining, but above the marginal cost curve. Setting P=AC results in an output
level of Z A and zero economic profits. The figure illustrates, however, that the
marginal benefit of more output exceeds the marginal cost, so the efficient level
of production occurs at P=MC, or an output level Z*>Z A . The deadweight loss is
the area between the demand curve D Z and marginal cost curve, going from Z A to
Z*. If output were at the efficient level, however, there would be economic losses
rather than zero profits.
d. One notion of horizontal equity is that people in equal positions should be treated
equally by the tax system. Under this traditional notion of horizontal equity, the
fact that Tom’s workplace provides free access to a fitness room suggests this
kind of compensation should be taxed; Jerry pays “full taxes” on his
compensation while Tom does not. Another notion of horizontal equity relies on
the utility definition of horizontal equity. This concept says that if two individuals
have the same utility without taxes, they should have the same utility with taxes,
and the taxes should not affect the utility ordering. One implication of the utility
definition is that any existing tax structure does not violate the notion of
horizontal equity if individuals are free to choose their activities and expenditures.
If Tom and Jerry have free choice between the two different jobs (and identical
preferences), then the net after-tax rewards (including amenities) must be the
same at both jobs; otherwise there would be migration. In this case, the beforetax wage on Tom’s job adjusts for the fact that there is a fringe benefit.
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Chapter 16 – Efficient and Equitable Taxation
9. Tax avoidance is altering behavior in a way so as to reduce legal tax liability. Tax
evasion is not paying taxes legally due. If the customer is rolling their own cigarettes,
and not buying a pack of cigarettes already made, then the tax is not applicable, so this is
tax avoidance.
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Part 5 – The United States Revenue System
Chapter 17 – The Personal Income Tax
Brief Outline
1. Basic Structure
2. Defining Income
a. Items Included in H-S Income
b. Some Practical and Conceptual Problems
c. Evaluating the H-S Criterion
3. Excluded Forms of Money Income
a. Interest on State and Local Bonds
b. Some Dividends
c. Capital Gains
d. Employer Contribution to Benefit Plans
e. Some Types of Saving
f. Gifts and Inheritances
4. Exemptions and Deductions
a. Exemptions
b. Deductions
c. Impact on the Tax Base
d. Tax Expenditures
e. The Simplicity Issue
5. Rate Structure
a. Effective versus Statutory Rates
6. Taxes and Inflation
a. How Inflation Affects Taxes
b. Tax Indexing
7. The Alternative Minimum Tax
8. Choice of Unit and the Marriage Tax
a. Background
b. Analyzing the Marriage Tax
9. Treatment of International Income
10. State Income Taxes
Suggested Answers to End of Chapter Questions
1. The Haig-Simons definition of income is the net change in the individual’s power to
consume 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 individual’s
power to consume should be subtracted in determining income. Overall, it reflects the
broadest possible base of income. Allowing greater capital losses to be deductible
against other forms of income would move the tax system more in the direction of the
Haig-Simons criterion.
2. It is not clear that this is a meaningful measure of average income. The Haig-Simmons
definition of income used to calculate taxable income excludes many types of income,
such as interest on state and local bonds, some dividends, capital gains, employer
contributions to benefit plans, some types of saving, and gifts and inheritances. Further,
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Chapter 17 – The Personal Income Tax
the H-S income is subject to exemptions and deductions before arriving at “taxable
income,” which significantly reduces the denominator of the calculation from actual
income.
3. Suppose Singh buys the oil stock for $1,000 at the start of period 0. At the start of
period 1, he has two options: A) hold the oil stock one more period, then sell or 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 of period.
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 assuming a 28 percent rate
applies to capital gains, the capital gains tax is 28 percent of $210 or $58.80. Thus, Singh
is left with $1,210 - $58.80 or $1,151.20 after tax.
If Singh follows Option 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 Singh has $1072 left over to 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” because the unrealized capital gains in the oil
stock are treated preferentially by the tax code. This is the “lock-in” effect.
4. Forgiving mortgage debt is essentially giving the recipient a free house (or part thereof),
which is a gift in kind. According to the Haig-Simmons criterion income in kind is
income.
5. For an itemizer, a $500 tax deduction lowers the tax bill by t*deduction. Thus, for an
itemizer 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, in
this case, $500.
6.
a. With a tax rate of t=0.35, and a nominal interest rate of i=0.13, the nominal aftertax rate of interest is (1-t)i=(1-0.35)0.13=0.0845. With an expected inflation rate
of π=0.08, the real after-tax rate of interest is (1-t)i-π=(1-0.35)0.13-0.08=0.08450.08=0.0045.
b. If the expected inflation rate increased by 3 percentage points to π=0.11, and the
nominal interest rate also increases by 3 percentage points to i=0.16, then the real
after-tax rate of interest is now (1-t)i-π=(1-0.35)0.16-0.11=0.104-0.11=-0.006.
The real after-tax rate of return falls from 0.45% to -0.6%. This is because the tax
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Part 5 – The United States Revenue System
system taxes nominal, not real, returns. A person actually loses money in real
terms.
c. In general, consider two rates of inflation, π<π’. The key question is when taxes
are present, by how much must the nominal interest rate increase in order to have
the same real rate of return. This is calculated by equating real rates of return
under different inflation rates (holding constant taxes): (1-t)i-π=(1-t)i’-π’. One
can rearrange this equation: (π’-π)=(1-t)(i’-i), or (i’-i)= (π’-π)/(1-t). This can in
turn be expressed as: Δi=Δπ/(1-t). Intuitively, the left-hand side of this final
equation is the change in nominal interest rates that keeps the real after-tax rate of
interest unchanged. It is equal to the change in the expected inflation rate divided
by (1-t). Thus, returning to part 6b, for a 3 percentage point change in the
inflation rate and a marginal tax rate of t=0.35, nominal interest rates would have
to increase by approximately 4.6 percentage points.
7. The Haig-Simons definition of income provides no rationale for reducing or eliminating
the tax rates on certain types of income. Winning an Olympic gold medal is a form of
work, therefore the income should be taxed according to the Haig-Simmons.
8. The Haig-Simons definition of income provides no rationale for reducing the tax rates on
certain types of income. Some economists believe that increased tax rates on dividends
and capital gains will weaken incentives to work, save, and invest. Others are not
convinced, and there are many arguments on both sides of the issue.
9. A tax expenditure is a loss of tax revenue because some item is excluded from the tax
base or accorded some other preferential treatment. In this case, private school tuition
can be granted a tax credit, meaning that tax revenue cannot be collected on income spent
on this tuition. Because this is revenue loss, not government spending directly, the
Supreme Court ruling seems appropriate. The initial ruling specifically refers to
government spending. This is lower government revenues, not direct spending.
10. The domestic partners who divide their incomes and report on the individual tax form
would have a lower tax liability. Married couples must pay taxes on the full amount and
because of higher marginal tax rates, will end up paying a higher average tax rate.
11. Of the $4,000 of earnings that Sanchez has, he is able to invest (1-t I )*earnings in the
market, or (1-0.25)*$4,000=$3,000. Assume that when she saves the money in a taxable
account, she has to pay taxes each year on the capital gains, and that those capital gains
are treated as ordinary income and taxed at 25%. In this case, her after-tax rate of return
is (1-t I )*r, or (1-0.25)*8%, or 6%. Thus, after 10 years of investment, the amount of
money in the taxable savings account is $3,000*(1.06)10=$5,372.54. If she invests the
money in a Roth IRA, the money accrues at the before-tax rate of return, and there is no
tax liability at the end. Thus, the amount in the Roth IRA is $3,000*(1.08)10=$6,476.77.
17-3
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Part 5 – The United States Revenue System
Chapter 18 – Personal Taxation and Behavior
Brief Outline
1. Labor Supply
a. Theoretical Considerations
b. Some Caveats
c. Labor Supply and Tax Revenues
2. Saving
a. Tax-Preferred Savings Accounts
b. Taxes and the Capital Shortage
3. Housing Decisions
a. Proposals for Change
4. Portfolio Composition
5. A Note of Politics and Elasticities
Suggested Answers to End of Chapter Questions
1. The supply of labor (and other factors) in and out of a city is more elastic than the supply
of factors to the nation as a whole. Therefore, an income tax reduction at the city level is
likely to lose less revenue than such a reduction at the federal level, ceteris paribus. Just
as one can think of “welfare-induced” migration for poor households, one can think of
“tax-induced” migration for businesses and possibly workers. If the city lowers tax rates
(and other cities do not respond accordingly), then one imagines that a number of
businesses will enter that state and spur economic activity, increasing the revenues.
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 with
respect to a change in the net wage rate.
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Chapter 18 – Personal Taxation and Behavior
3. If health care benefits are excluded from being tax-exempt, the price of health care
increases. Both the income and substitution effects reduce the purchase of health care
benefits.
4. The “wrong side” of the Laffer Curve is the side on which increasing tax rates will not
increase tax revenue. If Denmark and Sweden have tax rates are on the right-hand side of
the Laffer Curve (Figure 18.6), where the tax rate exceeds t A , they cannot raise taxes and
expect to increase revenues.
5.
Future Consumption
Current Consumption
Increase in endowment
from tax rebate
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Part 5 – The United States Revenue System
Intuitively, the additional income from the rebate is spread over a person’s entire life and
not simply consumed immediately. Graphically, in this two-period simplification the
endowment point will shift out by the amount of the rebate, but the slope of the line does
not change because there is no change in the interest rate or the tax rate. This acts as a
pure income effect increasing both present and future consumption (meaning current
consumption goes up less than the amount of the tax rebate). If the rebate were permanent,
the new endowment point would shift the budget constraint even further out, and each
period’s consumption would increase by more.
6. This phenomenon can be explained by the fact that after-tax income has increased for the
boxers. Therefore, the income effect says that they will box fewer matches because they
feel richer, but the substitution effect says they will box more matches because the
relative price of leisure has gotten higher. Because they box more matches, the
substitution effect is greater than the income effect.
7. A rational person will increase savings in reaction to reduced interest rates, as suggested
by the financial columnist, if the income effect is stronger than the substitution effect.
This would result in a downward-sloping supply of savings curve.
8. The individual receives a benefit equal to the market rental value of the house because he
lives in the house. Whether he lives in the house or not, he receives a net benefit; the
only difference is that when he rents out the house, he explicitly receives the rent in cash,
while if he lives in the house, he effectively pays himself. Implicit or not, it is still
income, and under a Haig-Simons income tax, it should be taxed.
9. Using the definition of elasticity and its midpoint formula, if the after tax share increases
by 0.08%, taxable income should decrease by 0.096%. (1.2 * % change in after tax share
= % change in taxable income).
10.
a. The supply curve is given by S = -100 + 200w n . The gross wage is w = 10, and
the net wage is w n = (1-t)w = (1-t)10. The difference, then, between the gross and
net wage for any tax rate is w - w n = 10t. This is the tax collected per hour of
work.
The tax revenue for any given hours of work is then the product of the tax
collected per hour of work and the labor supply curve:
tax revenue
= 10t*(-100+200(1-t)10)
= -1,000t + 20,000t -20,000t2
= 19,000t - 20,000t2
The tax rate t = 0.7 is beyond the revenue maximizing point (this can be shown by
computing tax revenue for a slightly lower tax rate, like t=0.69.
Tax Revenues
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Chapter 18 – Personal Taxation and Behavior
Tax Rates
b. Taking the derivative:
dTax Revenue/dt=0
yields 19,000-40,000t=0, or
t = (19,000/40,000), or
t = 0.475 as the revenue maximizing tax rate.
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Part 5 – The United States Revenue System
Chapter 19 – The Corporation Tax
Brief Outline
1. Why Tax Corporations?
2. Structure
a. Employee Compensation Deducted
b. Interest, but Not Dividends, Deducted
c. Depreciation Deducted
d. Investment Tax Credit
e. Treatment of Dividends versus Retained Earnings
f. Effective Tax Rate on Corporate Capital
3. Incidence and Excess Burden
a. A Tax on Corporate Capital
b. A Tax on Economic Profits
4. Effects on Behavior
a. Total Physical Investment
b. Types of Asset
c. Corporate Finance
5. State Corporation Taxes
6. Taxation of Multinational Corporations
a. Global versus Territorial Taxation
7. Corporation Tax Reform
a. Full Integration
b. Dividend Relief
Suggested Answers to End of Chapter Questions
1. This statement implies that it makes more sense to have a tax treatment that prefers
dividends rather than retained earnings so that corporations don’t grow so large that good
management is difficult.
2. The blogger ignores that corporations are owned by people, and only people can be taxes.
If Mr. Romney’s investments in corporations are taxed, thereby reducing his returns, then
his income was taxed more than his simple income tax percentage indicates.
3.
a. The real value of depreciation allowances, Ψ of equation (19.1), falls when
inflation rises. This is because as inflation rises, the real value of the series of
deductions declines.
b. When Ψ falls, the user cost of capital increases because Ψ enters negatively in the
numerator of equation (19.5).
c. A policy that permitted depreciation allowances to be inflation-indexed would
undo the effect of part a.
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Chapter 19 – The Corporation Tax
4. Corporate tax revenues rise and then fall after an increase in the tax rate because it takes
time for firms to adjust the location of their capital. As the capital flows out, tax
revenues decrease. More open economies would have a lower revenue maximizing rate
because in such economies it is easier for capital to flow out to lower-tax countries if
taxes become too high.
5.
a. If the $20 million is expensed, the firm gets a deduction of $20 million in the
current year. If the $20 million is depreciated, the deductions are spread over
time (in a way that depends on the specifics of the depreciation schedule). The
present value of the future flow of deductions is less than $20 million.
b. Because the package design will yield benefits that extend over a period of time,
it would seem sensible to view it as a capital expenditure. If so, depreciation is
appropriate, and the IRS was right.
6. A reduction in the corporate tax rate will lead to a migration of capital to the corporate
sector (because the after-tax rate of return increases) until the after-tax rate of return is
equalized again. The reduction will also have the effect of moving capital from foreign
countries back to the United States. Efficiency would improve because it would reduce
the double taxation of capital income. Effects on equity are less clear: It depends largely
on whether workers were made more productive by the additional capital.
7. This statement assumes that the corporate tax is equivalent to an income tax. Table 14.2
shows that a proportional tax on both capital and labor is equivalent to an income tax.
Thus, the statement assumes that the corporate tax is a proportional tax on both capital
and labor.
8. If the tax rate on dividends increases, the user cost of capital increases by 11.5 percent.
Therefore, investment in wind energy should decline by 17.25 percent.
9. One would calculate the depreciation of a cow based on the life expectancy of the cow
and the cow’s milk production. If the cow produces the same amount each year of her
life, then the depreciation should be 1/L where L is life expectancy. If the milk
production is less the longer the cow lives, then the depreciation in early years should be
higher than in later years, a more complicated depreciation scheme. If the depreciation in
the first year increases, the tax savings from the depreciation will increase and the user
cost of capital will decrease.
10. The effective tax rate declines when allowed to book losses against previous profits for a
longer period. This lowers the user cost of capital. The accelerator model indicates that
this will have no impact on investment. The neoclassical model indicates that this will
increase investment. If the reduced tax increases cash flow, firms may also invest more.
11. The user cost of capital (ignoring depreciation allowances and investment tax credits) is
given by equation (19.4) in the textbook, C=(r+δ)/[(1-θ)(1-t)], where r=after tax rate of
return in the capital market, δ=economic depreciation, θ=corporate tax rate, and
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Part 5 – The United States Revenue System
t=individual tax rate. Substituting the numbers from the problem into the formula, gives
the user cost: C=(.08+.01)/[(.65)*(.7)]=.1978. Since the project’s return, 30%, is higher
than this user cost of 19.8%, the company does invest in the project.
12. This nature of the corporation implicit in this statement is that corporations are entities
separate from individuals, implying that taxing corporations has no effect on individuals.
Most economists view this as incorrect because the corporation is owned by individuals.
If a corporation is taxed, the individuals who own it are also being taxed.
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Part 5 – The United States Revenue System
Chapter 20 – Deficit Finance
Brief Outline
1. How Big is the Debt?
a. Interpreting Deficit and Debt Numbers
b. Summing Up
2. The Burden of the Debt
a. One Hand Borrows from the Other
b. An Overlapping Generations Model
c. Neoclassical Model
d. Ricardian Model
e. Overview
3. To Tax or To Borrow?
a. Benefits-Received Principles
b. Intergenerational Equity
c. Efficiency Considerations
d. Deficits and Functional Finance
e. Federal Debt and the Risk of a Fiscal Crisis
f. Moral and Political Considerations
g. Controlling the Deficits
h. Overview
Suggested Answers to End of Chapter Questions
1.
a. The government borrowing to finance a Memorial Day parade increases the
national debt. In designing an accounting system for the government, the
borrowing in this case should, in fact, increase the national debt.
b. The sale of the Statue of Liberty to private entrepreneurs would decrease the
national debt under current measurement. In the discussion on capital spending,
the exercise here is similar to the sale of nondefense federal buildings in 2002. In
designing an accounting system, this transaction is simply an exchange of assets
and should have no effect on the debt, rather than decreasing the debt. The
current system ignores tangible assets.
c. The law promising free (future) medical care to children under five affects future
spending, not current spending. As such, it does not affect the current
measurement of the debt. This is similar to the discussion of the implicit
legislative promises about Social Security. In designing an accounting system,
the present value of the entitlement should be counted as a current expense, so the
debt should increase. The current system ignores implicit obligations.
d. The $100 tax would reduce the size of the national debt. The implicit promise to
pay Lynne back $105 next year does not increase the size of the debt, assuming
this is similar to the implicit promise to pay Social Security in the future. In
designing an accounting system, again, this implicit promise should be counted.
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Chapter 20 – Deficit Finance
Assuming the present discounted value of the of the $105 paid back next year
equals the $100 tax this year, then the impact on the debt should be zero, rather
than to decrease it.
e. The $100 bond would increase the size of the national debt. The present value of
these payments is the amount by which the bond contributes to the debt. In
designing an accounting system for the government, the borrowing in this case
should, in fact, increase the national debt.
2. Greece’s government owns tangible assets. Selling the gold might give the appearance of
temporarily reducing the current year deficit, but is not a sensible long-term strategy.
Also, it is exchanging one asset for another, so in reality, it is not changing anything.
3. The arrival of surpluses in the late 1990s and the subsequent spending spree are
consistent with Milton Friedman’s view of deficits and government spending. His view
is that, “What is predetermined is not spending but the politically tolerable deficits.”
Since the deficit is fixed, increases in revenue lead to one-to-one increases in spending.
4. If the elasticity is zero, then taxing labor markets creates no distortion in workers’ laborleisure decisions. This suggests tax finance would have a smaller excess burden.
5. Whether or not the burden of the debt is borne by future generations is controversial.
One view is that an internal debt creates no net burden for future generations because it is
simply an intragenerational transfer. However, in an overlapping generations model, debt
finance can produce a real burden on future generations. The burden of the debt also
depends on whether debt finance crowds out private investment. If it does, future
generations have a smaller capital stock and, hence, lower real incomes, all other things
equal. In a Ricardian model, voluntary transfers across generations undo the effects of
debt policy, so crowding out does not occur.
6. The benefits-received principle, which states that the beneficiaries of a particular
government spending program should pay for it, suggests that deficit finance is
appropriate for mitigating an existing economic crisis if the benefits are received by
future generations. An efficiency standpoint would say that debt is appropriate if the
expenditure is temporary, and there are not major pre-existing distortions in capital
markets.
7. The Ricardian equivalence models states that the “old” generation cares about the young
generation and see that government borrowing will hurt the young generation. Therefore,
they will mitigate the future higher taxes by providing bequests to offset. This
observation is a restatement of the Ricardian equivalence model.
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Part 5 – The United States Revenue System
Chapter 21 – Fundamental Tax Reform: Taxes on Consumption and Wealth
Brief Outline
1. Efficiency and Equity of Personal Consumption Taxes
a. Efficiency Issues
b. Equity Issues
2. Retail Sales Tax
a. Rationalizations
b. Efficiency and Distributional Implications of State Sales Taxes
c. A National Retail Sales Tax
3. Value-Added Tax
a. Implementation Issues
b. A VAT for the United States?
4. Hall-Rabushka Flat Tax
5. Cash-Flow Tax
6. Income versus Consumption Taxation
a. Advantages of a Consumption Tax
b. Disadvantages of a Consumption Tax
c. Problems with Both Systems
7. Wealth Taxes
8. Estate and Gift Taxes
a. Rationales
b. Provisions
c. Reforming Estate and Gift Taxes
9. Prospects for Fundamental Tax Reform
Suggested Answers to the End of Chapter Questions
1.
a. The income tax is 50 percent, so Zach pays 50%*$10000 = $5000 in income taxes
in the first period. He saves half of what is left after taxes and earns 10%,
therefore he saves $2,500 and earns $250 in interest, but pays half of that interest,
$125, in taxes. The present value of his lifetime tax payments is $5000 +
$125/1.1 = $5113.64
b. In the second period, Zach has savings and interest equal to $2750. He will use
all this savings on consuming and paying consumption taxes. He will pay $1375
in consumption taxes, so the present value of his tax payments is now $5000 +
1375/1.1 = $6247.73
These calculations demonstrate the transitional problem in moving to a
consumption tax because Zach had to pay high taxes during period 1 when he
earned most of his income, and then had to pay high taxes during period 2 when
he did his consuming.
2. The burden of the estate tax includes the resources used in estate planning and the effects
of estate planning. Many families may alter their behavior in reaction to the estate tax
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Chapter 21 – Fundamental Tax Reform: Taxes on Consumption and Wealth
and, if this results in less efficiency, the estate tax creates an excess burden that is not
reflected by the number of taxable estates or the amount of tax revenue collected.
3. There is a fundamental confusion here. There is no reason to assume that the incidence
of a general consumption tax (a VAT) will be the same as the incidence of a partial factor
tax (corporate income tax).
4.
a. For a fan giving a million-dollar ball to McGwire or Sosa, there would be a
federal gift tax liability. The person receiving the gift owes no tax.
b. If the fan keeps the ball, the fan would owe no tax now. But the ball would
become part of his or her estate, taxable after death under the estate tax.
c. The fan can avoid tax entirely by giving the ball to a charity, since he could
entirely deduct the value of the ball from his taxable income. The charity could
sell the ball; the proceeds from the sale would not be taxed.
d. If the fan sells the ball, the fan owes tax on the net proceeds, just as the seller of
any property would. The transaction would put the fan in the highest tax bracket,
so that the marginal tax rate on the proceeds would be 35 percent.
e. If the fan holds onto the ball for a year, it becomes a long-term capital asset,
subject to the maximum capital-gains tax rate of 28 percent. Unless the fan thinks
that there is going to be a substantial drop in the market value of the ball, he or
she should hold onto it for a year.
5. The efficiency of this tax seems to be good because it would not change incentives.
However, it does increase the likelihood that the government will do it again, as it was
done once.
6. Bradford was right. In the simplest possible case, the budget constraint is pC = wH,
where p is the price of consumption, C is units of consumption, w is the wage rate, and H
is hours of work. With an income tax, pC=(1-t)wH, where t=income tax rate. With a
consumption tax, (1+τ)pC=wH, where τ=consumption tax rate. Thus, for any income tax
rate t, we can find a consumption tax rate, τ, that is equivalent by solving the expression:
(1+τ)=1/(1-t).
7.
a. We can conclude that an income tax generates an excess burden if it creates a tax
wedge between the amount a borrower pays and the amount a lender receives.
With a 25% income tax and an interest rate of 8%, lenders receive (1 – t)r = 6%.
Since interest paid is tax deductible, borrowers pay (1 – t)r = 6%. Therefore,
there is no tax wedge and no excess burden.
b. If interest payments are not tax deductible, then borrowers pay 8%, while lenders
receive 6% after taxes. Since there is a wedge between the two rates, the income
tax creates an excess burden in this case.
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Part 5 – The United States Revenue System
c. If the income tax rate is t = 0.25, then (1+τ) = 1/(1-0.25) = 4/3, so the equivalent
consumption tax is τ = 1/3. A consumption tax leaves unchanged the market rate
of return because the receipt of interest income by itself does not create a tax
liability. If interest payments are not tax deductible, there is no wedge between
the rate lenders receive and the rate borrowers pay, so there is no excess burden.
d. If interest payments are tax deductible, then there is a wedge between the rate
lenders receive and the rate borrowers pay, so the tax creates an excess burden.
With a consumption tax rate of 1/3, borrowing $1 and paying 8% interest causes
the tax liability to fall and the after-tax interest rate borrowers must pay is (1 – t)r
= (2/3)0.08 = 5.36%. In this case, the wedge between the rate lenders receive (8%)
and the rate borrowers pay (5.36%) is even larger than for a 25% income tax
when interest payments were not tax deductible, so the excess burden is larger.
Note that there is an excess burden associated with an income tax only when
interest payments are not tax deductible, while there is an excess burden
associated with a consumption tax only when interest payments are tax deductible
8. Under an income tax, Amy's burden is $1,000*t in the first period, and .08($800)t in the
second period (e.g., her investment income is taxed). Shirley's burden is identical in the
first period, $1,000*t, but is lower in the second period, equal to .08($700)t. This is
because Shirley consumed more in the first period and saved less. Thus, Amy has a
higher lifetime tax burden because she has higher investment income. Under a
proportional consumption tax, Amy and Shirley have the same lifetime tax burden,
$1,000*τ, where τ is the consumption tax rate.
9. The corporation earns a 7% return, but must pay 35% of its return in taxes. In addition,
Aviva must pay 15% in taxes on the annual dividends she receives. This yields an aftertax rate of return of 3.8675% [=.07(1-.35)(1-.15)]. Applying this net rate of return for 25
years to an investible income of 65 cents results in $1.68 [=.65(1.038675)25]. This is the
amount that Aviva will have in her account 25 years from now for each dollar she earns
today. After subtracting a 45% estate tax, her family receives $.92 for each dollar earned
today. If there were no taxes, $1 would compound annually at 7%, yielding a payout of
$5.42 [=1.0725] to her family.
21-3
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Education.
Part 6 – Multigovernment Public Finance
Chapter 22 – Public Finance in a Federal System
Brief Outline
1. Background
2. Community Formation
3. The Tiebout Model
a. Tiebout’s Assumptions
b. Tiebout and the Real World
4. Optimal Federalism
a. Disadvantages of a Decentralized System
b. Advantages of a Decentralized System
c. Implications
d. Public Education in a Federal System
5. Property Tax
a. Incidence and Efficiency Effects
b. Why Do People Hate the Property Tax So Much?
6. Intergovernmental Grants
a. Types of Grants
b. The Flypaper Effect
7. Overview
Suggested Answers to End of Chapter Questions
1. Federal safety regulation may impart economies of scale or a lower cost of compliance
than state-by-state systems for companies. It would also impart a lower cost of policing.
There is little reason to expect that states would have consistently different populations so
that the preferences for consumer safety would be different.
2. From a Tiebout perspective, standardizing taxes would be inefficient as people would not
be able to find the mix of public services and taxes that best suits them.
3. This is a perfect reflection of the Tiebout model, although it is an extreme measure. A
refitted oil rig would have no services provided by the government, and the people living
there would pay no taxes. Alternatively, if there was something like a government on the
oil rig, the provision of public goods would be perfectly tailored to the preferences of the
inhabitants. The people who chose to live on the rig would lose the economies of scale
for the public goods that may be required.
4. Superficially, it seems a violation of horizontal equity for two people with identical
properties to pay different taxes on them. However, the phenomenon of capitalization
requires that we distinguish carefully between the owners at the time the tax is levied and
the current owners. A property with an unduly high tax rate will sell for a lower price,
other things being the same. Thus, a high tax rate does not necessarily make an
individual who buys the property after the tax is imposed worse off. Indeed, equalizing
assessment ratios could generate a whole new set of horizontal inequities.
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Chapter 22 – Public Finance in a Federal System
5.
a.
b.
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Part 6 – Multigovernment Public Finance
c.
d.
6. Because the cantons are competing with lower taxes an incentive exists for the cantons to
provide public services more efficiently and cost-effectively. If the low taxes implied a
level of government services that were too low, the companies would not relocate
(according to the Tiebout model).
7. Communities are formed by groups of people with common interests. Foreign policy is a
common interest for all people in the United States, therefore, it seems that individual
communities should not engage.
8. In the figure below, the (constant) marginal cost of hiring a firefighter is C. The demands
for the two communities are D 1 and D 2 . Suppose that initially the quantity is set at Q 0 .
After decentralization, each community hires firefighters up to the point where the
marginal benefit equals marginal cost, i.e., where their respective demand curves
intersect C. This is at Q 1 for community 1 and Q 2 for community 2. Community 1 gains
abc. Community 2 gains dbe. Community 1 gains more because its demand curve is
more inelastic.
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Chapter 22 – Public Finance in a Federal System
9. The “user-fee” view of property taxes regards property taxes as payment for local public
services. The statement “its presence would raise property values and the extra tax
revenues would easily repay the construction costs” reflects this view -- that people pay
for the recreational services made available by the part with their property taxes. The
statement is not consistent with the “traditional view” or the “new view,” both of which
ignore the local services aspect.
10. Originally, the effective state price of $1 spending on welfare recipients was $0.50 with a
one-for-one federal match rate. If the federal match rate changes to two-for-one, the
effective state prices of $1 spending falls to $0.33, or a 34 percent change in the price.
Using Baicker’s (2001) elasticity estimate of 0.38, a 34 percent change in price should
increase state spending by 12.92% (=0.38*34%).
11. This would be more appropriately handled at the local level. Communities are built on
common interests. If a community is concerned with drunk driving, then the law can be
established.
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