C h a p t e r
16 PUBLIC GOODS
Key Concepts A political equilibrium occurs when the choices of
voters, politicians, and bureaucrats are compatible and
no group can make itself better off with a different
The Economic Theory of Government choice.
Government economic action often results in response
to four problems: Public Goods and the Free-Rider Problem
♦ Public goods — goods or services that can be con-
A public good can be consumed simultaneously by
sumed by everyone and from which no one can be
everyone and no one can be excluded. The two features
excluded (discussed in this chapter).
of a public good are that it is:
♦ Taxes and redistribution — government actions
♦ Nonrival — one person’s consumption does not
modify the distribution of income (see Chapter 15).
reduce the amount available for anyone else.
♦ Monopoly — monopolies and cartels restrict the
♦ Nonexcludable — no one can be excluded from con-
amount of output produced (see Chapter 17).
suming the good.
♦ Externalities — when the production or consump-
Nonexcludability means that public goods are subject
tion of goods and services create a cost or benefit
to free riding:
that falls on someone who did not participate in the
transaction (discussed in Chapter 18). ♦ A free rider is someone who consumes a good
without paying for it.
Public goods, monopoly, and externalities can create
market failure, when an unregulated market results in Free riding creates the free-rider problem, which is the
inefficiency. tendency for too little of a public good to be provided if
it is produced and sold privately.
Public choice theory treats the government sector as a
political marketplace, analogous to the economic mar- The total benefit of a public good is the total dollar
ketplace. Participants in the political marketplace are: value placed on it by all citizens, while the marginal
benefit from a public good is the change in the total
♦ Voters — the consumers of the outcomes of the
benefit from a unit change in its quantity. The net
political process. They express their demand by
benefit is the total benefit minus the total cost.
voting, lobbying, and making campaign contribu-
tions. The efficient quantity of a public good is the amount
that maximizes net benefit, which occurs when the
♦ Politicians — the officials elected by voters. Their
marginal benefit of another unit equals the marginal
objective is to get elected and reelected.
cost of supplying it.
♦ Bureaucrats — the hired officials who work in the
government and are appointed by politicians.
288 CHAPTER 16
♦ With private provision, free riding limits the the average tax rate is the same at all levels of income
amount produced and results in an inefficiently low — or regressive — when the average tax rate falls as
level of output. income increases.
♦ Government provision can attain efficiency because Income taxes decrease employment and create dead-
free riding is prevented by imposing taxes to finance weight losses. With a progressive income tax, the de-
payment for the good. crease in employment and deadweight loss are greater
The amount of the good that is provided by the gov- for high-wage workers than for low-wage workers.
ernment depends on the political marketplace and the High-income citizens want to pay lower tax rates; low-
actions of politicians, bureaucrats, and voters. income individuals want them to pay higher tax rates.
Politicians often follow the principle of minimum dif- Politicians balance these desires according to the me-
ferentiation: dian voter theorem:
♦ Principle of minimum differentiation — the ten- ♦ Median voter theorem — political parties pursue
dency for competitors (political parties) to be identi- policies maximizing the net benefit of the median
cal in order to appeal to the maximum number of voter.
clients or voters. Because the median voter is a low-income voter, in-
Bureaucrats try to maximize the budgets of their come taxes are progressive.
agencies. The corporate profits tax is imposed on corporations’
♦ If voters are well informed, politicians won’t allow profits. This tax decreases the quantity of capital,
bureaucrats to expand expenditure beyond the level thereby decreasing productivity and workers’ incomes.
that maximizes net benefit. Social security taxes are levied on wages. The propor-
♦ Voters might be rationally ignorant; that is, they tion of the tax really paid by workers and employers
decide not to acquire information because the per- depends on the elasticity of labor demand and labor
sonal cost of acquisition is larger than the personal supply, not on the fractions specified in the law.
benefit from having the information. Property taxes, collected by local governments, finance
If voters are rationally ignorant, politicians, influenced local public goods, public goods consumed by local
by bureaucrats and lobbyists representing special inter- residents. Elementary, middle, and high schools are
ests, might allow inefficient overprovision of the public examples of local public goods.
good. If the government is inefficiently providing too An excise tax is a tax on the sale of particular good.
many public goods, a voter backlash might occur when ♦ An excise tax decreases the supply of the good being
voters act to shrink the size of the government. taxed. An excise tax is illustrated in Figures 16.1 and
Two theories of government action are: 16.2 (both on the next page). The amount of tax is
♦ Public interest theory — predicts that governments the same in both figures and equals the length of the
act to eliminate waste and achieve economic effi- double-headed arrow.
ciency. ♦ The tax raises the equilibrium price and decreases
♦ Public choice theory — predicts that government can the equilibrium quantity. In Figures 16.1 and 16.2,
create inefficiency. the price including the tax rises the price from 2? to
2J and the quantity decreases from 3 ? to 3 J .
♦ The tax creates a deadweight loss, also shown in
Taxes Figures 16.1 and 16.2.
Most of the federal government’s revenue comes from ♦ Comparing of Figure 16.1 and Figure 16.2 shows
income taxes. that taxes imposed on goods with more elastic de-
♦ The marginal tax rate is the percentage of an addi- mand create larger deadweight losses. Hence the
tional dollar paid as taxes. government more commonly taxes goods with ine-
♦ The average tax rate is the percentage of total in-
come paid as taxes.
Taxes can be progressive — when the average tax rate
rises when income increases — or proportional — when
PUBLIC GOODS AND TAXES 289
though they are provided by the government. In-
deed, in many communities, the same services are
The Effect of an Excise Tax provided by the private sector.
2. THE MARGINAL BENEFIT FROM A PUBLIC GOOD :
Price (dollars per unit) S + tax The properties of nonrivalry and nonexcludability
associated with pure public goods imply that the
S marginal benefit curve for the economy as a whole
is different from that for private goods.
A private good is rival in consumption. Therefore,
Pc to obtain the marginal benefit curve for the entire
economy, we sum the individual marginal benefit
Deadweight curves horizontally. For instance, at a price of $8
you demand 5 units and I demand 5 units. Because
the goods are rival in consumption, none of the 5
D units you will consume at this price can be the same
as any of the 5 units I will consume. So, we sum
the quantities so that at $8, in total we demand 10
Quantity (units per month) units.
However, for the economy’s marginal benefit curve
for a public good, we sum the individual marginal
benefit curves vertically. For instance, for 5 units
Deadweight Loss with an Elastic Demand
you are willing to pay $8 and I am willing to pay
$8. If 5 units are provided, because the public good
Price (dollars per unit)
Deadweight S + tax is nonrival, the 5 units that you consume are pre-
loss cisely the same as the 5 units that I consume. So,
S we sum the prices so that for 5 units, in total we are
willing to pay $16.
The key difference — that for a public good we
Pc consume the same units but for a private good we
must consume different units — is the reason that
the marginal benefit curve for a public good is de-
rived differently from that for a private good.
3. POLITICAL MARKETS AND PRODUCT MARKETS :
Public choice theory provides a theory of the politi-
cal marketplace that parallels the economic theory
Qt Qc of markets for goods and services. Drawing analo-
Quantity (units per month) gies between the operation of political markets and
ordinary markets is a good way to grasp their simi-
In political markets the demanders are voters,
whereas in ordinary markets, the demanders are
1. PUBLIC GOODS AND GOVERNMENT PROVIDED consumers. In both cases, demanders are concerned
GOODS : Not all goods provided by the govern- about their costs and benefits.
ment are public goods. A public good is defined by
The suppliers in political markets are politicians
the characteristics of nonrivalry and nonexcludabil-
and bureaucrats, and in ordinary markets, the sup-
ity, not by whether it is publicly provided. For ex-
pliers of goods and services are firms.
ample, some cities and communities provide
swimming pools; others provide utility services such In political markets, voters express their demands
as electricity. None of these are public goods even by means of votes, political contributions, and lob-
290 CHAPTER 16
bying because the suppliers (politicians) in this 13. If the demand for labor is perfectly inelastic, work-
market desire to retain political office. In ordinary ers pay the entire amount of the social security tax.
markets, consumers express their demands by
14. Provision of local public goods usually is financed
means of dollars because suppliers are motivated by
with excise taxes.
a desire to maximize profit.
In both markets, in equilibrium there is no ten- 15. The more inelastic the demand for a good, the
dency to change because participants cannot be- larger is the deadweight loss created by an excise tax
come better off by making a different choice or by levied on it.
engaging in an additional transaction.
The Economic Theory of Government
11. Which of the following is NOT a source of market
True/False and Explain failure?
a. The existence of public goods
The Economic Theory of Government b. The presence of externalities
11. Market failure refers to the situation in which the c. The fact that some goods are rival in consump-
private market fails to produce the efficient amount tion
of output. d. The existence of monopolies
12. Political equilibrium occurs only in the absence of
12. Market failure refers to the situation when
a. a market does not create a deadweight loss.
Public Goods and the Free-Rider Problem b. a market uses resources inefficiently.
13. Any product supplied by government is a public c. the government prohibits free riding.
good. d. None of the above.
14. A movie shown in an uncrowded movie theater is
Public Goods and the Free-Rider Problem
both nonexcludable and nonrival in consumption.
13. Which of the following is nonrival and excludable?
15. Public goods — but not private goods — face the a. The defense services provided by a new stealth
free-rider problem. bomber
16. The marginal benefit curve for a public good is b. A pair of pants
obtained the same way as the marginal benefit c. A beautiful sunset
curve for a private good. d. An uncrowded theme park such as Walt Disney
17. A private, unregulated market produces less than
the efficient quantity of pure public goods. 14. To two fishermen, a codfish swimming in the mid-
dle of the ocean is a good that is
18. Rational ignorance is the situation wherein politi-
cians are uninformed about certain voters’ desires. a. nonrival and nonexcludable.
b. nonrival and excludable.
19. The public choice theory predicts that the govern- c. rival and nonexcludable.
ment makes choices that achieve efficiency. d. rival and excludable.
15. To two farmers, a steer (owned by one of the farm-
10. The U.S. income tax is a progressive tax. ers) grazing in the middle of the farmer’s pasture is
11. An income tax decreases employment. a. nonrival and nonexcludable.
b. nonrival and excludable.
12. To be elected, politicians choose platforms that
c. rival and nonexcludable.
appeal to the median voter.
d. rival and excludable
PUBLIC GOODS AND TAXES 291
16. A free rider is someone who 11. The idea that political parties will have similar policy
a. does not pay taxes. proposals reflects
b. cannot be excluded from consuming a public a. free riding.
good even though he or she did not pay for the b. rational ignorance.
good. c. government failure.
c. paid more than his or her fair share for the provi- d. the principle of minimum differentiation.
sion of a public good.
d. cannot be forced to pay for his or her consump- 12. Amy realizes that her personal benefit from becom-
tion of a private good. ing an expert on welfare reform is limited, so she
does not learn about this issue. Amy’s decision best
17. Governments provide pure public goods such as reflects
national defense because a. free riding.
a. governments know how to produce these goods. b. the nonexcludability principle.
b. of the free-rider problems that result in under- c. the median voter theorem.
production by private markets. d. rational ignorance.
c. people do not value national defense very highly.
d. of the potential that private firms will make ex- 13. The amount of a public good that maximizes the net
cess profits. benefit to the economy is likely to be provided if
a. voters are well informed.
18. The economy’s marginal benefit curve for a public b. rational ignorance is combined with special in-
good is obtained by terest lobbying.
a. summing the individual marginal cost curves c. politicians are well informed.
horizontally. d bureaucrats are rationally ignorant.
b. summing the individual marginal cost curves
vertically. 14. Public choice theory predicts that
c. summing the individual marginal benefit curves a. the government conducts policies that move the
horizontally. economy toward an efficient use of resources.
d. summing the individual marginal benefit curves b. politicians and bureaucrats tend to be more con-
vertically. cerned about the public interest than individuals
in the private sector.
19. The efficient amount of a public good c. the choices of government maximize net benefits.
a. is as much as the public demands. d. the choices of government can create ineffi-
b. cannot be provided unless the problem of nonex- ciency.
cludability is overcome.
c. equates total benefit and total cost. Taxes
d. is such that the marginal benefit equals the mar-
15. Income taxes ____ employment and ____ a dead-
10. Suppose that the marginal benefit from another unit a. increase; do not create
of a public good exceeds the marginal cost of pro- b. increase; create
ducing it. Then c. decrease; do not create
a. the net benefit from the product is at its maxi- d. decrease; create
mum, and its provision is at the efficient level.
16. Voters are asked to vote for either proposition A or
b. the net benefit from the product is at its maxi-
proposition B. Proposition A will win if it
mum, but the provision of the product is not at
its efficient level. a. is closer to efficiency.
c. less of the product should be produced because b. is supported by bureaucrats.
its provision exceeds the efficient level. c. is preferred by the median voter.
d. more of the product should be produced because d. generates greater total social benefits than total
its provision is less than the efficient level. social costs.
292 CHAPTER 16
17. When income increases, a regressive tax’s average tax 21. The amount of deadweight loss created is
rate ___ and an example of a regressive tax is ____. a. $12 million.
a. increases; the income tax b. $8 million.
b. decreases; the income tax c. $6 million.
c. decreases; a sales tax d. $1 million.
d. increases; a sales tax
22. The deadweight loss triangle from an excise tax is
Figure 16.3 illustrates the effects from an excise tax that the loss of
has been imposed on compact discs. Use this figure for a. only consumer surplus.
the next four questions. b. only producer surplus.
c. consumer surplus plus the loss of producer
Multiple Choice Questions 18, 19, 20, 21 surplus.
d. consumer surplus plus the loss of producer sur-
Price (dollars per compact disc)
S + tax plus minus the tax revenue collected.
14 S 23. Suppose that the demand for wine is not perfectly
inelastic and that initially 5 million bottles of wine
are produced and consumed in the United States. If
13 the government imposes an excise tax of $1 per bot-
tle of wine, the government will collect
12 a. more than $5 million in tax revenues.
b. $5 million in tax revenues.
c. less than $5 million in tax revenues.
11 d. An amount that might be more than, equal to, or
less than $5 million in tax revenues, depending
on the elasticity of demand.
0 3 4 5 6 7
Compact discs (millions per year) 24. Products with elastic demands often are lightly taxed
18. The amount of the tax per CD is a. they usually are goods consumed largely by the
a. $14. poor.
b. $13. b. the amount of the deadweight loss created is
c. $12. large.
d. $2. c. free riders ensure that the government’s tax reve-
nue is small.
19. The equilibrium price, including the tax, after the d. The premise of the question is wrong because
tax has been imposed is products with elastic demands usually are taxed
a. $14. heavily.
c. $12. Short Answer Problems
1. Explain the nonrivalry and nonexcludability fea-
20. The amount of tax revenue the government tures of a pure public good. Why are both necessary
collects is for the good to be a pure public good?
a. $70 million. 2. What is the free-rider problem? For what type of
b. $52 million. goods is the free-rider problem particularly acute?
c. $44 million Why does free riding hinder private firms from
d. $8 million. producing the efficient amount (or any amount!) of
a public good?
PUBLIC GOODS AND TAXES 293
c. Suppose that the lighthouse was constructed but
TABLE 16.1 that one company did not help pay for it. What
Security at Parkin Springs Apartments is this company’s profit from the lighthouse?
d. Based on your answers to parts (b) and (c), what
Number of Total cost benefit per benefit to all incentive does each company have?
guards of guards resident residents e. If one company decides not to pay for the light-
(dollars ) (dollars) (dollars) house, will it be constructed?
1 $300 $10 $____ f. What might the government do in this case?
2 600 4 ____
6. Explain why voter ignorance might be rational.
3 900 2 ____
4 1,200 1 ____ TABLE 16.2
Income Tax Rates
3. Parkin Springs Apartments has 100 residents who
all are concerned about security. Table 16.1 gives Person Desired income tax rate
the total cost per day of hiring a 24-hour security April 80%
guard service and the marginal benefit per day to Brian 40
each of the residents.
a. Why is a security guard a public good for the Diane 30
residents of Parkin Springs Apartments?
b. Why will no guards be hired if each of the resi-
dents must act individually? 7. Table 16.2 shows the citizens in a (small!) demo-
c. Complete the last column of Table 16.1 by cratic nation and their desired income tax rates.
computing the marginal benefit of security The political parties are trying to decide what in-
guards to all the residents combined. come tax rate to propose.
4. Now suppose that the residents form an Apartment a. Who is the median voter? What income tax rate
Council that acts as a governing body to address will be proposed by the parties? Why?
the security issue. b. Before the next election, April changes her mind
a. What is the efficient number of guards? What is and decides that she wants an income tax rate of
the net benefit of this amount? 50 percent. What income tax rate will now be
b. Show that net benefit is less for either one less proposed? How does this tax rate compare with
guard or for one more guard than the net bene- that in part (a)? If it is different, why is it differ-
fit for the efficient number of guards. ent; if it is the same, why is it the same?
c. How might the Apartment Council pay for the c. April continues to change her mind and before
guards it will hire? the third election she decides that she wants an
5. The ships of 10 companies must navigate a treach- income tax rate of 20 percent. Now what in-
erous section of coastline. Each year each shipping come tax rate will be proposed? How does this
line incurs $200,000 in shipping costs from ships tax rate compare with those in parts (a) and (b)?
running aground there. If a lighthouse was built, If it is different, why is it different; if it is the
these costs would fall to zero. Building and main- same, why is it the same?
taining the lighthouse would cost $1,900,000 a 8. Suppose the demand for labor is perfectly elastic.
year. If it was constructed, all the ships that pass What is the effect on the wage rate of a social secu-
that way would benefit from the lighthouse and rity tax that workers must send to the government ?
none would run aground. How is the tax divided? Use a diagram to illustrate
a. From society’s point of view, is building the your answer.
lighthouse efficient? 9. Suppose the demand for labor is perfectly inelastic.
b. From a company’s point of view, if each com- What is the effect on the wage rate of a social secu-
pany pays ¹/10 the total cost of building a light- rity tax that workers must send to the government?
house, is building it profitable? Who pays the tax? Use a diagram in your answer.
294 CHAPTER 16
Short Answer Problem 10 (c)
The Initial Market for Shoes
Price (dollars per pair of shoes)
Price Quantity of shoes Quantity of shoes 90
(dollars per pair supplied demanded
of shoes) (millions) (millions) 85
$55 70 90 80
60 75 85
65 80 80
70 85 75 70
75 90 70 65
80 95 65
TABLE 16.4 55
The Market for Shoes After the Tax
0 65 70 75 80 85 90 95 100
Price, Quantity (millions of shoes per year)
including tax Quantity of shoes Quantity of shoes
(dollars per pair of supplied demanded
shoes) (millions) (millions) d. After the tax is imposed, what is the equilibrium
$55 60 ____
price (including the tax) for a pair of shoes? The
60 65 ____
65 ____ ____
e. How much of the tax do suppliers pay?
70 ____ ____
75 ____ ____
f. What is the amount of deadweight loss from
this tax? (Hint: Figure 16.4 should be helpful
80 ____ ____
when answering this question.)
10. Table 16.3 shows the initial demand and supply
schedules for shoes. You’re the Teacher
a. Based on Table 16.3, what is the initial equilib- 1. “I don’t see why the government would ever do
rium price of a pair of shoes? The equilibrium anything that leads to inefficiency. Inefficiency
quantity? hurts the nation and I thought that the government
b. Suppose that the government imposes a tax of would try to help us.” Comment on this student’s
$10 per pair of shoes that the supplier must pay. views and give an example of how the government
Complete Table 16.4, showing the demand and might take actions that create inefficiency.
supply schedules after the tax has been levied.
c. In Figure 16.4, illustrate the effect of the tax on
the market for shoes by drawing the pre-tax and
post-tax supply and demand curves.
PUBLIC GOODS AND TAXES 295
Answers 14. F Local public goods are usually financed with
15. F The more elastic the demand, the larger is the
True/False Answers deadweight loss from a tax.
The Economic Theory of Government
11. T This is the definition of market failure. Multiple Choice Answers
12. F Political equilibrium occurs when neither voters, The Economic Theory of Government
politicians, nor bureaucrats have an incentive to 11. c Nonrivalry, not rivalry, can create market
change their actions. failure.
12. b Government action can sometimes help over-
Public Goods and the Free-Rider Problem
come the problem of market failure.
13. F Public goods are characterized by nonrivalry and
nonexcludability. Public Goods and the Free-Rider Problem
14. F The movie is nonrival but not nonexcludable 13. d The uncrowded theme park is nonrival because
because a theater can easily exclude people who your enjoyment does not limit my enjoyment of
do not pay to see the movie. it, but it is excludable as anyone who ever tried
15. T Public goods are nonexcludable and so they face to sneak into Walt Disney World can testify.
a severe free-rider problem. 14. c If one fisherman catches the fish, the other can-
16. F The marginal benefit curve for a public good is not, so the codfish is rival; but in the middle of
derived by adding vertically each individual’s the ocean no fisherman can exclude another
marginal benefit curve; the marginal benefit from trying to catch the fish, so the codfish is
curve for a private good is derived by adding nonexcludable.
horizontally each person’s marginal benefit curve. 15. d The farmer who owns the steer can use it but the
17. T Because of the free-rider problem, a private un- other farmer cannot, so the steer is rival; in the
regulated market might produces less than the middle of a pasture, the first farmer can exclude
efficient amount of a public good. the other farmer from trying to catch the steer.
18. F Rational ignorance occurs when a voter is unin- Note the fundamental difference between the
formed about an issue because the benefit to the steer, which is owned and therefore is both rival
voter of becoming informed is less than the cost and excludable, and the codfish, which is not
to the voter. owned and therefore is rival but nonexcludable.
19. F The public interest theory predicts that the gov- 16. b This answer is the definition of a free rider.
ernment makes choices to achieve efficiency; the 17. b The free-rider problem limits the private mar-
public choice theory says that government ket’s ability to produce the efficient amount of
choices can result in inefficiency. public goods.
18. d Vertical summation shows the price everyone in
Taxes total is willing to pay for any particular quantity.
10. T Because the income tax’s marginal tax rates in- 19. d If the marginal benefit from any good equals the
crease with income, the average tax rate also rises marginal cost, the efficient amount is produced.
10. d If one more unit is produced, the gain to society
11. T An income tax decreases employment and cre- (the marginal benefit) exceeds the cost to society
ates a deadweight loss. (the marginal cost), so the additional net benefit
12. T By appealing to the median voter, the politician from the unit is positive.
will attract more than half the votes and so win 11. d Both parties want to appeal to the median voter.
the election. Hence both parties present similar proposals and
13. F If the demand for labor is perfectly inelastic, so follow the principle of minimum differentia-
employers pay the entire amount of the social se- tion.
296 CHAPTER 16
12. d Amy is pursuing her own self-interest and ra- FIGURE 16.5
tionally decides not to become an expert on Multiple Choice Question 21
15 S + tax
Price (dollars per compact disc)
13. a If voters are well informed, they can ensure that
politicians force bureaucrats to provide the effi-
cient amount of the public good. 14 S
14. d Public choice theory says that rational ignorance
might lead to inefficient outcomes. a
15. d By decreasing employment, income taxes create 12 b
a deadweight loss.
16. c If the median voter supports proposition A, 11
proposition A will receive a majority of votes and c
will win. D
17. c The sales tax is a regressive tax because wealthy 0 3 4 5 6 7
people pay a lower fraction of their income on Compact discs (millions per year)
the sales tax than do poor people.
18. d The vertical distance between the supply curve public good means that everyone can consume the
with the tax and the supply curve without the good simultaneously. Limiting the consumption to
tax equals the amount of the tax, $2 in this case. one person at a time would be inefficient because
19. b After the tax, the quantity supplied equals the others can consume the product without denying it
quantity demanded at $13. to anyone else. In addition, private goods are sold
20. d The equilibrium quantity is 4 million CDs, and by firms so that the firms’ owners can earn an in-
the government imposes a tax of $2 on each come and thereby purchase goods and services for
CD. So the total tax revenue is $8 million. themselves. Public goods are nonexcludable, which
21. d The deadweight loss is shown as triangle abc in means that anyone can consume the product re-
Figure 16.5. The triangle’s area is (½)(1 million gardless of the amount paid. This fact gives people
CDs)($2 per CD), so the deadweight loss is $1 the incentive to free ride. Free riding makes the pro-
million. vision of such goods by private companies unlikely
22. c Both producers and consumers suffer a loss from because the firm will not be able to collect any reve-
an excise tax. nue from selling the product.
23. c The new equilibrium quantity of wine is less 2. The free-rider problem is that people will try to
than 5 million bottles, so the government col- avoid paying for a public good. In unregulated mar-
lects less than $5 million in tax revenue. kets the free-rider problem results in the production
of too little of a pure public good because there is
24. b The more elastic the demand for a product, the
little incentive for individuals to pay for it. The free
more a tax decreases the quantity produced and
rider will not pay because that payment will likely
the greater is the deadweight loss.
have no perceptible effect on the amount the person
will be able to consume. Hence avoiding payment is
Answers to Short Answer Problems rational. This incentive creates a problem for the
private sector when it attempts to provide the prod-
1. A good has the nonrivalry feature if its consumption
uct. In particular, suppliers — firms — produce
by one person does not reduce the amount available
goods in exchange for payments because the suppli-
for others. The nonexcludability feature means that
ers want to use their income to buy goods and serv-
if the good is produced and consumed by one per-
ices for themselves. If people do not pay for the
son, others cannot be excluded from consuming it.
goods, suppliers receive no income and hence have
Both characteristics are necessary for the good to be no incentive to produce the goods.
a pure public good. The nonrivalry feature of a
PUBLIC GOODS AND TAXES 297
($900). So the net benefit of $800 is greatest for
Short Answer Problem 3
c. The apartment council might pay for the guards
Marginal Marginal by collecting a security fee of $6 per day from
Number of Total cost benefit per benefit to all each of the 100 residents in order to hire two se-
guards of guards resident residents curity guards.
(dollars ) (dollars) (dollars)
5. a. Yes, building the lighthouse is efficient. The
1 $300 $10 $1,000 marginal benefit to society from the lighthouse is
2 600 4 400 the saving in shipping costs because of its exis-
3 900 2 200 tence. Each firm would save $200,000 annually,
4 1200 1 100 so society as a whole would save $2,000,000 an-
nually. The marginal cost of building and run-
3. a. A security guard is a public good in this case. ning the lighthouse is $1,900,000 annually, so,
Because the guard has the features of nonrivalry on balance, society would be better off by
and nonexcludability. Employment of the guard $100,000 a year if the lighthouse was con-
involves nonrivalry because one resident’s con- structed.
sumption of the security provided does not re- b. Yes, building the lighthouse would be profitable.
duce anyone else’s security. Nonexcludability is The company would incur a cost of $190,000,
involved because, once a security guard is in its ¹/10 share of the cost. But the company would
place, all residents enjoy the increased security save $200,000 in shipping costs. So, on balance,
and none can be excluded. each company comes out $10,000 ahead.
b. If each resident must act individually to hire a c. After the lighthouse is built, the company would
security guard none will be hired because each save $200,000 in shipping costs. If the company
resident receives only $10 in benefit from the did not help pay for the lighthouse, its profit
first guard, who costs $300 per day. would increase by $200,000.
c. The entries in the last column of Table 16.5 d. Each company has the incentive to free ride, that
show the total marginal benefit. These answers is, to not pay for the lighthouse. If the company
are obtained by multiplying the marginal benefit can avoid payment, its profit increases by
per resident by the number of residents, 100. $200,000, but if it must pay its ¹/10 share of the
This multiplication is the numerical equivalent cost, its profit increases by only $10,000.
of summing the individual marginal benefit e. If one company decides not to help pay for the
curves vertically for each quantity of guards. lighthouse, the lighthouse will not be con-
4. a. If the apartment council hires each guard for structed. In this case, each of the other compa-
whom the marginal benefit exceeds the marginal nies would have to pay ¹/9 the cost of the light-
cost, they will hire the efficient number of house, or $211,111.11 annually. But the
guards. The marginal cost of each additional lighthouse saves them only $200,000 in ship-
guard is $300. The marginal benefit of the first ping costs, so building the lighthouse would not
guard is $1,000, so this guard is hired. Similarly, be a profitable venture for the 9 firms that would
the marginal benefit of the second guard is jointly pay the cost.
$400, and this guard also is hired. f. Free riding might prevent the lighthouse from
However, the marginal benefit of the third guard being built. Because providing the lighthouse
is only $200, which is less than marginal cost. would be efficient, the government might use its
Therefore the efficient number of guards is 2. taxing powers to tax each company $190,000
For 2 guards, the net benefit is $800, the total and then use the funds to construct and operate
benefit ($1,400) minus the total cost ($600). the lighthouse.
b. For one guard, the net benefit is $700, the total 6. Most issues have only a small and indirect effect on
benefit ($1,000) minus the total cost ($300). most voters. So for a voter to spend much time and
For three guards, the net benefit also is $700, effort to become well informed about such issues
the total benefit ($1,600) minus the total cost would be irrational because the additional cost in-
298 CHAPTER 16
curred by the voter would exceed any additional FIGURE 16.6
benefit enjoyed by the voter. Only if the voter is sig-
Short Answer Problem 8
nificantly and directly affected by an issue does be-
coming well informed pay. As a result, most voters
(dollars per hour)
will be rationally ignorant about any specific issue. LS + tax
7. a. Diane is the median voter: April and Brian want
higher tax rates; Christopher and Eric want LS
lower tax rates. The parties will propose the in-
come tax rate that appeals to the median voter,
W = Wt LD
so they will propose an income tax rate of 30
percent. If a party proposed a lower tax rate, it
would gain the votes of Eric and Christopher,
but the competing party would win votes from
April, Brian, and Diane by proposing a 30 per-
cent tax rate. Analogously, if a party proposed a
tax rate higher than 30 percent, only April and
Brian would vote for it, and the party would lose Lt L
the election when its competitor proposed a tax Labor (hours per week)
rate of 30 percent.
b. The income tax rate will be 30 percent. This tax FIGURE 16.7
rate is the same as in part (a) because Diane is Short Answer Problem 9
still the median voter. Even with April’s change,
two voters (April and Brian) still want higher tax LD
Wage rate (dollars per hour)
rates than Diane, and two voters (Christopher LS + tax
and Eric) want lower tax rates. Note that there is
no response to April’s switch in this case. Wt LS
c. The proposed tax rate will be 25 percent. This
tax rate is lower than those in parts (a) and (b).
The tax rate is different because the median W
voter has changed. With April’s desire for a
lower tax rate, Christopher has become the me-
dian voter (April and Eric want lower tax rates,
whereas Brian and Diane want higher tax rates),
which results in a change in the proposed tax
rate. The answers to parts (b) and (c) make the
point that the policy proposal is insensitive to L = Lt
changes that do not affect the median voter. Labor (hours per week)
However, a change that affects the median voter
will alter the policies that are proposed. from W to 9 J . In this case, firms pay the entire tax
8. Figure 16.6 shows the effect of the social security in the form of a higher wage rate.
tax when the demand for labor is perfectly elastic. Comparing the answers to problems 8 and 9 dem-
The wage rate does not rise; that is, the wage rate onstrates that firms pay a greater share of a tax im-
that includes the tax,9 J , equals the initial wage posed on labor the less elastic is their demand for
rate, W. When the demand is perfectly elastic, the labor. Conversely, the more elastic the demand for
wage rate does not rise, and so in this case workers labor, the greater the share of a tax paid by workers.
are forced to pay the entire tax. 10. a. The initial equilibrium price of a pair of shoes is
9. Figure 16.7 shows the impact of the social security $65, and the initial equilibrium quantity is 80
tax when the demand for labor is perfectly inelastic. million pairs of shoes.
The wage rate rises by the entire amount of the tax,
PUBLIC GOODS AND TAXES 299
Short Answer Problem 10 (c)
Short Answer Problem 10 (b)
Price (dollars per pair of shoes)
S + tax
including tax Quantity of shoes Quantity of shoes
(dollars per pair of supplied demanded 85
shoes) (millions) (millions) S
$55 60 90
60 65 85 75
65 70 80 a
70 75 75
75 80 70 65 c
80 85 65 60
b. Table 16.6 shows the demand and supply 55
schedules after the tax. The tax does not change
the demand schedule. Consumers demand, say, 0 65 70 75 80 85 90 95 100
80 million pairs of shoes if the price is $65 re- Quantity (millions of shoes per year)
gardless of whether suppliers receive all $65 or if
suppliers receive only $55 and $10 is sent to the
government as taxes. However the supply sched- You’re the Teacher
ule does change. If the price including the tax is 1. “The idea that the government won’t create ineffi-
$65, suppliers receive only $55, because they ciency is called the ‘public interest’ theory of gov-
must send $10 to the government. The initial ernment. It’s based on the assumption that govern-
supply schedule indicates that, when suppliers ment actions lead to efficiency. However, ‘public
receive $55, they produce 70 million pairs of choice’ theories of government suggest that at times
shoes. Hence, when the after-tax price is $65, government actions can result in inefficiency, that
suppliers — who receive only $55 for themselves is, can cause government failure. Public choice theo-
— produce 70 million pairs of shoes. The rest of ries assert that well-informed special interest groups
the answers are calculated similarly. are able to induce the government to undertake
c. Figure 16.8 shows the effect of the tax. Note programs that do not maximize net benefits because
that the supply curve with the tax lies above the most voters are rationally ignorant. For most voters,
supply curve without the tax by $10, the amount being well informed about any particular issue does
of the tax. not pay. As a result, a small, well-informed interest
d. From either Figure 16.8 or Table 16.6, the new group has an influence on government programs
equilibrium price is $70 and the equilibrium that greatly exceeds its size relative to all voters.
quantity is 75 million pairs of shoes. “Suppose there are three large producers of copper
e. The price rose from $65 to $70, so demanders in the United States. If they can convince the gov-
pay $5 of the tax in the form of a higher price. ernment to tax foreign copper $1 per ton, each U.S.
Suppliers initially received $65 per pair; after the copper producer may benefit by $80 million dollars.
tax they receive only $60, so they pay $5 of the Meanwhile, this tax might cost each consumer in
tax in the form of lower receipts per shoe. the United States 80¢. It seems clear to me that the
f. The deadweight loss is the area of the darkened copper producers are going to lobby like crazy for
triangle abc in Figure 16.8. The height of this this policy and contribute a lot of dough to candi-
triangle is $10 per pair, the amount of the tax. dates’ campaigns. But you and I aren’t going to care
The base of the triangle is 5 million shoes, the much. It sure isn’t in our personal interest to study
decrease in the quantity. Hence the area equals this issue because we can gain, at most 80¢! So we’ll
one-half the base times the height, or (½)(5 mil- stay rationally ignorant, but the copper producers
lion shoes)($10 per pair) = $25 million. will lobby hard, so this policy might be enacted.”
300 CHAPTER 16
Chapter Quiz 16. What characteristic of a public good makes free
11. An externality can be a. The nonrival characteristic.
a. either a cost or a benefit. b. The rival characteristic.
b. a cost, but not a benefit. c. The nonexcludable characteristic.
c. a benefit, but not a cost. d. The excludable characteristic.
d. neither a cost nor a benefit.
17. In the public choice theory of government, the ob-
12. “Government failure” is predicted by jective of politicians is to
a. public interest theory. a. remove all inefficiency.
b. rational ignorance theory. b. eliminate market failure.
c. public choice theory. c. decrease rational ignorance.
d. market failure theory. d. get elected and reelected.
13. A pure public good is necessarily 18. Who might opt to be rationally ignorant?
a. nonrival and nonexcludable. a. Special interest groups.
b. nonrival and excludable. b. Voters.
b. rival and nonexcludable. c. Politicians.
d. rival and excludable. d. Bureaucrats.
14. The best example of a pure public good is 19. If the average tax rate increases with income, the tax
a. a rock concert in a large stadium. is ____ and the U.S. income tax is a ____ tax.
b. a radio broadcast of news. a. progressive; progressive
c. building a large apartment for low-income b. progressive; regressive
families. c. regressive; progressive
d. producing paper for use in newspapers. d. regressive; regressive
15. Which theory of government says that the govern- 10. The deadweight loss from an excise tax is largest
ment acts to eliminate inefficiency? when taxing goods with
a. Public good theory. a. elastic demands.
b. Public choice theory. b. inelastic demands.
c. Public interest theory. c. unit elastic demand.
d. Political marketplace theory. d. rationally ignorant consumers.
The answers for this Chapter Quiz are on page 368