Anderson, PUBLIC FINANCE
Chapter 19
End-of-chapter problems with solutions
1. Many states permit agricultural producers to form a voluntary market association to promote
their commodities. For example, a Corn Producers Association may be formed to
promote consumption of corn-based products including corn chips and ethanol-based
fuel. To fund these marketing activities these associations often require a so-called
“check-off,” which is a per unit of production fee (alias tax) required of producers. Why
would individual corn farmers join such as association and be willing to pay the checkoff fees for such services? Explain using club theory.
Answer: The association provides benefits that are enjoyed by each member, thus
justifying the payment of a fee to cover the cost. The following figure illustrates the
optimal quantity of the service to provide an association of n members. Members would
be willing to pay a fee in order to obtain the benefits of x* units of the club good.
Total
benefit and
cost per
person
C(n)
B(n)
x*
Club good
quantity
2. Mancur Olson states in his book The Logic of Collective Action that “...the larger the group,
the farther it will fall short of providing an optimal amount of a collective good.”
Explain why this may be so in light of the theory of club goods.
Answer: As the club size grows, Figure 19.2 illustrated that the optimal quantity of the
club good generally increases. The problem that arises with increased club size,
however, is the per member benefits are reduced and there is a smaller incentive to join
the club and pay the dues. The incentive to free ride grows with membership size
increasing (recall chapter 3 and the problem of the free rider).
3. The definition of a club says that members derive benefits from either sharing costs,
association with one another, or from consuming a congestible public good. For each of
the following groups specify which of these three benefits is likely to be the dominant
factor that encourages membership:
a. Blockbuster video club
b. Iowa Pork Producers Association
c. Unofficial Studebaker Drivers Club
d. Second Wives Club
e. Moral Majority
f. American Civil Liberties Union (ACLU)
Answer:
a. Blockbuster video club—sharing costs.
b. Iowa Pork Producers Association—sharing costs and consuming a congestible
public good (lobbying).
c. Unofficial Studebaker Drivers Club—association with one another.
d. Second Wives Club—association with one another.
e. Moral Majority—association with one another and sharing costs (political
activism costs).
f. American Civil Liberties Union (ACLU)—sharing costs (litigation) and
consuming a congestible public good (legal services).
4. Suppose that in Figure 19.1 the cost of the swim club is F = $350,000 and the marginal cost is
MC = 100n2.where n is club membership.
a. Compute the optimal membership size for the club.
b. Suppose that the marginal cost rises to MC = 200n2 Explain the impact on the optimal
membership.
Answer:
a. With F = 350,000, MB = 350,000/n. Setting MB = MC gives 350,000/n = 100n2
which implies that n = 3,500.
b. Setting MB = MC now gives 350,000/n = 200n2 which yields the solution n = 1,750.
5. What happens in Figure 19.7 if the V functions for both communities are constantly rising,
rather than peaking then falling as drawn? Explain the implications for community
formation in this situation.
Answer: Everyone should live in one community—the one providing the higher V level
at 2N* population.
6. The following data depict the fiscal characteristics of two school districts in a metropolitan
area, each composed of identical single-family houses with one pupil per household.
Wolverine School
District
Characteristic
Spartan School
District
$250,000
2%
$5,000
per-pupil property value
property tax rate
per-pupil expenditure
$50,000
10%
$5,000
The voters who have chosen to live in each district desire educational expenditures of
$5,000 per pupil. Each district then finances education with a property tax, but because
the Spartan District has small houses (with low value) while the Wolverine District has
large houses (with high value) the tax rate in the Wolverine District is much higher.
a. Would a voter in the Spartan District prefer to live in a small house ($50,000) in
the Wolverine District? (Assuming that the tax rate is unchanged at 2%)
Explain.
b. Suppose there is a third district, Buckeye District, to choose from with an equal
number of big and small houses so that per-pupil value is $150,000. What tax
rate is required in Buckeye District in order to spend $5,000 per pupil on
education? If small houses cost $50,000 in this district, are small house
consumers better off here or in Spartan District? If big houses cost $250,000 in
this district, are big house consumers better off here or in Wolverine District?
Explain.
c. Given your answer in part b, what do you expect will happen to the demand for
big and small houses in Buckeye District? What will happen to the prices of these
houses in this mixed district?
Answer:
a. Yes, because the per-pupil expenditure is the same while the tax rate is
lower.
b. The required tax rate is 3.33% (5,000/150,000). Small house consumers
would be better off in this district than in the Spartan District, since their
tax liability would be smaller. The presence of large homes in the district
reduces the required tax rate.
c. We would expect that the price of small homes in the Buckeye District
would be bid up while that for large homes would be bid down.
7. Explain the economic issues involved in NATO expansion as countries such as
Hungary and the Czech Republic approach membership in the defense organization.
Specifically, how will admission of new members affect the costs and benefits
provided to existing members? What are the issues related to public good provision
when the good is defense?
Answer: Increasing NATO membership size can be analyzed in a diagram like
Figure 19.3. For a given level of defense, increasing membership size reduces the
benefit per member and the cost per member. Whether this is advantageous depends
on whether NATO was at its optimal membership size before expansion. When the
public good in question is defense, the cost of providing the public good may rise
substantially as the area being defended grows (as the geographic perimeter of the
alliance grows the area within the alliance grows more than proportionately).
8. Consider club membership in the European Union. How would the decision to join
the EU be different if membership required that the country also join the EMU?
Explain in the context of club theory.
Answer: Being forced to join the EMU in order to join the EU would reduce the net
benefit of membership (see discussion on p. 588), at least that is the view of the UK,
Demark, and Sweden at this point since they have chosen to join the EU but have
refused to join the EMU. By making the EU and EMU memberships separable, the
EU has gained three members that would otherwise have not chosen to join in all
likelihood.