Econ 742
WVU
Public Economics
Take-Home Midterm Exam
Spring 2016
R.Congleton
Answer all of the following questions. The answers should be entirely your own work.
Answers should be submitted via e-mail by midnight March 23. Your entire set of answers
should be less than nine pages long. When answering short answer and essay questions be sure
to give your interpretation of the question as part of the answer.
I.
Concepts and Definitions ( 5 points each, 4-5 sentences):
i
Externality
ii Neutral Tax
iii Ramsay Tax
iv Tullock Contest Success Function
v Knightian uncertainty
II. Elementary Public Finance
1. (5 pts) Income Taxation
i
Determine marginal and average tax rates for the following tax schedule:
T = C + BY
ii Is this tax progressive, regressive, or proportional? Explain.
2. (10 points) Al's marginal benefit curve for a pure public good is MBa = 300-6Q and Bob's
MB curve is MBb = 100 - 6 Q. Suppose that the Al controls the activity level and that
production exhibits constant returns to scale with MC = 120.
i
Characterize the private supply of this externality generating activity in the absence of
collective or governmental action.
ii Characterize the Pareto optimal level of this externality generating activity.
iii Determine the Pigovian subsidy rate which can induce Al to produce the Pareto
optimal level of the externality generating activity. (Hint: a diagram may help.)
3. (10 points) Suppose that N individuals have the same underlying utility function for private
and public goods Ui = u( Xi, G) where X is a pure private good, and G is a pure public
good. Let 100 = X 2 + G 2 be the production possibility frontier faced. Derive the
Samuelsonian conditions for the optimal level of public good G.
III. Political Economy
1. (10 points) Suppose that the level of a public service is to be determined through a series of
majority decisions (as with a series of referenda). Suppose that there are three types of
voters with the following marginal benefit curves: MBa = 300 - 6Q, MBb = 200 - 4Q, and
MBc = 50 - Q.
i
Suppose that the marginal cost of the service is MC = 75 and that the tax system will
assign equal cost shares to each voter type. Characterize the median voter outcome.
ii Contrast the median voter outcome with the Pareto efficient (SNB maximizing) level
of the public service.
iii Is the majoritarian result closer to the ideal than the private “high demander provides”
result?
iv Characterize the Lindalh tax system for this service. (Hint: a diagram may help.)
2. (10 points) Analyze the concept of rent seeking.
i
Construct a 3-person rent seeking contest using a Tullock contest success function.
Define all variables, determine the strategies of each player and the Nash equilibrium
of your contest.
ii Do institutions matter in determining the degree of rent dissipation? If so, discuss
how such effects are or can be incorporated into your model.
iii Under what circumstances, if any, are rents completely dissipated by socially wasteful
expenditures?
3. (10 points) Essay: (a) Contrast the cooperative (contractarian) and extractive (authoritarian)
rationales for the emergence of the state. (b) Both cooperatives and authoritarians normally
have to choose institutions for governance. Compare and contrast some of the likely
difference in the institutions chosen. (c) Explain why government officials are more likely to
be elected under contract theories of the state than authoritarian ones. [About one page, be
sure to cite relevant literature.]
IV. Risk Uncertainty and the Welfare State
1. (10 points) Essay: Government spending in the United States and most other Western
countries more closely resembles insurance products than solutions to pure public goods
problems. (a) Explain the difference between the two theories of government spending.
(b) Explain why insurance programs are normally considered pure private goods although
risks are pooled. (c) What factors would be expected to affect the median voter’s demand
for public services under an insurance model of the government services?
2. (10 points) Consider a federal, state, or local public service that appears to be explained by
the risk-management model of the state. (a) How would you distinguish between the
risk-management explanation of the level of this service and a public goods or externality
explanation? What kind of empirical test would enable you to distinguish between these
hypotheses. (b) How would you distinguish the risk-management model of the state from
the rent-seeking model of the state? What kind of empirical test would enable you to
distinguish between these hypotheses?
After completing the exam:
email a pdf or doc file to roger.congleton@mail.wvu.edu,
with a header Public Econ Exam.
Your exam’s file name should be: ECON 742_your last name_exam.