2020 MA/MS Exit Exam
SMU Department of Economics
January 20, 2024
Instructions: You should complete all questions in both sections of this exam. You must pass both sections
separately in order to pass the overall exam.
Microeconomics Section
1. [Monopoly and Duopoly] Consider a market of one good with demand P = ABQ where A and B
are positive constants and Q is the industry output. We assume throughout that there are no costs of
production for any firm operating in the market.
(a) Suppose there is a monopolist serving the entire market. Find the monopolist's optimal quantity and
optimal profit.
(b) Now suppose the market is a duopoly market with two firms. Firm 1 chooses its quantity of output
91 and firm 2 chooses 92. Write down the profit functions of the two firms, find the best response
functions of the firms, and calculate the equilibrium quantities for firms 1 and 2 in this market. Is the
total equilibrium quantity of the two firms higher than the monopolist's optimal quantity in part [a]?
(c) Now suppose the firms 1 and 2 could agree that for every unit of output produced by firm 1, the firm
must pay a tax t₁ to firm 2, and that firm 2 must similarly pay a tax t2 to firm 1 for every unit of
output produce by firm 2. Explain how these taxes can increase the profits of both firms. Assuming
that ti = = t2 = t, find the equilibrium quantities with the taxes. What is the tax level that maximizes
the firms' profits.
2. [Utility Maximization] Consider the utility function
u(x, y) = x + lny
with budget constraint pxx + PyY = I.
Remark: You must consider the possibility of corner solutions in answering the following questions (oth-
erwise, you'll get 0 points for the question).
(a) Find the consumer's Marshallian demand functions for x and y.
(b) Find the own-price elasticities, income elasticities, and cross-price elasticities for both x and y. Is it
possible for x to be an inferior good? What about y?
(c) Find the consumer's indirect utility function.
3. [Perfectly Competitive Firms] Each of 10 firms in a competitive market (this is a simplification-
in practice we would think that a competitive market must have many more firms) has a cost function
C(q) = 9+ q². The market demand function is Q 120 p, where Q is the total quantity sold in the
market and p is the market price.
=
(a) What is the equilibrium price, quantity per firm, market quantity, and level of profit per firm? Is this
a short-run or long-run analysis, and how do you know?
(b) Keep the cost function fixed at C (q) = 9+ q², but suppose that firms will enter or exit until profits
equal zero. Find the long-run equilibrium price, quantity per firm, and market quantity.
1 (c) Suppose the government imposes an excise tax of 50 cents on this good when a consumer pays a
price p for the good, the firm receives only p/2. Find the long-run equilibrium price, quantity per
firm, market quantity, profit level, and the equilibrium number of firms. What effect does this excise
tax have on the competitive market? In particular, who bears the burden of the tax?
4. [Uncertainty] Consider a labor market in which times can be either good or bad. If times are good (state
1), the market wage is 81. If times are bad (state 2), the market wage is 36. Workers in this market are
expected utility maximizers, with utility function
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U (x1, x2)=√x₁ + (1 − π) √√×2.
(a) Are these workers risk neutral, risk averse, or risk seeking? Explain your answer here as precisely as
you can (there are multiple ways to do it and it's fine to pick one of them).
(b) Suppose that workers in this market receive the market wage, and hence are paid 81 in state 1 and
36 in state 2. Assuming that the probability of state 1 is 3, what is the expected wage, and what is
the workers' expected utility and certainty equivalent?
(c) An insurance company offers the workers in this market income insurance, charging a premium P and
paying compensation C in the bad state. Assuming that the insurance is actuarially fair, show that
the workers in this market will fully insure. What is their resulting consumption in each state, and
what is the workers' expected utility
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5. [Exchange Economy] Consider an economy with two people, Alice and Bob, and two goods, x1 and
x2. Alice's utility function is u (x^, x^) = x^ (x4)³ and Bob's utility function is u (x³‚x) = (x³)³ x².
Assume that Alice is endowed with one unit of good 1 and no good 2, i.e., (w₁ = 1, w₁ = 0) and Bob with
one unit of good 2 and no good 1, i.e., (wß = 0, wỗ = 1).
(a) Find the competitive equilibrium for this exchange economy (let good 1 be the numeraire so that
P₁ = 1).
(b) Now suppose that Bob's endowment of good 2 doubles, from one unit to two units, i.e., (ŵß = 0, ŵỗ = 2),
and Alice's endowment is the same as before (w₁ = 1, w₁ = 0). We would certainly expect this to
make Bob better off. What effect does it have on Alice's utility?
(c) Now suppose instead that Alice's endowment of good 1 doubles, to two units, i.e., (ŵª = 2,ŵ₁ = 0),
and Bob's endowment is the same as before (wB = 0, w₁ = 1). What effect does it have on Alice's
utility? How does this compare to your answer to part (b)?
(d) Now think of Alice and Bob as countries rather than individuals, and think of an increase in endowment
as a resource discovery, such as the discovery of oil or natural gas. Use your answers to part (b) and
part (c) to discuss the circumstances under which you would rather have such a discovery in your own
country, and those in which you would rather have it in another country. Keep your answer briefly
and to the point.
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