Spring 2008 Microeconomics
Qualifying Examination
Examiners: T. Borcherding, A. Denzau, and D. Filson
May 28, 2008 – Five Hours
Spend the first hour reading this examination and outlining your answers. There are three
sections below. Answer no more and no less than the number required in each section.
Note that Section A has two parts, both required. Husband your time in accord with the
weights of the answers. Good luck.
Section A1: Basic Economics (20 points)
Answer question 1 and three of the four short questions from questions 2 to 5 below.
Question 1 counts double.
1. The California milk board, a government agency sanctioned by Depression-era
federal laws, sets the price of fresh milk in this state. It allows the market for
“industrial milk” to be unfettered. (Think of it as milk products not in the bottles,
jugs, or boxes.) It also prohibits entry of milk from other states in the fresh
market, but does not limit entry of industrial milk from outside or dairies and
producers into the state which will produce fresh milk.
Each producer gets paid from the Milk Board according to the formula:
mR = PFQF + PIQI
where m is a share dependent on a firm’s contribution of milk to the total of all
milk. Assume there is no difference between fresh and industrial milk.
a. Describe this equilibrium, including its deadweights.
b. What happens to the price in each market as the marginal cost of
producing milk shifts up due to input cost changes as is happening today?
2. Coase’s theorem is interpreted (by some) to mean that the locus of property
ownership is unimportant in realizing gains from trade. True or false? Why?
3. In a two-good world, X and a composite good Y, if the marginal utility of Y is
constant, there is no difference between the two Hicksian measures of consumer
surplus, the Equivalent and Compensating Variations. True or False? Why?
4. How come labor unions in manufacturing in the U.S. have done terribly in
membership numbers and power to keep wages up over the last forty years, while
state and local government and teachers’ unions have done well both in relative
memberships and in wage growth? [Hint: think of the Marshall-Hicks four laws
of derived demand in crafting your answer.]
5. Why is it that the demand for arugula, a trendy salad green, is more price elastic
than the demand price elasticity for the composite of all salad greens?
Section A2: Neoinstitutional Economics (15 points)
Answer one of the two questions, but not both.
1. Comment on the following statement:
The study of policy with the thought of improving it is an act of scholarly
arrogance. Economics tells us that all of the actors involved in transactions – and
politics clearly is one such exchange – inform themselves to the point where
returns at the margins equal their incremental costs. Thus, policy study is purely
inframarginal at best; at worst, it introduces noise since external observers are not
as likely to get it right as the participants themselves. It follows that ex post
policy analysis of the sort economists usually do reduce social welfare (and the
world would be a better place if economists stopped doing this.)
2. In a recent New York Times article, columnist David Brooks argued that
limitations on entry of skilled workers into the U.S., caused by a paltry number of
HI5 visas, really is no problem, since an American-based firm can always
outsource the activity or set up a shop abroad. The ubiquity of free trade in goods
and services, outside of agriculture and textiles, means outsourcing is a great
substitute for limitations on entry of skilled labor. Using your knowledge of the
theory of the firm and agency costs, critique this position.
Section B: Questions Based on Economics 316 (30 points)
Answer question 1 or 2, but not both.
1)
Suppose a firm faces an inverse demand function
p = x - 5q,
where x is a random variable taking the value 100 or 200 with equal probabilities.
Average cost is constant at 10.
(a)
If the firm must set price before knowing which outcome would occur,
what would the price be if the firm is risk-neutral?
(b)
What would the firm pay an economist for knowledge of the value of x, if
you are certain she could tell you before you set price?
2)
Consider a small economy with 3 goods, x1, x2 and x3. Each can be produced
using only Labor, requiring ai units of labor per unit of xi produced. There is a total of
2400 units of Labor supplied in the economy.
Consumers have preferences that can be represented by a utility function:
U(x) = x1 x23 x32 .
Suppose initially that there are 100 consumers, each supply 24 units of Labor,
with no other sources of income.
a.
What are equilibrium prices in the economy?
b.
What are transaction quantities?
c.
Suppose that technology improves so that each unit of labor produces
twice as much output. How does this change the equilibrium?
d.
Let a1 = 6, a2 = 2, a3 = 4. What are the equilibrium quantities?
Section C: Questions Based on Economics 317 (35 points)
1. Two firms are competing to be the first to introduce a new good. If a firm succeeds it
gets a payoff of V; otherwise it gets a payoff of 0 (it is possible that neither firm
succeeds). Each firm is either good (G) or bad (B). Each firm knows its own type but not
the other firm’s type. The ex ante probability that a firm is good is p. Each firm
simultaneously decides whether to spend c or not, where c > 0. A firm’s likelihood of
success depends on its own type, the other firm’s type, whether it spends c, and whether
the other firm spends c. The probability of success is either 0, q1 , q2 , or q3 , where 0 < q1
< q2 < q3 . If a firm does not spend c, its probability of success is 0 and it gets a payoff of
0. The following table considers the case where firm 1 spends c and describes how firm
1’s probability of success depends on each firm’s type and on whether or not firm 2
spends c. The first column lists each firm’s type; the second lists whether firm 2 spends c,
and the third lists each firm’s probability of success (firm 1 is listed first, then firm 2):
q1 , q1
{G,G}
2 spends
q3 , 0
{G,G}or {G,B}
2 does not spend
{G,B}
2 spends
q2 , 0
{B,G}
2 spends
0, q2
{B,G} or {B,B}
2 does not spend
q2 , 0
{B,B}
2 spends
q1 , q1
a. What conditions on V, p, c, q1 , q2 , and q3 make it optimal for both firms to always
spend c?
b. What conditions make it optimal for both firms to never spend c?
c. What conditions make it optimal for each firm to spend c if it is good and not spend
c if it is bad?
d. What conditions make it optimal for firm 1 to spend c if it is good and not spend c
if it is bad and for firm 2 to never spend c?
e. Describe how the Bayesian Nash Equilibrium of this game depends on the
parameters V, p, c, q1 , q2 , and q3 .
2. Consider a firm with n shareholders and n shares, where n is odd and n ≥ 3 .
Initially, each shareholder has 1 share. Suppose the initial value of a share is v , where v
> 0. Consider the following game. In the first stage, a bidder offers a price p per share
for the n shares of the firm, where p can be any non-negative real number. In the
second stage, after observing the bidder’s offer, the shareholders simultaneously decide
whether to accept or reject the bidder’s offer.
If a majority of the shareholders accept the bidder’s offer, the bidder gains control of
the company, and the value of each share rises to v + x , where x > 0. If the bidder does
not gain control of the company the value of each share remains at v . Shareholders that
accept the bidder’s offer receive a payoff of p whether or not the bidder gains control of
the company. Shareholders that do not accept the bidder’s offer receive a payoff of v if
the bidder does not gain control, and a payoff of v + x if the bidder does gain control.
The bidder’s payoff depends on the number of shares the bidder ends up with, and
whether or not the bidder gains control. Denote the number of shares the bidder obtains
n
n
by k. If k < , then the bidder’s payoff is k (v − p) . If k > , the bidder’s payoff is
2
2
k (v + x − p) . Please answer the following questions:
a. A shareholder’s strategy is a function that specifies, for every possible offer, accept
or reject. Does a shareholder have any strictly dominated strategies? Any weakly
dominated strategies?
b. A bidder’s strategy is a bid, p . Does the bidder have any strictly dominated
strategies? Any weakly dominated strategies?
c. Calculate the pure strategy subgame perfect Nash equilibria of this game.