S.P.E. Microeconomics Qualifying Examination
Examiners: Borcherding, Denzau, Filson, and Marks
January 30, 2007
Both Ph.D. students in Economics and in the Interfield have one hour to read over this
examination, take notes, and plot their answer strategies. Ph.D. students in Economics then have
four hours to answer Sections A, B, and C. Interfield Ph.D. students then have two hours to
answer Section A, though they are required to answer more questions. Interfield students do not
answer Sections B and C.
Please write legibly, use lots of space and do not crowd your pages up with your answers. Blank
paper is a free good today.
Good luck!
Section A: Basic Economics (30 pts.)
There are eight fairly brief questions in this section. Every student must answer question 1.
Ph.D. Economics students must then pick three more from the remaining seven questions for a
total of four. The Interfield students must also answer question 2 and any three more for a total
of five.
1. The cholesterol-lowering prescription drug Lovastatin sells for $128 in California. In
Canada, because of government-imposed price caps, it sells for about half that amount. There is a
movement in the California legislature to allow buyers of this drug and all other expensive
prescription drugs to have their prescriptions filled with Canadian pharmacies via 800 numbers
or internet sales.
a. Under U.S. law, it is currently illegal to have U.S. prescriptions filled in Canada. That
law is being flouted by perhaps 5% of U.S. patients. Suppose the U.S. regulatory
authority totally ignores enforcement for California but no other state. In the long run,
what would happen to prices in Canada and the U.S. of Lovastatin and other prescription
drugs? What would happen to Canadian exports? What about Canadian imports?
b. Suppose U.S. law changes and any American can order from Canada, but only over the
phone or internet? What if not only individuals, but also HMOs and group health servers,
can buy from Canada?
In your answers, consider how Canadian public authorities and pharmaceutical firms respond
strategically to changes in American policy. You may wish to formulate simple games to
illustrate the optimal Canadian and firm reactions to U.S. policy changes.
2. ING Direct has been offering 4.5% interest in an online savings account for quite some time,
and it is not alone in offering such a high rate to consumers. In fact, many online savings
accounts have higher rates. HSBC offers 5.05%. Recently, Citibank and Washington Mutual,
two large bricks-and-mortar banks, have begun offering online savings accounts with 5% interest
rates. Traditional bricks-and-mortar savings accounts have rates much closer to zero (0.2% is a
typical example). How have traditional savings accounts managed to survive for so long despite
this high difference in rates? Why haven’t more bricks-and-mortar banks followed the lead of
Citibank and Washington Mutual? Discuss bank-specific factors that might affect adoption
delays.
3. Jessica Mitford in The American Way of Death (1963) claimed that the funeral industry was
both non-competitive and predatory. Consumers (the bereaved – relatives and friends) faced
with a decision about disposal of remains (the deceased) had bad information relative to
suppliers (funeral homes). This was exacerbated by state laws (driven by suppliers’ rentseeking) which limited “shopping,” e.g. coffins had to be obtained only through licensed
suppliers. Things have changed since 1963 though Ms. Mitford, known to friends as “Red
Dekka,” never acknowledged them before her death in 1996. These changes certainly did not
happen in the Sixties, or even much in the Seventies. It was the Eighties through today when the
“American Way of Death” became more friendly to the economic interests of the bereaved.
Predict these changes based on the effects of (a) changes in information technology since the late
1970s and (b) the “Deregulation Revolution” since the early 1980s. Make up stuff, since you are
not held to historical accuracy, but instead to intelligent, theory-driven speculations.
4. Suppose that in 2010 a new widget can be added to the engine of an internal combustion
engine so that it gets twice the gas mileage it previously had.
a. What determines whether a household would use more or less gasoline at the same price
for gasoline?
b. Using a supply and demand analysis, what would happen to the price of gasoline?
5. Suppose that a firm takes $70 million from its bank account to build a new factory. Once the
factory is built, the salvageable value is only $50 million. Interest rates are 10 percent per year.
Suppose for simplicity that the factory does not depreciate, and that its fixed costs come only
from interest expense. As soon as the factory opens, the industry hits hard times, and at its
optimal output the factory now earns $8 million in revenues annually and incurs $2 million in
variable costs annually.
a. Would the firm have wanted to build the factory, had it anticipated these conditions in
advance? Explain.
b. Will the firm want to keep the factory open in the long run, now that it is built? Explain.
6. Ninety percent of American and Canadian economists believe that free-trade is the optimal
policy of their governments to pursue compared to a restrictive protectionist policy. About half
of these free-traders believe, however, that “losing” groups need adjustment aid. The remaining
half feel that everyone should adjust to unfavorable pecuniary externalities on their own.
a. If free-trade is Pareto efficient why all the worry over losers?
b. The other half of free-traders who want little adjustment aid worry about the
consequences of adjustment policy as potential rent-seeking impediments. How so?
Doesn’t government adjustment compensation convert Kaldor-Hicks to Paretian moves,
or at least nudge them in this way?
7. The standard proposition in economics holds that government minimum wage impositions
always reduce employment. However, Card and Kreuger in studying fast-food restaurants in
New Jersey found little effect. They compared employments in a sample taken before and after a
large minimum wage increase. Critique their findings.
8. In the last five or six years, regulated cab fares in New York City have been held constant,
yet the cost-of-living has risen by at least 15 percent, possibly by 20 percent. Some folks think
that the cab drivers’ wages amount to only $8 to $10 per hour. Cab drivers are generally
unorganized, but they have demonstrated in front of the NYC “hack bureau,” which sets cab
fares, for a rise in mileage and pick-up fees. Cab drivers in NYC are almost entirely immigrants,
a high fraction of them undocumented. Cab companies have only a limited number of
“medallions,” the metal badge which every legal cab must post prominently so that a passenger
knows she or he are in an approved and hack-licensed vehicle. The stock of medallions has
practically stayed fixed over the last ten years. Predict the effects of a rise in allowed fares on
wages, cab-usage, company profits, and the value of medallions, which are tradeable.
Section B: Advanced Neoclassical Micro Theory (30 pts.)
Answer one question from the three in this section.
1.
Suppose that the production function of a firm is given by
q = f(L, K) = L.5K.5,
and that the firm is paying w = 2, and r = 1 for L and K in price-taking input markets.
a)
If the firm is a competitor in its output market, then what is the firm's long-run
supply price?
b)
Let market demand be given by the function
Q = 400 - p,
and all firms have the same cost structure. What is the market equilibrium output and
price?
c)
In the situation of (b), suppose that the firm is able to gain a monopoly on its
output market. How would this affect the market output and price, compared to the competitive
organization?
d)
At an interest rate of 10%, what would the value of this monopoly be, assuming it
would go on in perpetuity?
2.
Suppose a consumer's direct utility function is
U = x10.5 x20.5.
a.
Derive the expenditure function, and the indirect utility function.
Let p2 = 1, and income $100. Suppose that p1 rises from $1 to $4.
b.
What is the initial utility level? The final utility level after the price change?
c.
How must more income would enable the consumer to get back to the original
utility level?
d.
At the old prices, how must less income would enable the consumer require to get
to the final utility level?
Suppose the consumer had a utility function,
U = x1 x2 .
e.
How would this affect your answers to parts c and d above?
3. Firms in a perfectly competitive industry have a fixed-coefficient production technology
y = [min(L, K)]0.5
Output y can be sold at a price p. The wage for labor L is w, and the rental rate for capital K
is r. Factor prices w and r are positive and finite.
a. Solve for the profit function for individual firms in the industry as a function of
output and factor prices.
b. Supposed that usage of capital is fixed in the short run at K0. Obtain expressions for
the output-price elasticity of output supply in the short run, when capital is fixed, and
in the long run, when usage of both factors can be varied.
c. Derive the cost function as a function of factor prices and the level of output.
d. Suppose that, in addition to these labor and capital costs, the government imposes a
fixed business registration fee F per firm per period, which adds to the costs of doing
business and cannot be avoided, even in the long run, by any firm that remains in the
industry. Solve for the long-run competitive equilibrium output per firm and market
price, if w = 3, r = 1, and F = 100.
e. How many firms will the market sustain in long-run competitive equilibrium if
demand is
QD = 10000 – 25 P ?
Section C: Game Theory (40 pts.)
Answer either question 1 or question 2 in this section.
1. Consider the following model of bargaining and conflict. There are two players, a dissatisfied
state D and a satisfied state S. The two players disagree about the appropriate distribution of a
prize with a value normalized to 1. At the beginning of the game, D has the share x of the prize,
and S has 1 – x. Call this the status quo.
In stage 1 of the conflict, D moves first. She can either attack, do nothing, or make a proposal to
re-divide the prize. If she attacks, both players pay a cost of fighting c. D wins with probability p,
and if she wins, she obtains the whole prize and the game ends. If she loses, S obtains the whole
prize and the game ends. If D does nothing, stage 2 begins, and S can either attack, do nothing,
or make an offer. If S attacks, D wins with probability q, where p > q (there is an attacker’s
advantage), payoffs are determined as in the stage 1 battle, and the game ends. If S does nothing,
the status quo is restored, and payoffs are x and 1 – x. If S makes an offer, then stage 3 begins.
In the stage 3 that follows D’s initial choice to do nothing and S’s subsequent choice to make an
offer, D can either accept S’s offer, attack, or make a counter offer. If D accepts S’s offer, then
payoffs are z and 1 – z, where z is S’s suggestion for re-dividing the prize. If D attacks, D’s
probability of winning is p, as in stage 1. If D makes a counter offer then the game proceeds to
stage 4. In stage 4, S either accepts, in which case payoffs are y and 1 – y, where y is D’s
suggestion for re-dividing the prize, attack, in which case D’s probability of victory is q, or
simply do nothing, in which case the status quo is restored.
If D makes a proposal to re-divide the prize in stage 1, then in stage 2, S either accepts, in which
case payoffs are y2 and 1 – y2, where y2 represents the proposal, or attacks, in which case the
probability that D wins is q, or make a counter offer. If S makes a counter offer, then the game
proceeds to stage 3, where D can either accept, in which case payoffs are z2 and 1 – z2, where z2
represents the proposal, attack, in which case the probability that D wins is p, or do nothing, in
which case the status quo is restored.
a. Draw the game tree.
b. Can there be an equilibrium where S attacks along the path? If so, describe one. If not,
explain why.
c. Can there be an equilibrium where D attacks in stage 3 along the path? If so, describe
one. If not, explain why.
In the remaining parts, assume that p – c > x.
d. Can there be an equilibrium where D does nothing initially? If so, describe one. If not,
explain why.
e. Can there be an equilibrium where D makes an initial offer and then the status quo is
restored in stage 3 (on the path)?
f. Can there be an equilibrium where D makes an initial offer, S makes a counter offer, and
D accepts S’s counter offer in stage 3? Would this equilibrium survive if there were even
the smallest costs of delay in reaching a resolution to the conflict?
g. Can there be an equilibrium where D makes an offer that S accepts? Does this
equilibrium survive even the smallest costs of delay?
h. What is the only equilibrium path that remains in the presence of even small costs of
delay? What is the intuition for this result?
2. Consider the following model of bargaining and conflict. There are two players, a dissatisfied
state D and a satisfied state S. The two players disagree about the appropriate distribution of a
prize with a value normalized to 1. At the beginning of the game, D has the share x of the prize,
and S has 1 – x. Call this the status quo.
There are n types of D. If the conflict escalates to war, the probability that type i wins is given
by pi , where p1 < p2 < ... < pn .
In stage 1 of the conflict, D moves first. She can either make a proposal to re-divide the prize or
simply propose that the status quo be maintained. S observes D’s proposal, updates his beliefs,
and then decides whether to accept D’s proposal or reject it. If S accepts D’s proposal (call it y),
then the game ends, and D gets the payoff y and S gets the payoff 1 – y. If S rejects the proposal,
then D decides whether to attack or not. If D attacks, then D gets the (expected) payoff pi − c
and S gets the payoff 1 − pi − c , where c is the cost of fighting a war. If D does not attack, then
the status quo is maintained, and payoffs are x and 1 – x. S can use a mixed strategy in deciding
whether to accept D’s proposal or not.
a. Describe the general requirements that must be satisfied in a separating weak perfect
Bayesian equilibrium (SWPBE). Describe the general requirements that must be satisfied
in a pooling weak perfect Bayesian equilibrium (PWPBE).
b. Is a SWPBE likely to exist in this game? Describe any additional assumptions you need
to make to ensure existence and characterize the SWPBE, or show that one cannot exist.
Can war be a zero-probability event in a SWPBE of the game?
c. Is a PWPBE likely to exist in this game? Describe the additional assumptions you need to
make and characterize the PWPBE, or show that one cannot exist. Can war be a zeroprobability event in a PWPBE of the game?
d. A partially-separating equilibrium (or partially-pooling equilibrium) allows some types to
choose the same strategy while other types choose different strategies. Is a partially
separating WPBE likely to exist in this game? Describe the additional assumptions you
would need to make and characterize the partially-pooling equilibrium, or show that one
cannot exist. Can war be a zero-probability event in such an equilibrium?
e. Are there any partially or fully separating equilibria where stronger types are less likely
to end up fighting in equilibrium than weaker ones? If so, can you think of reasonable
restrictions on off-the-path beliefs that would rule out this possibility? If this cannot
happen in equilibrium for any off-the-path beliefs, prove that it cannot happen.