Economics
812 Midterm Answer Key
Prof.
Bryan Caplan
Spring,
2012
Part 1: True, False, and Explain
(10 points each  2 for the right answer, and 8 for the explanation)
State whether each of the following six propositions is true or false. Using 23 sentences AND/OR equations, explain your answer.
1. Let “CK”=”the results of the CardKrueger minimum wage study.” Suppose the p(econometrics is reliable)=.8, p(CKeconometrics is reliable)=.3, and p(~CKeconometrics is reliable)=.7.
True, False, and Explain: P(econometrics is reliableCK)>70%.
FALSE. Using Bayes’ Rule:
_{}
We do not know P(CK~reliable). But _{}
only
if P(CK~reliable)<.514.
Questions 2 and 3 refer to the following information:
Bryan, Tyler, and John play a game with three possible strategies: Comics, Chess, and Opera. Their payoffs are:

Bryan 
Tyler 
John 
Everyone Plays
Comics 
10 
1 
2 
Everyone Plays
Chess 
1 
5 
5 
Everyone Plays
Opera 
4 
4 
4 
All Other Cases 
0 
0 
0 
2. True, False, and Explain: This game has one PSNE if the players play sequentially, but three PSNE if the players play simultaneously.
FALSE. For the simultaneous game, (Comics,
Comics, Comics), (Chess, Chess, Chess), and (Opera, Opera, Opera) are all PSNE
equilibria. But so is every
situation where each players plays a different
strategy: e.g. (Comics, Chess, Opera).
This gives everyone zero payoffs, but no individual can increase his
payoff by switching. For the
sequential game, there is only one subgame
perfect PSNE, where the first mover picks the strategy that he most prefers
everyone to play – Comics for Bryan, Chess for Tyler or John. But every PSNE in the simultaneous game
remains a PSNE in the sequential game.
3. A MSNE also exists.
True, False, and Explain: In this MSNE, Tyler is indifferent when:
P(Bryan plays Comics)*P(John plays Comics)=P(Bryan
plays Chess)*P(John plays Chess)=
P(Bryan plays Opera)*P(John plays Opera)
FALSE. This would only be true if all the
payoffs for Tyler were equal, which they are not. Tyler is actually indifferent when:
1*P(Bryan plays
Comics)*P(John plays Comics)=5*P(Bryan plays Chess)*P(John plays Chess)=
4*P(Bryan plays Opera)*P(John
plays Opera)
4. Consider a simple contestable monopoly model where an incumbent faces an equally productively efficient potential entrant. Both have constant marginal costs and zero fixed costs of production. Both firms know that there is a probability p that – if the incumbent remains in business – the government will prosecute the incumbent for antitrust violations. If this occurs, the incumbent loses a fixed cost K. The entrant never faces antitrust prosecution.
True, False, and Explain: Equilibrium quantity is decreasing in both p and K.
TRUE. pK
is effectively a fixed cost. Since
only the incumbent faces this cost, the entrant will inevitably drive him from
the market. The entrant chooses the
highest price consistent with driving the incumbent from the market, an epsilon
below the point where the incumbent’s AC curve intersects the demand
curve. The higher p and K, the
higher the incumbent’s AC, and the higher the price the entrant can
safety charge.
5. True, False, and Explain: With zero costs of production, Kreps (A Course in Microeconomic Theory) shows that consumers are better off in
a Stackelberg equilibrium than a Cournot equilibrium.
TRUE. Kreps shows that under Cournot, total
output equals 2(Ak)/3, while under Stackelberg, total output equals
3(Ak)/4. With zero costs of
production, k=0, so Cournot output equals 2A/3, while Stackelberg output equals
3A/4.
6. Consider the following oneshot game:

Attack 
Submit 
Attack 
1, 1000 
100,1 
Submit 
1,100 
50,50 
True, False, and Explain: There are two PSNE and one MSNE, but only
(Attack, Submit) is focal.
TRUE. This is just the HawkDove game, so
(Attack, Submit) and (Submit, Attack) are the two PSNE, and there is also a
MSNE. But given the fact that
(Attack, Attack) is extremely bad for
player 2, (Attack, Submit) is a strong focal point: Both players will look at
it and think “Player 2 won’t want to risk attacking.”
Part 2: Short Answer
(20 points each)
In 46 sentences AND/OR equations, answer all three of the following questions.
1. Are any of the main
assumptions of general equilibrium theory true in the real world? Carefully explain your answer.
The
assumptions that there are I
consumers, K commodities,
nonnegative consumption, and endowments are all trivially true; even an
endowment vector of all zeros is still an endowment. But none of the other assumptions are
empirically true:
a.
Utility is not increasing in all commodities, because some people actually
dislike some goods and/or reach satiation points.
b.
The market price vector is not continuous, because the penny is the smallest
unit.
c.
Given a price vector, people are sometimes indifferent between different
consumption bundles (e.g. blue shirts vs. green shirts), so U_{i}(p)
does not have a unique solution for everyone.
d.
There are some goods (e.g. air) where people satiate at price=0, so total
demand does not always exceed total endowment for a low enough price.
e.
There are lumpy goods and discrete reactions, so the total demand function is
not continuous in p_{k}.
2. Why does popcorn cost more at movies? You should either (a) offer an answer Landsburg fails to consider in The Armchair Economist, or (b) argue that Landsburg prematurely rejects the right answer.
I think Landsburg prematurely rejects the price discrimination story. Yes, there are many theaters, but they are hardly perfect substitutes for each other. Theaters are at best monopolistically competitive. Every theater has a least a mild geographic monopoly; people won’t want to drive an extra 15 minutes to cut the cost of popcorn by a $1. Why price discriminate on popcorn, but not the restrooms? Probably because of fairness norms: Theater goers would be very resentful if they had to pay extra to use the restroom, leading to less repeat business.
3. Compare the maximum deadweight costs of a government grant of monopoly to the deadweight costs of outright prohibition of a product. How would your answer change for a product with negative externalities? Use graphs to clarify your answer.
The
worstcase scenario for a government grant of monopoly is when (a) the
government gives the grant to a productively inefficient firm, and (b) there is
full rent dissipation during the struggle to get the grant. The only social benefit is the triangle
of consumer’s surplus under the demand curve and above the monopoly
price.
The
worstcase scenario for Prohibition is even worse: If the ban is strictly
enforced, all the surplus in the market is destroyed.
With negative externalities, however, a grant of monopoly or outright prohibition might actually be the most efficient policy. It depends on the severity of the externalities: You have to compare socially optimal output to output under perfect competition, monopoly, and prohibition. The larger the externality, the more likely monopoly (or even prohibition) will be welfareenhancing. For small externalities, however, it may be more efficient to have overproduction due to competition than underproduction due to monopoly.