Economics
812 Midterm
Prof.
Bryan Caplan
Spring,
2010
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 nine propositions is true or false. Using 23 sentences AND/OR equations, explain your answer.
1. True, False, and Explain: Landsburg’s
Indifference Principle undermines the standard efficiency rationale for taxing
negative externalities.
FALSE. The Indifference Principle implies that taxes
on e.g. air pollution raise rents, leaving tenants no better off. However, the owners of fixed resources are better off by an amount equal to the
increase in rent! In other words, the
Indifference Principle has implications for who
benefits from taxes on negative externalities, not whether these taxes have benefits.
2. Two types of agents consume guns (g) and butter (b). The Type A agents have U=.5 ln g + .5 ln b, and initially own 10 units of guns and 10 units of butter. The Type B agents have U=.3 ln g + .7 ln b, and initially own nothing. 10% of the agents are Type A; the other 90% are Type B.
True, False, and Explain: The equilibrium price of guns will equal the equilibrium price of
butter.
Using the formula from the
notes:
_{}.
But there’s no need to use
the formula. Since the Type B agents
have nothing to sell, they’re irrelevant to the market. And since the Type A agents have equal
endowments of both goods and value both goods equally, the price ratio has to
be 1:1. (To get full credit, you had to
note these facts).
3. True, False, and Explain: In an Ultimatum game, a 50/50 split is the only SGPPSNE; in a Dictator game, a 100/0 split is the only SGPPSNE.
FALSE. In an Ultimatum game, a 100ε/ε split is the only SGPPSNE; as long as the giver offers more than
0, the receiver has an incentive to accept, so the giver offers as little as
possible. (There are an infinite number
of PSNE, but only one is SGP). In the
Dictator game, a 100/0 split is the only SGPPSNE, because there’s no reason for
the giver to share anything.
4. Landsburg says that the “obvious” explanation for why popcorn costs more at movies is wrong.
True, False, and Explain: The problem with “obvious” explanation, according to Landsburg, is that even the simplest monopoly problem has multiple NE.
FALSE. The “obvious” explanation, according to
Landsburg, is monopoly. But under normal
assumptions, a monopolist would want to charge a high ticket price, then sell everything else (popcorn, bathroom
privileges, etc.) at MC.
5. Suppose
you have the following Hawk/Dove game.
Players do not discount the future.
In the one shot game, the two players flip a coin to decide who plays
Hawk and who plays Dove.


Player 2 

Player 1 

Hawk 
Dove 
Hawk 
100,100 
5,1 

Dove 
1,5 
4,4 
True, False, and Explain: If they
play this game twice, the players can
both on average earn more per turn than they would in the oneshot game.
TRUE. The players could agree to play Dove, Dove on
turn 1. Then, if either played Hawk in
turn 1, the other player would play
Hawk in turn 2. If both cooperate (or
both defect) in turn 1, they would flip a coin to decide who plays Hawk and who
plays Dove in turn 2. The result:
Players get [4+(.5*5+.5*1)]/2=3.5 per turn instead of 2*(.5*5+.5*1)/2=3 per
turn.
6. Suppose the government gives one car manufacturer a monopoly privilege. The lobbying process leads to full rent dissipation. Each firm has the same constant marginal cost of production, and demand is linear.
True, False, and Explain: Deadweight
costs fall when demand falls or firms’ costs increase.
TRUE. Under these assumptions, deadweight costs
equal the usual Harberger triangle plus the Tullock rectangle – and output
equals half the competitive level. (There’s
no productive inefficiency because firms have the same costs, and the shift
involves an increase in firms’
costs). If demand falls, both the
triangle and rectangle shrink. The same
happens if costs rise.
Part 2: Short Answer
(20 points each)
In 46 sentences AND/OR equations, answer all three of the following questions.
1. Consider a Cournot
model with two firms. P=10Q, and Total Cost=K for each firm. In equilibrium, all firms that produce must
be profitable, and all firms that can profitably produce do so. Graph market price as a function of K. Explain your reasoning.
Key
fact to remember: In the Cournot model, each firm’s revenue is given by: _{}. So if two firms
remain in the market, each earns 100/9 – K, and if only one firm remains, it earns
25K.
From
this we can immediately deduce that if K>25, zero firms will remain in the
market, and the effective price of the good will be infinite (since it’s no
longer available at any price).
If
K≤100/9, similarly, both firms stay in the market, and
we get the Cournot duopoly result: q=10/3, Q=20/3, P=10/3.
What
if 100/9>K>25? Then there’s only
one firm, and it charges the monopoly price – unless it foresees that this will
provoke entry. The monopoly price is 5, and the monopoly quantity is 5 as
well. Will charging the monopoly price
ever provoke entry? No. If the incumbent firm produces 5, an entrant
would maximize:
_{}, which reaches a maximum at q_{e}=2.5, which is only
profitable for K≤25/4, which is less than 100/9.
Bottom
line: For low K, there are two firms and the Cournot duopoly result. For medium K, there is one firm and the
monopoly result. For high K, there are
no firms at all.
2. In the real world, why don’t reputational incentives eliminate all fraud?
Some
of the obvious reasons: In the real world, time preference, number of turns,
and utility functions all vary widely – and none of them are knowable with
certainty. So in the real world, it is
often hard to tell whether or not reputational incentives will work – and
people often decide it’s better to just take their chances. Another key problem: In the real world,
honest mistakes happen, so trigger strategies just aren’t practical. But even setting all of these problems aside,
there’s a more fundamental reason why fraud will never disappear completely: As
the rate of fraud falls, so does the optimal level of effort to prevent fraud. But as antifraud effort falls, the incentive
for fraud increases. Think about this as
a game where sellers can be Honest or Dishonest, and buyers can either be
Trusting or Cautious. In the MSNE, 100%
Honesty will never be an equilibrium, because if 100% of sellers were Honest,
100% of buyers would be Trusting, which means that Dishonesty pays.
3. “Free
market economists typically express confidence in the ability of markets to
produce public goods... At the same time, free market economists tend to be
pessimistic about the stability of cartels in an unregulated market. If markets successfully produce local public
goods, however, why are stable cartels not more prevalent?” (Cowen and Sutter
1999)
Explain Cowen and Sutter’s argument using basic game theory. Does it make sense in the real world? Why or why not?
Their
argument is that producing public goods and maintaining cartels are both
Prisoners’ Dilemmas. (In fact, you could
say that “maintaining the cartel” is
a public good from the point of view of the participating firms). While is in the collective interest of members
to cooperate, it is in their individual interests to defect.
The
argument makes some sense in the real
world. Private production of public
goods and stable, voluntary cartels are both rare. However, there are some important
differences. Many people get a “warm
glow” from contributing to public goods production – showing a little altruism
makes them feel like better people. It’s
a lot harder for cartels to appeal to members’ altruism. Unions are a good exception – and it’s
interesting to note that unions often enroll a few percent of the workforce
even without government help. Another
point worth mentioning: The shortrun gains from undercutting a cartel are much
larger than the shortrun gains of refusing to contribute to a public
good. The firm that cheats on a cartel
can steal the whole market; the donor who cheats on a voluntary public good
just saves his donation.