Economics
812 Midterm
Prof.
Bryan Caplan
Spring,
2007
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: One benefit of the war on drugs that
Landsburg's efficiency analysis overlooks is the salaries paid to the extra
government employees required to enforce these laws.
FALSE. The salaries paid are actually a social cost, because the government employees
could have done something else instead with their time. If the employees' opportunity cost equals
their current wage, then their entire salaries are a social cost; if they are
paid more than their opportunity cost, then the difference between their actual wage and their alternative wage is
a transfer, and the remainder is a social cost.
Students
who answered false on the grounds that the salaries are a transfer got a little
credit, but not much.
2. True, False, and Explain: Contestable
monopoly leads to "secondbest" efficient outcomes, whereas Bertrand
competition leads to "firstbest" efficient outcomes.
FALSE. If there are zero fixed costs and the most
efficient firm faces an equally efficient competitor, both yield the firstbest efficient outcome of P=MC. If there are fixed costs and the most
efficient firm faces an equally efficient competitor, both yield the secondbest efficient outcome of P=AC. If the most efficient firm does not face an
equally efficient competitor, then price can exceed both MC and AC.
3. There are two
islands with equal numbers of agents.
All agents live for two periods and are endowed with 1 unit of a consumption
good in period 1 and 1 unit in period 2.
The period 1 good spoils if not consumed in period 1. On the
True, False, and Explain: If trade between islands is possible, the interest rate will exceed
50%. If trade between islands is not
possible, the interest rate on
FALSE. With trade, the interest rate will indeed
exceed 50%. Using the GE formula:
_{}, an interest rate of 200%.
However, with isolated islands,
Questions 4 and 5 refer to the following game:

Trust 
Doubt 
Truth 
2,2 
0,0 
Lie 
4,2 
2,0 
4. This game has two PSNE, plus a MSNE where players play (Truth, Trust) with probabilities (.5,.5).
FALSE. There are zero PSNE, but the MSNE given is
correct. For the PSNE, notice that at
(Trust, Truth), Player 1 wants to switch; at (Truth, Doubt) Player 2 wants to
switch; at (Trust, Lie) Player 2 wants to switch; and at (Lie, Doubt) Player 1
wants to switch. For the MSNE,
similarly:
Player
1 is indifferent when:
2σ+0(1σ)=4σ2(1σ),
implying σ=.5.
Player 2 is indifferent when:
2φ2(1φ)=0, implying φ=.5.
5. Suppose both players have a discount rate, β=1, and play this game twice.
True, False, and Explain: There
is a NE where players play (Truth, Trust) in the first turn, and the MSNE of
the oneshot game in the second turn.
FALSE. Since this is a finitelyrepeated game, and
there is only one equilibrium in the second game, the only equilibrium is to
play the MSNE each turn. After all, if
Player 1 switches to Lie in turn 1, how is Player 2 going to punish him?
6. Two players play an Ultimatum game, followed
by a Coordination game.
True, False, and Explain: There
are an infinite number of SGPPSNE, some of which have a 50/50 split in the
first turn.
TRUE. As long as one Coordination game has lower
payoffs for Player 1, there is a viable threat.
Suppose, for example, that:
·
β=1
·
in turn 1, the
players are splitting 2
·
in turn 2 (Left, Left) yields a payoff of (5,5) and
(Right, Right) yields a payoff of (3,3) (and of course (Left, Right) and
(Right, Left) yield (0,0)).
Then
the following is an equilibrium: in turn 1, a 50/50 split; in turn 2, (Left,
Left) if Player 1 offered at least 50/50 in turn 1, and (Right, Right)
otherwise. If player 1 offers 100/0
instead of 50/50, he gains 1 in turn 1, but loses 2 in turn 2.
Now
notice that since payoffs are continuous, this is just one out of an infinite
number of equilibria. The above approach
could also sustain 50.01/49.99, 50.02/49.98, etc.
7. Suppose there are two firms able to produce a good. Firm #1 has TC=$50 + $0Q; Firm #2 has TC=$0 + $10Q. The demand curve is given by Q=20P.
True, False, and Explain: Firm #1 will drop out of the market and Firm
#2 will charge the monopoly price.
FALSE. By producing 10.01 units and charging $9.99,
Firm #1 can make a profit of 10.01*$9.99$50, or approximately $50. But Firm #2 loses money at this price, so it
will drop out of the market.
Intuitively, since Firm #1 has fixed costs but no marginal costs, and
Firm #2 has marginal costs but no fixed costs, the thing to check is whether
Firm #1 remains profitable at a price just below Firm #2's MC.
8. Suppose two Bertrand competitors collude in an infinitelyrepeated game, but the first firm insists on getting the "lion's share" of the profits. The first firm gets 90% of the monopoly profits. The second firm gets the remaining 10%.
True, False, and Explain: This
is a NE as long as β≥.1 for both firms.
FALSE. The first firm will not defect as long as _{}, so its β≥.1. But the second
firm will defect unless: _{}, so its β≥.9.
9. Satellite television has enormous fixed costs, but nearzero marginal costs. Suppose the current market structure, where two firms (Dish Network and Direct TV) supply satellite television, was the outcome of Cournot competition with free entry. Suppose further that no additional entry is legally allowed.
True, False, and Explain: A
merger to monopoly will increase productive efficiency, hurt allocative
efficiency, and decrease overall efficiency.
FALSE. The merger will increase productive
efficiency by halving fixed costs.
(Students who explicitly claimed that all costs were sunk got full
credit, though that's got to be incorrect – there are lots of alternative uses
for satellites, and they eventually have to be replaced). And in the Cournot model, going from 2 firms
to 1 reduces allocative efficiency.
However, the net efficiency
effect is ambiguous, because we do not know the relative sizes of the two
effects.
Part 2: Short Answer
(20 points each)
In 46 sentences AND/OR equations, answer all three of the following questions.
1. "As with other fundamentals of
action, doubts about probability are selfrefuting." (Caplan,
"Probability, Common Sense, and Realism.") Carefully explain Caplan's argument. Is he right?
Caplan
claims that arguing against probability is selfrefuting because (a) people
argue against it in order to change others' minds, even though (b) they know
that arguing against probability does not always work. As he states in his article:
One cannot even argue against
probability theory without implicitly holding some belief about the probability
that doing so will change listeners’ minds. Few Misesians would be naive enough
to imagine that attacking probability theory has to reduce its number of adherents. Rather, they attack
probability theory because, given their beliefs about the probability of
changing people’s minds, they see it as the most valuable way to use their
time. Any attack on probability presupposes it.
The
best objection a student offered is that people might argue just for the fun of
it, even though they don't believe that they have any chance of persuading anyone. I would reply that, even in this case, they must
assign some probability to the view "Arguing against probability will be
fun."
2. N players are deciding whether to contribute
to a public good. The public good is discrete: it is produced at the
optimal level so long as one person contributes. If the public good is
produced, everyone gets a benefit of 3 if they didn't contribute, and 2 if they
did. If no one contributes, everyone
gets 0. Find the MSNE. When is the MSNE KaldorHicks efficient?
(Hint: If p is the probability that one player contributes, the probability that no other player contributes equals _{}, and the probability that at least one other player contributes is _{}).
If
you contribute, then you get (31)=2 for sure.
If you don't contribute, you get 3 if at least one other player
contributed, and 0 otherwise. Therefore,
by symmetry, each player is indifferent if:
2=0*_{}+3*(_{})
This
implies indifference when _{}, implying that _{}.
The
MSNE is efficient in all cases where one and only one player contributes.
Students
who correctly solved the 2player version got substantial partial credit.
3. Throughout history, the usual system has been for heads of state (such as kings) to serve for life. In modern times, however, heads of state often leave office voluntarily long before their deaths. Using all of the game theory you have learned, provide the best possible explanation for both of these patterns. Why has there been a transition from one pattern to the other?
Here
is one possible answer:
Historically
and today, the system of government succession is a Coordination game with
culturally determined focal points. When
people expect leaders to serve for life, remaining in office provokes little
negative reaction. Stepping down, in
contrast, signals weakness and confusion  which invite attack. However, when people expect leaders to step down after their term expires, a leader who refuses
to leave office seems powerhungry or crazy, which typically provokes negative
responses from other leaders and the population. In contrast, stepping down when people expect
it is not a sign of weakness or confusion, so leaders aren't scared to do
so. The bottom line is that it is usual
safest for leaders to do what people expect, and dangerous to do the opposite.
Why
did this transition occur? My short
answer is that revolutions and elite ideological change in favor of democracy
gradually changed cultural expectations.
If you built a skyscraper in NYC that was twice the size of the