Economics
812 Midterm
Prof.
Bryan Caplan
Spring,
2011
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. Two types of agents live for two periods. In each period, they receive an endowment of perishable consumption goods – storage over time is not possible. Type A agents have U=ln c_{1} + ß ln c_{2}; Type B agents have U= ln c_{1} + ρ ln c_{2}. Both types of agents are equally numerous and have endowments of 1 in each period.
True, False, and Explain: The equilibrium interest rate r equals 2/(ß+ρ).
FALSE. (1+r)
equals the price ratio of period 1 consumption to period 2 consumption. So just normalize the utility functions to
be:
_{} and _{}
Then apply the 2good GE formula from lecture:
_{}. Since this is equal
to (1+r), r=_{}1,
which does not equal 2/(ß+ρ).
2. Consider the following normal form:

Left 
Right 
Left 
1,1 
0,0 
Right 
0,0 
2,2 
True, False, and Explain: If two players play this game sequentially,
there are three NE but only one SGPNE.
FALSE. Played sequentially, there are only TWO NE
(L,L) and (R,R). The MSNE from the
simultaneous version of the game does not exist, because if player 1
randomizes, player 2 gets to see whatever he played, and will therefore copy
whatever he did with certainty. Out of
the two NE, only (R,R) is SGP. You can
show this with backwards induction: since player 1 knows that player 2 will
match him in the second turn, he always wants to play R.
Questions 3 and 4 refer to the following information:
An Incumbent and an Entrant infinitely repeat the following game.

Enter 
Don’t Enter 
Predate 
10,10 
10,0 
Don’t Predate 
2,2 
10,0 
Consider the candidate equilibrium where the Incumbent always plays Don’t Predate, and the Entrant plays Enter until the Incumbent plays Predate once. After the Incumbent plays Predate, the Entrant never plays Enter again.
3. True, False, and Explain: This is not a NE unless the Incumbent’s discount factor is less than .6.
FALSE
(but see below). Playing the candidate
equilibrium is Nash if:
_{}. This simplifies to:
_{}, so _{}. Since deviating has
a shortrun cost and a longrun benefit, low discount rates are required
to sustain the equilibrium.
If
you answered TRUE and said the above, I gave you full credit. Technically, though, since the question says
“less than .6” rather than “less than or
equal to .6,” the correct answer is FALSE.
4. Suppose that every turn, there is a p>0 that the entire industry disappears due to exogenous technological innovation.
True, False, and Explain: Predation may still be sustainable.
TRUE. You could interpret β as a continuation probability (1p) rather than a
discount factor and just use the math for Question 3. Or you just revise the inequality, flip the
sign, and solve. Predation is
sustainable as long as:
_{}, implying:
_{}.
5. True, False, and Explain: Bertrand
competition between identical firms with fixed costs yields a secondbest
efficient outcome.
TRUE. The firstbest outcome is when one firm
produces at MC, avoiding any allocative inefficiency from P>MC (the
Harberger triangle). But in Bertrand
competition with fixed costs, competition leads one firm to drop out, and the other to set P=AC – a standard
secondbest result. At lower prices,
firms would lose money and exit.
Bertrand competition will NOT lead to wasteful duplication of fixed
costs; if it did, either firm could profit by slightly cutting its price and
stealing all its competitors’ customers.
6. Consider the following oneshot game:

Attack 
Submit 
Defend 
Attack 
10,10 
5,3 
20,5 
Submit 
3,5 
0,0 
0,1 
Defend 
5,20 
1,0 
1,1 
True, False, and Explain: There
is a MSNE, but no PSNE.
FALSE. Defend is strictly dominated by Submit for
both players, so this game simplifies to a standard Hawk/Dove game with the
four upperleft cells. In such games,
there are two PSNE – (Attack, Submit) and (Submit, Attack) in this case, plus a
MSNE.
Part 2: Short Answer
(20 points each)
In 46 sentences AND/OR equations, answer all three of the following questions.
1. “People may be unable to articulate, for example, that ‘I would be willing to pay $200 per month in additional rent to live in a safer neighborhood.’ They might even nonsensically assert that ‘You can’t put a price on safety.’ But in acting, they implicitly make such tradeoffs.” (Caplan, “Probability, Common Sense, and Realism”)
What objection to probability theory is Caplan trying to answer? Does he succeed?
Caplan is answering the objection that probability
theory is unrealistic because normal
people rarely explicitly calculate probabilities. He argues that probability is no more
unrealistic than the standard assumption that people have a willingness to
pay. Normal people rarely explicitly
state their willingness to pay, but their behavior reveals that they still have a willingness to pay. Similarly, normal people rarely explicitly
state their probabilities, but their behavior shows that they have probabilities. As Caplan writes, “In short, just as demand theory does not commit us
to the view that the typical person explicitly ponders, ‘How much Gouda cheese
would I buy if the price were a penny per pound? probability theory does not
commit us to the view that the typical person explicitly ponders, ‘What is the
probability that I have an evil twin?’”
2. Modify the Hawk/Dove game to explain why in the real world – unlike Thomas Hobbes’ Leviathan – two shipwrecked people are unlikely to try to murder each other. Carefully explain why your model is a good description of the choices and payoffs that human beings would actually face in this situation.
The
simplest way to modify the Hawk/Dove game is to change the payoffs. In the real world, (Dove, Dove) is usually
more profitable for both parties than (Hawk, Dove) or (Dove, Hawk). Unilateral aggression could easily lead to
the breakdown of trust and cooperation, and require frequent, costly
monitoring. And depending on how
“dovish” Dove is, unilateral aggression might even result in some costly
injuries for the aggressor as well as the victim. As a result, Dove becomes a strictly dominant
strategy.
You could simply keep the usual Hawk/Dove payoffs and model the situation as a repeated game, but then you’d have to explain why repeated play seems likely to lead to cooperation rather than a struggle for dominance. Focal points, perhaps?
3. With full rent dissipation,
roughly what would U.S. rentseeking as a percentage of GDP be? Is this a reasonable estimate of actual U.S. rentseeking
as a percentage of GDP? If not, what is
the best explanation for the discrepancy?
With
full rent dissipation, you’d expect U.S. rentseeking would equal government
spending as a percent of GDP, roughly 40%.
This is an unrealistically high estimate; nothing like 40% of GDP is
spent on lobbying, however broadly defined.
The best explanation for the discrepancy is that most government
spending is NOT up for grabs. Politicians
largely have to satisfy voters to keep their jobs, and voters want money for
the elderly, defense, etc., not whoever lobbies the most. You could also observe that even with full
rent dissipation, 40% is an overstatement unless lobbyists are allowed to
simply keep their money without offering any costly goods and services in
exchange.