Economics
812 Midterm Answer Key
Prof.
Bryan Caplan
Spring,
2006
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 2-3 sentences AND/OR equations, explain your answer.
1. Situation A is a Kaldor-Hicks improvement over Situation B. Situation A is Pareto efficient.
True, False,
and Explain: Situation A must also be Kaldor-Hicks efficient.
FALSE. Just because A is a Kaldor-Hicks improvement
over B does not imply that there isn't another situation that would be a
Kaldor-Hicks improvement over A. The
additional information that A is Pareto efficient is irrelevant, because
virtually all situations are Pareto efficient.
2. Suppose 50% of all agents are certain (p=1)
that occupation of
True, False, and Explain: A general equilibrium can only exist if the prices of the two bets are equal.
FALSE. Assuming agents cannot sell short, the price
ratio will depend upon the amount that
people are willing to bet, which in turn depends upon wealth. If the people who believe that the invasion
will reduce terrorism are willing on average to bet twice as much as the people
who believe the opposite, for example, the betting market will clear when the
"reduce" bet pays half as much as the "increase" bet.
In
agents can sell short (or, equivalently, just issue notes offering to pay $1 if
X happens), there is no equilibrium. Due
to their certainty, both sides would happily offer offer an infinite amount of
notes that pay off if the other side turns out to be right, so the price ratio
would be undefined.
3. True, False, and Explain:
According to Kreps, economic experiments
confirm that general equilibrium analysis has little predictive value.
FALSE. On p.198, Kreps says exactly the opposite:
"The results obtained are usually striking in their support of Walrasian
equilibrium."
Questions 4 and 5 refer to the following game:
|
Left |
Right |
Left |
2,1 |
0,0 |
Right |
0,0 |
1,2 |
4. This game has a MSNE with expected payoffs equal to (1.5, 1.5).
FALSE. To make Player 2 indifferent, Player 1 plays
L with probability σ:
1σ+0=0+2(1-σ), so
σ=2/3
To make Player 1 indifferent, Player 2 plays L with
probability φ:
2φ + 0=0 + (1-φ), so φ=1/3
To find expected pay-offs, simply plug the
probabilities back into the above equalities: the expected payoffs in
equilibrium are (2/3, 2/3). Alternately,
you could note that (L,L) happens 2/9 of the time, (R,R) happens 2/9 of the
time, and something else happens 5/9 of the time, so expected payoffs for
Player 1 are 2/9*2+2/9*1+5/9*0=2/3, and expected payoffs for Player 2 are
2/9*1+2/9*2+5/9*0=2/3.
5. True, False, and Explain: Played
simultaneously, this game has two SGPPSNE.
Played sequentially (with Player 1 moving first), this game has two
PSNE, but only one is SGP.
TRUE. The simultaneous game only has one subgame,
so both (L,L) and (R,R) are SGPNE. The
sequential game still has two PSNE: Player 1 will play L if he believes Player
2 will play L, and R if he believes Player 2 will play R. However, once Player 1 plays L, Player 2
would definitely want to play L too, so by backwards induction, only (L,L) is
SGP.
6. Suppose there are two firms able to produce a good. Firm #1 has TC=$1000 + $0Q; Firm #2 has TC=$0 + $10Q.
True, False, and Explain: If demand goes up high enough, Firm #1 will
drop out of the market and Firm #2 will set its price just below Firm #1's AC.
FALSE. The opposite holds: Firm #2 has lower AC at
low quantities, but Firm #1 has lower AC at high quantities. If quantity>100, Firm #1 can charge just
below $10 and take the whole market at a profit.
7. True, False, and Explain: If firms set prices (as opposed to
quantities), firms would never want to split into additional firms, even
if the game were infinitely repeated and β=1.
FALSE. If β=1, Bertrand
collusion is definitely sustainable, and if each firm gets an equal share of
the monopoly profit, then splitting could increase your profits from a 1/N
share of the monopoly profit to a 2/(N+1) share, which is greater for N>1.
Firms
might also want to split if there are diseconomies of scale, though I gave less
credit for this answer since it didn't use the information about repeated play
and the discount rate.
8. 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 1 person contributes. Contributing costs the individual who contributes C, and 0 otherwise. If the public good is produced, everyone gets a benefit of B; otherwise they get a benefit of 0. B>C.
True, False, and Explain: There are
two PSNE, only one of which is Kaldor-Hicks efficient.
FALSE. There are
9. In Leviathan,
Hobbes argues that, in the absence of government, individuals always prefer war
to peace, leading to a "war of all against all" equilibrium.
True, False, and Explain: This
precisely what the Hawk/Dove game predicts.
FALSE. For PSNE, the Hawk-Dove game predicts that
you will never see universal war;
instead, you'll see one aggressor and one appeaser. In the MSNE of the Hawk-Dove game, (War, War)
can occur, but it is an unlucky coincidence, not a typical result.
Part 2: Short Answer
(20 points each)
In 4-6 sentences AND/OR equations, answer all three of the following questions.
1. Give an example of lexicographic
preferences. How can lexicographic
preferences preclude the existence of a general equilibrium? Is it possible for a general equilibrium to
exist given the existence of lexicographic preferences? Explain.
I lexicographically preference my sons' lives to money – I wouldn't part with them for any amount of money. Lexicographic preferences can preclude the existence of general equilibrium because if everyone shares the same preferences, they won't sell the lexicographically preferred good to buy more of other goods at any p>0 – but if the price of other goods falls to 0, they want more of these other goods than exist. There are many ways that general equilibrium could co-exist with lexicographic preferences: (1) Some people have these preferences, others don't, and the former buy all of the lexicographically preferred good from the latter; (2) People have different lexicographic preferences; (3) People only have lexicographic preferences up to a certain quantity (e.g. everyone might have a lexicographic preference for one kidney, but not two).
2. Coordination equilibria are often persistent, but they also change. Give a real-world example. Then use game theory to explain how this change happened, paying particularly close attention to the incentives of the "first-movers."
My
example: It used to be almost impossible to publish survey research in
economics, and as long as no one would publish it, no economist wanted to do
it. This is no longer true. The reason is probably that there were some
economists who were burning to do
survey research, so they worked on it even when the chance of publication was
low. But once they published some work,
this raised the payoff. This led
slightly less enthusiastic economists to try survey research, which raised the
chance of publication, which led to more survey research... Heterogeneous preferences were the lever that
got the survey research ball rolling.
Another
class of good answer focused on the importance of market leaders. A market leader thinks that other people will
change if he changes too, so he feels safer doing something different. Continuing with my example, many of the
economists who started doing survey research – like Alan Blinder – were already
famous for other accomplishments. So they
could expect people to take them seriously even if they "broke the
rules," which helped change the rules.
3. Landsburg (The Armchair Economist) argues that laws restricting cosmetic surgery are an inefficient restriction on competition. Using the game theory you have learned so far, present and defend what you see as the strongest possible counter-argument to Landsburg's claim. (You don't have to agree with your argument; just present it as forcefully as possible).
You
can't just say that cosmetic surgery is a "Prisoners' Dilemma" for
women, because efficiency calculations require us to count the value to both
women AND men. (Analogously, you can't
just say that price supports are efficient because they benefit sellers; you
have to show that the gain to sellers outweighs the gain to buyers). Similarly, you can't just say that more
cosmetic surgery reduces the supply of non-cosmetic surgery: That's true for
all goods. Better answers:
Maybe
men value relative beauty, not absolute beauty; they want to marry a woman who
is better-looking than other women, but
don't particularly care how good-looking she is in absolute terms. If so, cosmetic surgery burns up resources
without making the average woman OR the average man better off.
Maybe people directly disvalue the average level of cosmetic surgery in their society, on the grounds that it "commodifies" or "cheapens" life. But since the average level of cosmetic surgery is non-excludable, no one factors it into his/her decisions, leading to too much cosmetic surgery. This is a common objection to e.g. human cloning.