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 2-3 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 "second-best" efficient outcomes, whereas Bertrand competition leads to "first-best" efficient outcomes.

FALSE.  If there are zero fixed costs and the most efficient firm faces an equally efficient competitor, both yield the first-best efficient outcome of P=MC.  If there are fixed costs and the most efficient firm faces an equally efficient competitor, both yield the second-best 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 Island #1, agents have U=ln c1; on Island #2, agents have U=ln c1 + ln c2.

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 Island #1 will exceed the interest rate on Island #2 by less than 100 percentage-points.

FALSE.  With trade, the interest rate will indeed exceed 50%.  Using the GE formula:

, an interest rate of 200%.  However, with isolated islands, Island #1 will have an infinite interest rate (since no one values c2), and Island #2 will have a 0% interest rate (since the two goods are equally abundant and equally valued).  Thus, Island #1's interest rate infinitely exceeds Island #2's.

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(1-σ)=4σ-2(1-σ), implying σ=.5.

Player 2 is indifferent when:

2φ-2(1-φ)=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 one-shot game in the second turn.

FALSE.  Since this is a finitely-repeated 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=20-P.

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 infinitely-repeated 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 near-zero 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 4-6 sentences AND/OR equations, answer all three of the following questions.

1.  "As with other fundamentals of action, doubts about probability are self-refuting." (Caplan, "Probability, Common Sense, and Realism.")  Carefully explain Caplan's argument.  Is he right?

Caplan claims that arguing against probability is self-refuting 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 Kaldor-Hicks 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 (3-1)=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 2-player 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 power-hungry 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 Empire State Building, the focal meeting place in NYC might change.  Similarly, after a democratic revolution, or after decades intellectual activism for democracy, the focal political system in a society might change.