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 2-3 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 100-ε/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 one-shot 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.

(20 points each)

In 4-6 sentences AND/OR equations, answer all three of the following questions.

1.  Consider a Cournot model with two firms.  P=10-Q, 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 25-K.

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 K100/9, 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 qe=2.5, which is only profitable for K25/4, 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 anti-fraud 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 short-run gains from undercutting a cartel are much larger than the short-run 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.