Economics 812 Midterm

Prof. Bryan Caplan

Spring, 2008

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.  Suppose your P(more abortions cause less crime)=.4, P(Levitt’s research results | more abortions cause less crime)=.6, and P(more abortions cause less crime | Levitt’s research results)=.8.

True, False, and Explain:  If you satisfy Bayes’ Rule, your P(Levitt’s research results | more abortions don’t cause less crime) must be .1.

TRUE.  Let A=more abortions cause less crime, and B=Levitt’s research results, then apply Bayes’ Rule and solve for P(B|~A):

.8=.6*.4/(.6*.4+P(B|~A)*.6)

.8=.24/(.24+P(B|~A)*.6)

so P(B|~A)=.1.

2.  True, False, and Explain:  If a state of affairs is Pareto efficient, then deadweight costs must be zero.

FALSE.  If a state of affairs is K-H efficient, then deadweight costs must be zero.  But Pareto efficiency does not imply K-H efficiency; in fact, most Pareto efficient situations are not K-H efficient.  Monopoly is a classic example: There are deadweight costs, but there is no feasible way to get rid of the deadweight costs without making the monopolist worse off.

3.  Suppose you have a betting market where half the participants are certain that Clinton will win the Democratic nomination, and the other half are certain that Obama will win.

True, False, and Explain: A general equilibrium will not exist.

TRUE.  If both sides are certain, they are willing to bet an infinite amount, and put zero value on claims that pay off if the other side is right.  (This is basically a problem of lexicographic preferences).  However, if short sales are not allowed, then the most each side can bet is their total assets.  If so, a general equilibrium will exist equal to the ratio of the amount each side bets.  (I gave full credit for FALSE if they discussed both possibilities).

4. Suppose a pirate robs ten people and puts all of their money inside a treasure chest.  When the police recover the chest (and before the pirate can spend a penny), they ask each of the ten victims to state how much money he lost.  To discourage lying, the police announce that if the total losses claimed by the victims exceeds the total amount of money in the chest, none of the victims will get any money back.

True, False, and Explain:  There is a unique NE in which every victim says the truth.

FALSE.  Truth-telling is one NE, and probably a focal NE.  But there are infinitely many NE: Any set of claims that sums to the total amount of money qualifies.

5. Suppose that two players play this PD game, followed by this Coordination game.

 Don’t Defect L R Don’t 3,3 0,4 L 5,5 0,0 Defect 4,0 2,2 R 0,0 5,5

True, False, and Explain: If ß=.5, the only SGPNE are (Defect, Defect), (L,L) and (Defect, Defect), (R, R).

FALSE.  Since both (L,L) and (R,R) pay the same, it might seem like punishment is impossible in turn 2.  However, this ignores the MSNE, which has an expected payoffs of (2.5, 2.5).  If players threaten to play the MSNE in turn 2 if someone plays Defect in turn 1, we have a NE as long as:

3+5β≥4+2.5β.  So if β=.5, we have 5.5≥5.25, implying a NE.

6.  If your rival(s) suspect that you are not rational, or even if they suspect that you suspect that they suspect that you aren’t rational, then the ‘rational’ actions for you can be quite different than if you ignore this possibility.” (Kreps, A Course in Microeconomic Theory)

True, False, and Explain:  This point explains why threatening to fail students for leaving early does not work in the real world.

FALSE.  Kreps’ point explains why threatening to fail students could work!  If everyone knows everyone is fully rational, there is no point threatening to fail students because no one believes you will do it.  But if you suspect that someone is irrational, or suspect that someone suspects that you are irrational, a “crazy” threat just might work.

7.  Suppose that two firms flip a coin, then play a contestable monopoly game with sunk costs.

True, False, and Explain: The coin flip allows the firms to raise their expected profits, even though the set of equilibria in the contestable monopoly game does not change.

TRUE.  With or without the coin flip, this game has a MSNE where expected profits are zero, and two PSNE where one firm earns monopoly profits and the other earns nothing.  However, if firms play simultaneously, neither of the PSNE is focal.  Flipping the coin creates a focal point: If the coin says heads, then firm 1 plays In and firm 2 plays out; if the coin says tails, the reverse happens.  This doesn’t change the set of equilibria, but it does make it easier for firms to reach the profitable equilibria.

8.  True, False, and Explain:  In a market with perfectly selfish consumers and producers, the existence of a public good implies both allocative and productive inefficiency.

FALSE.  A public good implies that market output is roughly zero, so there will be no productive inefficiency.  However, there will be massive allocative efficiency – all the area between the SB curve and the cost curve disappears.  When a good is not produced at all, the effective price is infinite, so P>>MC.

9.  Suppose that two firms compete in a market with linear demand and zero costs.

True, False, and Explain:  Collusion is easier to sustain in the Cournot model than it is in the Bertrand model.

FALSE.  From the notes, Bertrand collusion is feasible as long as β≥.5, but Cournot collusion is feasible as long as β≥.53.  This means that greater patience is necessary to sustain Cournot collusion.

(20 points each)

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

1.  Suppose country A has 1000 skilled workers and 1000 unskilled workers, and country B has 0 skilled workers and 10,000 unskilled workers.  Both countries initially prohibit all immigration.  Build on the Second Welfare Theorem to propose a Pareto-improving policy reform.

The K-H efficient outcome requires free migration, so skilled workers can move to country B, and unskilled workers can move to country A.  However, unskilled workers in country A are likely to suffer massive wage declines as a result of this move.  Fortunately, this is a very simply economy, so it is not difficult to create Pareto improvements using redistribution as the Second Welfare Theorem suggests.  The simplest solution would be to charge unskilled workers from B an entry fee and skilled workers from A an exit fee, and give the revenue to unskilled workers from A.

2.  Why does popcorn cost more at movies – and how is this possible in a market with free entry?  If you give an answer that Landsburg rejects, you must explain why he is wrong to reject your answer.

Landsburg ignores a simple possibility: Popcorn prices are high due to price discrimination, which is entirely possible because the market for movie theaters – like most retail! – is imperfectly competitive.   There are only a few movie theaters in a given area, and even these are imperfect substitutes.  They can charge P>MC and/or price discriminate because – due to fixed costs – existing firms are just breaking even, and new entrants are likely to actually lose money.

3.  Suppose two strangers meet on a desert island.  Is mutual warfare a NE?  A likely NE?  A unique NE?   Use all of the game theory you have learned – and common sense – to answer the question.

Since the question says “common sense,” I’m going to tell you what I think is really going on – not just repeat a model from class.  Here goes: Unless there are big differences in fighting ability between the two people, or only enough food for one person, mutual peace is probably the unique NE.  If both people play peace, they probably more than double their total output, and gain a friend as well.  If either person plays war, both lose these benefits, and risk severe injury even if they win the fight.  Realistically, if one person is stuck on an island, and another washes up on shore, the first person doesn’t start sharpening his spear.  Instead, he rushes to help out the new arrival, because he reasonably expects him to become a great ally.