Economics 812 Midterm Answer Key

Prof. Bryan Caplan

Spring, 2016

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 2-3 sentences AND/OR equations, explain your answer.

1.    Suppose all the assumptions of the First Welfare Theorem are true.

True, False, and Explain:  Markets are Pareto and Kaldor-Hicks efficient.

TRUE.  The First Welfare Theorem assumes no externalities, perfect information, and an exogenous price vector, and proves markets are Pareto efficient.  Given these assumptions, moreover, people sell ANYTHING they possess that ANYONE else values more highly than they do, so markets maximize total surplus and are therefore K-H efficient.

Most students answered FALSE, citing the notes on the fact that Pareto efficiency does not imply K-H efficiency.  This is true in the real world, but the assumptions of the First Welfare Theorem are so unrealistic that both Pareto and K-H efficiency follow!

2. Suppose 45% of all agents in an economy have U=ln x + ln y, and the other 55% have U=.75 ln x + .25 ln y.  All agents start with one unit of x and two units of y.

True, False, and Explain:  In general equilibrium, exactly 55% of the agents consume more y than x.

FALSE.  100% of agents consume more y than x.  To see this, first calculate the equilibrium price vector:

This implies all agents have income of 1*3.52+2*1=5.52.  Type 1 agents spend 50% of this income on x, 50% on y, so they consume 5.52*.5/3.52=.784 x and 5.52*.5/1=2.76 y, so y>x for them.  Type 2 agents spend 75% of their income on x, 25% on y, so they consume 5.52*.75/3.52=1.18 x and 5.52*.25/1=1.38 y, so y>x for them too.

3.    Suppose that two players play the following three games in order: Coordination game, Prisoners' Dilemma, Ultimatum game.

True, False, and Explain: Standard game theory predicts that this game will completely "unravel."

TRUE.  “Unraveling” means players play each stage of the game as if it were not repeated.  The last stage – the Ultimatum game – has only one SGPNE, where Player 1 offers \$.01 and keeps the rest for himself, and Player 2 accepts.  As a result, standard game theory says players cannot use punishments to avoid the standard (Defect, Defect) outcome in the PD stage.  This in turn implies that players treat the first stage – the Coordination game – as if it were a one-shot game.  Hence, complete unraveling.

4. “But once you’re in the theater, the owner has a lot of monopolies. He is the only supplier of rest rooms, for example. Why doesn’t he charge you a monopoly price to use them? (Landsburg, The Armchair Economist)

True, False, and Explain:  Landsburg concludes that customer diversity, not supplier monopoly, explains why popcorn costs more at movies.

FALSE.  Landsburg concludes you need BOTH diversity AND some degree of monopoly (i.e., imperfect competition): “Price discrimination can only work when the seller has a monopoly of the appropriate kind.”  Monopoly without diversity leads to high ticket prices and MC pricing for popcorn and other extras. Diversity without monopoly leads to MC pricing for everything.

5.  Suppose two players play the following normal form N times.  N is finite and known by both players.

 Left Right Left 5,1 0,0 Right 0,0 1,5

True, False, and Explain: Alternating back and forth between (L,L) and (R,R) is an equilibrium as long as N is even and β<1.

FALSE.  Alternating back and forth is ALWAYS an equilibrium.  Defecting reduces your payoff from 5 or 1 to 0, so there is no temptation to “cheat” regardless of number of turns or discount rate.

6.  Consider a Cournot model with two firms.  P=20-Q, and MC=0.

True, False, and Explain:  If one firm moves first, the unique SGPNE has a higher Q than it does with simultaneous play.

TRUE.  With simultaneous play, the Cournot notes tell us market output is 2/3*20=13.3.  With sequential play, player 2 sets q2=(20-q1)/2, so player 1 maximizes Pq1=(20-q1-(20-q1)/2)q1.  Differentiating implies 10-q1=0, so q1=10, and q2=(20-10)/2=5.  So q1+q2=15<13.3.

Part 2: Short Answer

(20 points each)

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

1. Construct a “second-best” efficiency defense of ONE existing policy you consider highly inefficient in a “first-best” sense.  Be as convincing as possible.

Under current U.S. law, extremely rare, highly unpopular religions like Satanism are legal.  This seems highly inefficient in a first-best sense: the total willingness of religious people to pay to ban Satanism probably vastly exceeds the totally willingness of Satanists to pay to keep their religion legal.  However, politically drawing the line between religions like Satanism and moderately unpopular religions like Scientology is extremely contentious, and risks banning religions that DO pass the cost-benefit test because their followers love them and they only mildly annoy the majority.  These costs and risks make across-the-board religious toleration a second-best optimum: While we have to tolerate a few inefficient religions, we avoid religious conflict and “false positives.”

2. “[I]t seems that the basic textbook commentary on bilateral monopoly and bargaining had it right.” (Kreps, A Course in Microeconomic Theory)  Carefully explain (a) what Kreps is claiming here, and (b) why he claims it.  Does a MSNE view of bargaining lead to a different conclusion?

Kreps is claiming that, according to standard textbook treatments, “bargaining outcomes depend on individual’s expectations as to what the outcomes should be”; furthermore, such expectations can be “manipulated.”  He claims this because experiments show precisely this: Playing bargaining games with computers that demand 20% of the surplus subsequently leads human beings to bargain harder with other humans than playing bargaining games with computers that demand 50% of the surplus.  The MSNE view leads to a somewhat different conclusion: While expectations do matter, some expectations are not stable.  In particular, if people expect too much, lowering your expectations leads to higher payoffs – and if people expect too little, raising expectations leads to higher payoffs.

3. What is the most empirically relevant model our class has studied so far?  The least empirically relevant model?  Justify both answers.

The reputation model is the most empirically relevant.  Reputation makes the business world go round, especially in the internet age of ubiquitous product reviews and ratings.  Businesses can almost always raise their SHORT-RUN profits by cutting corners today, but refrain from doing so because this destroys their LONG-RUN profits.

The ultimatum game model is the least empirically relevant.  It clearly predicts something that essentially NEVER occurs: offering people in disadvantageous bargaining positions an amount vanishingly close to zero.  Instead, human beings in such situations gravitate toward even splits.