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. True, False, and Explain: In the real world, taxes on goods with negative externalities are always the least inefficient way for governments to raise a given amount of revenue.
FALSE. Taxes on negative externalities have one clear advantage over lump-sum taxes: Lump-sum taxes don’t hurt efficiency, but taxes on negative externalities CAN actually increase efficiency by discouraging socially harmful behavior. But this beneficial side effect of taxes on negative externalities reverses as soon as the tax starts to push market quantity below the intersection of supply and Social Benefits. So if revenue the government wants is large or the negative externality is minor, taxes on negative externalities might be less efficient than, say, lump-sum taxation.
Problems 2 and 3 refer to the following information.
Agents live for two periods. They 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. There are two types of agents:
Type A: 50% of the agents have U=ln c2.
Type B: The other 50% have U=ln c1 + ln c2
2. True, False, and Explain: The general equilibrium interest rate will be less than 3%.
TRUE. Normalizing the utility function for the Type B’s, then applying the standard two-good GE result, yields: . This implies an interest rate of -67%, which is definitely less than 3%.
3. True, False, and Explain: If the two types of agents do not interact (i.e., there is one island for all of the A's and a different island for all of the B's), the interest rate will be negative for A’s but zero for B’s.
TRUE. On the island of the A’s, the interest rate is , or -100%.
On the island of the B’s, the interest rate is: , or 0%. Intuitively, the A’s place no value on period-1 consumption, so it’s free; and the B’s place equal weight on period-1 and period-2 consumption, and have equal amounts of both goods, so their prices are equal in equilibrium.
4. “In biology, there is no equivalent of the Invisible Hand.” (Landsburg, The Armchair Economist)
True, False, and Explain: Landsburg’s discussion implies that in game theory, there is an equivalent of the Invisible Hand.
FALSE. Landsburg identifies the Invisible Hand with the First Welfare Theorem. He explains that according to this theorem, rationality and individual utility maximization are insufficient to ensure efficiency. You also need competitive prices. Furthermore, game theory is specifically designed to analyze situations where the perfectly competitive model does not apply. Indeed, Landsburg’s uses both biological and game theory-type examples (such as educational signaling) to expose inefficient equilibria.
5. Suppose two players play the following normal form N times. N is finite and known by both players.
True, False, and Explain: Alternating back and forth between (L,L) and (R,R) is a SGPPSNE equilibrium for all N and all β>0.
TRUE. Even though this is a finite game, there is no incentive to deviate in the last turn, because deviation reduces your payment (of 1 or 5) to 0. Since there is no incentive to deviate in the last turn, the game never “unravels,” and playing the equilibrium strategies is fully credible. The discount rate is a red herring – even if both players attach ZERO weight to future outcomes, playing the equilibrium is selfishly optimal.
Note: A few students said FALSE because this is also an equilibrium for β=0. But if something is true for β≥0, it is automatically true for β>0, too.
6. Suppose Cournot firms have TC=2 (i.e., fixed cost of 2 with MC=0). The demand curve is P=10-Q.
True, False, and Explain: With free entry, the equilibrium number of firms is 5, with a deadweight cost of 8.
FALSE. From the notes, the equilibrium number of firms is given by the integer immediately below:
, so N=6, not 5. Since one firm could produce the entire output at the same cost as more firms, this implies a deadweight cost of 2 per additional firm, for a total of 10.
Note: A few students correctly observed that there would be additional deadweight loss caused by equilibrium prices exceeding MC=0. Although I gave full credit for saying that the deadweight cost is 10, I also gave full credit for saying it was 10 + the allocative inefficiency of P>MC.
Part 2: Short Answer
(20 points each)
In 4-6 sentences AND/OR equations, answer all three of the following questions.
1. “Mises is correct to point out that beliefs about the efficacy of action are implicit in action. But he at best misspeaks when he characterizes this necessary feature of action as knowledge of ‘causality.’ Instead, the necessary belief component of action is weaker; we don’t need to know—or even believe we know—any exceptionless causal laws. We merely require beliefs about conditional probabilities.” (Caplan, “Probability, Common Sense, and Realism”)
Use Caplan’s analysis of the connection between beliefs and actions to explain why you showed up for this evening’s exam.
[I’m now pretending I’m a student.] According to Mises, I showed up at the exam because I believe that showing up will cause me to succeed in the program. Caplan’s point is that Mises overstates. I could easily attend even though I realize that I might get in a car accident en route, or enter the classroom and discover that the exam’s been cancelled. I might attend even though I believe I’m likely to fail the exam, just as Caplan submits articles to the AER expecting rejection. Being here only shows that, in Caplan’s words, I think being here leads to a “better distribution of outcomes than any alternative plan.” Nothing more – and nothing less.
2. “Schelling points explain why countries rarely fight wars, but fail to explain why countries often fight wars over seemingly minor events.” Discuss, providing at least two real-world examples.
One of the most common way to avoid the War, War equilibrium of the Hawk/Dove game is territoriality: Fight on your own territory, Run away on other territory. But how is this “territory” defined? Schelling points provide an obvious explanation: Once two nations recognize each other’s national borders, each can avoid war by carefully keeping its military on its side of the border. This helps maintain peace, but also shows that the preceding quotation is wrong. Using national borders to reach the peaceful equilibrium creates the possibility of war over a minor territorial transgression (or alleged transgression): Once national borders become a Schelling point, one country’s decision to grab one square mile of another country could provoke a massive response from the country that claims that square mile. Two real-world examples: The Falkland Island crisis, where the United Kingdom fought against Argentina for seizing some sparsely-inhabited islands in the south Pacific; and the current Crimean crisis, which began when Russia unexpectedly occupied and annexed ethnically Russian territory in the Ukraine.
3. Suppose a society is in a very low-trust equilibrium: People don’t trust others because others aren’t trustworthy, and no one bothers to be trustworthy because no one will trust them. If you personally wanted to break out of this low-trust equilibrium – to become a widely trusted “honest broker” – what would you do? Carefully describe your strategy, step-by-step.
My steps: (1) Make some highly visible investments with large SUNK costs to show that I plan to be in business for a long time. (2) Create a tight-knit team of employees I know well personally, starting with friends and family. (3) Give NEW customers my products for free – and make sure I maintain quality. (4) Gradually increase prices for older customers – providing large discounts for customers who refer their friends and family members.
If this doesn’t work, I’d seek a “franchise” or other certification from a reputable outsider, such as a multi-national corporation.