## Econ 1: Fall 2010: Draft Problem Set #8

DRAFT Problem Set #8 : Due at the beginning of lecture Monday, December 6, 2010

(A) Economic Theory of Politics: Suppose that there are two political parties--the Caps and the Hats. Suppose voters’ preferences as to the size of federal government spending are uniformly distributed between a lower value of 10% of GDP and a higher value of 40% of GDP. Suppose also that each political party announces a single number as its platform for the federal government share of GDP, and that voters vote for the party whose platform is closest to their preference.

1. Suppose that the Caps announce a platform of 15% of GDP and the Hats announce a platform of 30% of GDP. What share of the vote do the Caps get?

2. Suppose that the Caps announce a platform of 25% of GDP and the Hats announce a platform of 30% of GDP. What share of the vote do the Caps get?

3. Suppose that the Caps announce a platform of 24.99% of GDP and the Hats announce a platform of 25.01% of GDP. What share of the vote do the Caps get?

4. Economists Anthony Downs and James Buchanan and political scientist Gordon Tullock have argued that a two-party system where politicians are most interested not in maintaining ideological purity but in getting elected and reelected does a good job in producing a government that governs according to the will of the people. What bearing do you think this problem has on this issue? Does it strengthen or weaken your assessment of the Downs, Buchanan, Tullock position?

(B) Economic Theory of Politics: Suppose that two-thirds of the voters have preferences as to the size of federal government spending that are uniformly distributed between a lower value of 10% of GDP and a higher value of 40% of GDP, and that one-third of the voters have no preference at all but vote for the party whose candidates’ advertisements have the highest production values. The rich who can afford to make campaign contributions all prefer a government of 10% of GDP. Suppose that there are two political parties: the Caps and the Hats. Each political party announces a single number as its platform for the federal government share of GDP, and that voters vote for the party whose platform is closest to their preference.

1. Suppose that the Caps announce a platform of 25% of GDP and the Hats announce a platform of 25.01% of GDP. What share of the vote do the Caps get?

2. Suppose that the Caps announce a platform of 25% of GDP and the Hats announce a platform of 20% of GDP. What share of the vote do the Caps get?

3. Suppose that the Caps have to announce first, and the Hats—who have no principles at all—then get to choose the platform that maximizes their vote share. If the Caps choose 25%, what do the Hats choose?

4. Suppose that the Caps have to announce first, and the Hats—who have no principles at all—then get to choose the platform that maximizes their vote share. If the Caps choose 15%, what do the Hats choose?

5. Suppose that the Caps have to announce first, and the Hats—who have no principles at all—then get to choose the platform that maximizes their vote share. What should the Caps choose in order to maximize their vote share assuming that the Hats will then make the best move in response?

6. Suppose that the Good Government Coalition puts a referendum on the ballot—a referendum abolishing private campaign contributions and establishing a public system of funding elections that gives each party equal amounts of money to make high production value advertisements. Do you vote for or against this referendum? Why?

(C) Social Choice: Alice thinks the government should build a bridge. If it can’t build a bridge, she thinks it should build a dam. Bobby thinks the government should build a dam. If it can’t build a dam, he thinks it should establish a nature preserve. Carla thinks the government should establish a nature preserve. If it can’t establish a nature preserve, she thinks it should build a bridge. You are brought in as a mediator to suggest a system for social choice that they could establish to decide what the government should do. What do you suggest?

(D) Adverse Selection: Suppose that half of all potential used-car sellers are people who have to sell because they are moving to Fairbanks, Alaska tomorrow and the other half are people who will sell only if they are offered a good deal. Suppose that, for each group, the value of the used car is uniformly distributed between 0 and $10000. 1. Suppose that you offer$2000 to a seller. What is the chance that you buy the car? What is the expected value minus cost to you if you do buy a car?

2. Suppose that you offer $4000 to a seller. What is the chance that you buy the car? What is the expected value minus cost to you if you do buy a car? 3. Suppose that you offer$6000 to a seller. What is the chance that you buy the car? What is the expected value minus cost to you if you do buy a car?

4. Suppose that you offer $8000 to a seller. What is the chance that you buy the car? What is the expected value minus cost to you if you do buy a car? 5. Suppose that you offer$10000 to a seller. What is the chance that you buy the car? What is the expected value minus cost to you if you do buy a car?

6. What would you offer, and why?

(E) Uncertainty: Suppose that your happiness bears a logarithmic relationship to your total lifetime income—that you gain as much happiness moving from a lifetime income of $2.5 million to$5 million than you gain from moving from a lifetime income of $5 million to$10 million. If so, which would you rather have: a certain lifetime income of $5 million, or... 1. A 50% chance of$2.5 million and a 50% chance of $10 million. 2. A 50% chance of$2 million and a 50% chance of $20 million. 3. A 75% chance of$2 million and a 25% chance of $50 million. 4. A 90% chance of$4 million and a 10% chance of $50 million. 5. An 80% chance of$2 million and a 20% chance of $150 million. 6. A 90% chance of$2 million and a 10% chance of $1 billion. 7. An 80% chance of$2 million and a 20% chance of $1 billion. 8. Do the answers to these calculations feel right or wrong to you? Why? (F) Information Goods: Consider an information good—that is, something with a marginal cost of zero, like a piece of software. It does, however, cost an amount C to invent and start to distribute the good. Demand for the good in terms of consumers’ willingness-to-pay is given by Q = Qmax(1 – P/20), where P is the price that people are charged in dollars. The government does not know Qmax: all it knows is that it is uniformly distributed between 0 and 1000. The government does not know C: all it knows is that it is uniformly distributed between 0 and$20000 independent of the value of Qmax. There is, however, a Megalomania Corporation that knows C and Qmax, and that offers to undertake production of the information good if it is either (a) given legal rights to stamp out software piracy and charge a price P that it chooses to all users, or (b) given a large enough payment from the government after which it will open-source and freely-distribute its software.

1. Suppose the government offers to pay $2000 to Megalomania Corporation. What is the consumer surplus minus the taxpayer cost if Megalomania Corporation undertakes the project? What is the chance that Megalomania Corporation will undertake the project? What is the expected social surplus? 2. Suppose the government offers to pay$4000 to Megalomania Corporation. What is the consumer surplus minus the taxpayer cost if Megalomania Corporation undertakes the project? What is the chance that Megalomania Corporation will undertake the project? What is the expected social surplus?

3. Suppose the government offers to pay $6000 to Megalomania Corporation. What is the consumer surplus minus the taxpayer cost if Megalomania Corporation undertakes the project? What is the chance that Megalomania Corporation will undertake the project? What is the expected social surplus? 4. Suppose the government offers to pay$8000 to Megalomania Corporation. What is the consumer surplus minus the taxpayer cost if Megalomania Corporation undertakes the project? What is the chance that Megalomania Corporation will undertake the project? What is the expected social surplus?

5. Suppose the government offers to pay \$10000 to Megalomania Corporation. What is the consumer surplus minus the taxpayer cost if Megalomania Corporation undertakes the project? What is the chance that Megalomania Corporation will undertake the project? What is the expected social surplus?

6. Suppose the government grants Megalomania Corporation enforceable property rights backed by Black Ice Hunter-Killer software bots so that everybody using its software must pay its price P to Megalomania Corporation. What price does Megalomania Corporation chooses to charge if it undertakes the project? What is the chance that Megalomania Corporation will undertake the project? What is the expected consumer surplus plus net monopoly profits?

7. What would you recommend that the government do?