Question

Part II.

Suppose there are students living in two dorms, called Gold and Blue. Students are each one of two types, Partiers and Studiers, which determines their preferences. Each dorm will vote on a tax rate, the proceeds of which will be used to fund a party. The mean of the votes will become the effective tax rate, and all residents of the dorm will be required to pay that fee. To simplify the problem, assume that all people may vote for either a tax of $0 or a tax of $100. (For example, if half of all people vote for $100 in a dorm, then the tax rate will be $50. The tax rate must be between $0 and $100.)

All students have a payoff (utility) equal to (1000−T)+μ(N ×T)

where T is the tax that they pay, and N is the number of people living in the dorm (so N × T is the total money spent on the party). The parameter μ is 0 for Studiers and 0.2 for Partiers.

Suppose that there are 100 Partiers and 100 Studiers. Initially, there are 70 Partiers and 30 Studiers in Gold Dorm, with the remainder in Blue. Given that allocation of people, what will be the tax rates in Gold and Blue? (2 points) (There will be two different tax rates.)

1. What is the total utility (payoff) in society (i.e., add up the payoff of all 200 students)?

2. Suppose now that people can move and sort. Suppose further that people choose where to go assuming that the tax rate and party size tomorrow is the same as it was yesterday. What will be the new tax rates in Gold and Blue after people sort?

3. What is the total utility (payoff) in society (i.e., add up the payoff of all 200 students)?

Answer 1