There are two types of residents in Brookline and Boston, professors and students. Professors have an income of Y 5 200; students have an income of Y 5 100. Both Brookline and Boston provide road repair services for their citizens. Professors value road repair more than students because they have nicer cars. In fact, the value of road repair to an individual takes the form ((Y × R)/10) - (R2 /2). The per-resident cost of road repair is 5R.

a. What is the marginal value of road repair for each type of individual? What is the marginal cost to each type of individual?

b. How much do professors want to spend on road repair? How much do students want to spend?

c. Assume that residents are distributed as follows:

If each town uses majority voting to determine how much road repair to provide, how much will each town provide? Are any residents unsatisfied with the amount of road repair?

d. Now assume that professors and students are able to migrate between Brookline and Boston. Which residents will choose to move? What will the equilibrium distribution of residents be? Are any residents unsatisfied with the amount of road repair now? Is the provision of road repair efficient? Why or why not?

e. Consider again the premigration equilibrium. The commonwealth of Massachusetts decides to pass a law about road repair. It requires that professors in Massachusetts must contribute 75 units toward road repair in the town where they live; students must contribute 25 units toward road repair in the town where they live. How much road repair will there be in each town under the new regime? Will any residents want to move and, if so, where and why?