. Suppose public radio station is being organized in a city with a population of 500. Voluntary contributions are being solicited to cover the cost. Each citizen is being asked to give $100. The more people contribute, the higher quality the radio station will be and the greater the benet to each citizen. But it is not possible to keep the non-contributors from listening; they get their share of this benet anyway. Suppose that when there are n contributors in the population, where n can be any whole number between 0 and 500, the benet to each citizen in monetary unit equivalents is (n2 n) dollars. Each contributor's payo is the benet minus the contribution. Each noncontributor's payo is the benet.

(a) If 40 citizens have contributed currently, will more citizens contribute? (b) Suppose that initially no one is contributing. You are the manager of the radio station. You would like everyone to contribute and can use persuasion on some people. What is the minimum number who needs to persuade before everyone else will join in voluntarily? (c) Find all the Nash equilibria of the game where each citizen is deciding whether to contribute. Which equilibrium(s) are stable? (d) Write down the social welfare as a function of the number of contributors, n. What's the value of n that maximize the social welfare?