3. All 101 residents of Carmel gain utility from income, M, and a pure public good, G, according to the utility function U = M - G. The public good is not chosen directly by residents, rather provided by the local Carmel government. The marginal cost of producing G is MC (G) = 250. Income net of all other taxes, M, has a uniform distribution over the interval [50, 150], with a mean and median of 100. [Think of each person having a resident humber from 1 to 101 based on income, from lowest to highest. Person 1 has M = 50, Person 2 has M = 51, ..., and Person 101 has M = 150.] a) Consider a proposal to increase G from the status quo level of 32 units to 34. The increase would be financed by a head tax, i.e., everyone in the community would be taxed the same amount. The Carmel town charter states that all new taxes must be approved in a referendum by a two-thirds "super-majority". Would the head tax proposal receive the necessary 66.67% 'yes' votes? b) Now consider the same increase in G from 32 to 34 units, but financed by a single tax rate on income. What income tax rate, , would raise the necessary revenue? Would this new proposal pass the super-majority requirement? c) Does an increase in G from 32 to 34 units pass a cost-benefit test? Does your answer depend on whether the government uses a head tax as in a) or an income tax as in b)? d) The utility function implies that each resident has demand for the public good given by: mwtp = % What is the socially efficient level of G