3. Public Goods and Political Economy The residents of Amity Island want the city government to renovate the beach. However, there is debate over how much to spend on renovations. Amity Island has 500 residents: 200 who live close to the beach (and will benefit more from the renovations), and 300 who live farther away (and will benefit less). The marginal benefits of the beach renovations for each resident are given by the below equations, where R represents the worker hours needed for renovations. For Each Close Resident: M Bs =55 R For Each Far Resident: M Br = 20 2R (a) If the beach renovations cost $1,000 per hour, what is the socially optimal hours of reno- vations R? (b) Now assume that renovations will cause traffic around the beach. Residents living close to the beach will suffer from the renovations according to the following formula: For Each Close Resident: MC- = 2R + 20 The far away residents do not suffer any extra cost as there is no extra traffic on their side of the island. Assuming the construction cost is still $1,000 per hours, what is the new socially optimal hours of renovations R? (c) Now we have to think about how to pay for the renovations. Assume that the cost will be split evenly among the residents, so that each individual must bear W%O of the $1,000 per hours monetary cost of renovations. Suppose the Amity Island's mayor, Larry Vaughn, is running for reelection next year and all residents will vote. Hoping to satisfy the pivotal voter, Mayor Vaughn plans to renovate enough to meet the median resident's demands. How many hours of renovations will the mayor undertake? (d) Before renovations can start, the far away residents consider moving to a new island, Block Island, and reincorporating as a new town distinct from Amity Island. Block Island also would need beach renovations. The marginal costs and benefits of Block Island's beach renovations for the new residents are the same as when they were far away residents, namely M B = 20 2R and MC = 0, but the renovations only cost $900 per hour. There are no traffic costs on Block Island. What is the socially optimal hours of renovations R for Amity and Block Island if the far away residents move? (Hint: Renovation costs for an island are only paid by that island's residents - i.e. close residents on Amity Island and far away residents on Block Island) By moving to Block Island and separately choosing their optimal beach renovation would the far away residents be better off than if they stayed on Amity Island and accepted Mayor Vaughn's plan? (Hint: The marginal benefit is the same for the far away residents on each island. What is the construction cost per resident under each plan?)