University Lake is a small body of water just outside Carrboro. It's used as the primary source of drinking water for Orange County, its municipal owner, but a limited number of recreational opportunities are also permitted on the lake. The lake is completely closed to the public on weekdays, with the exception of "Fishy Fridays", a day when the same 6 individuals show up every week to fish all day long. Each fisherman maximizes utility by catching as many fish as possible, with a constant marginal utility for each additional fish caught. There are three distinct areas of the lake that can be fished, each consistently yielding the following total catches, in tons: Total Fishermen West Point Total Catch (tons) North Shore South Harbor 6 2 7 3 7 357 4 8 11 4 7 9 9 5 7 10 6 6 7 11 4 a. (10 min) If a private company employs these fishermen, how will it allocate them between the three areas and what will be the catch? What will be the allocation and catch if they are self-employed and decide individually where to fish? Explain. b. (10 min) Orange County is considering adding infrastructure so that University Lake can be used for recreational swimming. Paying the initial construction costs for the new area will cost $100,000, and there are no additional costs per swimmer. Assuming that the beach is large enough to accommodate all relevant demand levels without externalities, graph the average and marginal cost curves that describe the cost of providing the beach to various numbers of swimmers. c. (10 min) There are 5000 potential swimmers in Carrboro, and each has individual demand for Q days of swimming: WTP-10-Q/10. Graph the individual and market demand for days for University Lake to be open for swimming. Should the county build the infrastructure?