Use a fisheries model in discrete time such that the returning stock in the beginning of period t (Rt) is R = S_ + aS_ (1 S-) -1 t-1 where S is the stock left behind after fishing. a) With a constant net price of fish equal to 1, ignoring costs, and a = 0.5, what is the stock that maximizes sustainable yield? b) What is the optimal stock to be left after fishing at 5 percent rate of discount? Why is this different from the stock that maximizes sustainable yield? Explain carefully. What is the sustainable yield of this stock? c) Suppose the stock is shared by two countries which engage in a competitive game against one another. One country always has a share 6 of the stock, but after fishing the stock grows and breeds as a unit. How much of the stock would this country leave behind after fishing if 6 = 0.75? How much would the other country leave behind? Explain carefully. d) What would be the catches of the two countries in this situation? e) Would the minor country accept a share of the catch in the cooperative solution (cf. b) equal to its share of the stock? f) Do you think you are likely to see an outcome like this in the real world? Why or why not?