PROBLEM 3 Consider the Antarctic baleen whale fishery which has a logistic net growth function, , and a production function given by , where F(X,) =rXt(1- Xt/K) H(E,,X,) =thX, X, refers to the stock of baleen whales in each period, E, is the fishing effort in each period, r is the intrinsic growth rate, K is the environmental carrying capacity of the Antarctic Ocean, and q is the catchability coefficient. Suppose that r = 0.05 per year, K = 400,000 BWU (baleen whale units), q = 1.6 X 10'3 per whalecatcher year. a) Algebraically calculate the MSY and corresponding effort levels for this fishery. Also find the level of effort just sufficient to drive the Antarctic baleen whales to extinction. b) Algebraically calculate the optimal stock levels X *, optimal sustained biological yields Y*, optimal effort levels, 13*, and optimal sustained economic rents R*, where .. .1. '5, p = $7,000 per BWU and c = $600,000 per whale-catcher R =pY - CE