Consider the Antarctic baleen whale fishery which has a logistic net growth function F(Xt)=rXt(1-Xt/K) , and a production function given by H(Et,Xt)=qEtXt , where Xt refers to the stock of baleen whales in each period, Et 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 whale-catcher year.

a) Algebraically calculate the MSY and corresponding effort levels for this fishery.

b) Find the steady state level of effort just sufficient to drive the Antarctic baleen whales to extinction.

c) Algebraically calculate the bio-economically optimal steady state stock level X*, yield Y*, effort, E*, and optimal sustained economic rents R*, where R*=pY*-cE* , p = $7,000 per BWU and c = $600,000 per whale-catcher year. Evaluate your answers for d = 0 and d = 0.1, and comment on the difference in the results obtained under the two discount rates.

d) Algebraically calculate the stock level Xinfinity, effort level Einfinity, and sustained yield Yinfinity corresponding to the open access equilibrium for the Antarctic baleen whale fishery. Explain why Yinfinity is not the same as Y*.

e) Verify your numerical answers to parts (a), (c) and (d) using Excel's Solver. In each case, carefully set up a spreadsheet showing the values corresponding to your initial guess as well as the final solution obtained by Solver. Be sure to mention the constraints and formulae used on your spreadsheet. You are free to choose your own, but sensible, initial guess value.