Question

On the island of Pago Pago there are 2 lakes and 20 anglers. Each angler can fish on either lake and keep the average catch on his particular lake. On Lake x the total number of fish caught is given by: Fx = 10Lx (1/2) Lx2 where Lx is the number of people fishing on the lake.

For Lake y the relationship is Fy = 5Ly

(a) Under this organization of society, what will be the total number of fish caught? (hint, in equilibrium average catch should be the same in each lake)

(b) The chief of Pago Pago believes it is possible to raise the total number of fish caught by restricting the number of people allowed to fish on Lake x. What number should be allowed to fish on Lake x to maximize the total catch of fish? What is the number of fish caught in this situation?

(c) The chief decides to require a fishing license for Lake x. If the licensing procedure is to bring about the optimal allocation of labor, what should the cost of the license be (in terms of fish?)