On the island of Pago-Pago, there are two lakes and 20 fishers. Each fisher gets to fish on either lake and gets to keep the average catch on that lake. On Lake X, the total number of fish caught is given by
FX = 10LX – 1/2 L2X
Where LX is the number of fishers on the lake. The amount an additional fisher will catch is MPX = 10 – LX. For Lake Y, the relationship is
FY = 5LY
a. Under this organization of society, what will the total number of fish caught be? Explain the nature of the externality in this equilibrium.
b. The chief of Pago-Pago, having once read an economics book, believes that she can raise the total number of fish caught by restricting the number of fishers allowed on Lake X. What is the correct number of fishers on Lake X to allow in order to maximize the total catch of fish? What is the number of fish caught in this situation?
c. Being basically opposed to coercion, 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 a license be (in terms of fish)?