Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 2

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

where l x is the number of people fishing on the lake. For Lake y, the relationship is

a. Under this organization of society, what will be the total number of fish caught?
b. The chief of Pago Pago, having once read an economics book, believes it is possible to increase 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 in order to maximize the total catch of fish? What is the number of fish caught in this situation?
c. Being 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)?
d. Explain how this example sheds light on the connection between property rights and externalities.