Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 1

Suppose that the oil industry in Utopia is perfectly competitive and that all firms draw oil from a single (and practically inexhaustible) pool. Each competitor believes that he or she can sell all the oil he or she can produce at a stable world price of $100 per barrel and that the cost of operating a well for one year is 10000
Total output per year (Q) of the oil field is a function of the number of wells (N) operating in the field. In particular,
and the amount of oil produced by each well (q) is given by
The output from the Nth well is given by
a. Describe the equilibrium output and the equilibrium number of wells in this perfectly competitive case. Is there a divergence between private and social marginal cost in the industry?
b. Suppose that the government nationalizes the oil field. How many oil wells should it operate?What will total output be? What will the output per well be?
c. As an alternative to nationalization, the Utopian government is considering an annual license fee per well to discourage over drilling. How large should this license fee be to prompt the industry to drill the optimal number of wells?