The Efficient Number of Firms:
Suppose the oil industry in some country is perfectly competitive and all firms extract oil from a common, and endless pool. The cost of operating a well is #1,000 for one year, and the firm can sell any amount it chooses at the world price of $10 a barrel.
If N wells are operating, the output per year in barrels will be
Q = 500N − N2
and we assume symmetry, so the output per year for each firm is q = Q/N = 500 − N. In what follows, ignore integer constraints.
(1) A competitive equilibrium is a number of firms (wells) that will drill for oil such that the profits of each well from sales, net of production costs, equal to zero. Find the competitive equilibrium number of wells. Is there divergence between the private and the social marginal cost in the industry?
(2) Suppose now that the government nationalizes the oil field. How many oil fields will it operate? How will output and output per well differ from (1) above?
(3) As an alternative to nationalization, the government is considering an annual license fee to operate a well and discourage over-drilling. How much should this license be in order to achieve the optimal number of wells in a competitive equilibrium?