**Question: **Suppose the oil industry in Utopia is perfectly competitive and that all firms draw oil from a single (andpractically inexhaustible) pool. Assume that each competitor believes that it can sell all the oil it canproduce at a stable world price of $10 per barrel and that the cost of operating a well for one yearis $1,000.Total output per year ðQ Þ of the oil field is a function of the number of wells ðnÞ operating in thefield. In particular,Q ¼ 500n n2,and the amount of oil produced by each well ðqÞ is given byq ¼Qn ¼ 500 n. (19.75)

a. Describe the equilibrium output and the equilibrium number of wells in this perfectly competitivecase. Is there a divergence between private and social marginal cost in the industry?

b. Suppose now that the government nationalizes the oil field. How many oil wells should itoperate? 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 licensefee per well to discourage overdrilling. How large should this license fee be if it is to prompt theindustry to drill the optimal number of wells?

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