完全競爭&外部性...請高手幫忙.... - 經濟

題目是這樣子的

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 $10 per barrel and that the cost of operating a
well for one year is $1,000. Total output per year (Q) of the oil field is a
function of the number of wells (N) operating in the field. In particular,
Q=500N-N^2 and the amount of oil produced by each well (q) is given by
q=Q/N=500-N.

a. Describe the equilibrium output and the equilibrium number of wells in
this perfect 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 overdrilling. How
large should this license fee be to promote the industry to drill the optimal
number of wells?


老實說這題我苦思不得其解，a小提我是在猜用極大化Q，這樣社會的總收益應該會最大，

後面兩題就真的沒有頭緒了....

只好PO上來請高手幫忙


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