The private marginal benefit for commodity X is given by 10 - X, where X is the number of units consumed. The private marginal cost of producing X is given by 4 + x and producing this commodity creates a negative externality, the marginal external cost is constant at $2.

(a) How much X is produced without government intervention and at what price? What are producer and consumer surplus in this case?

(b) What is the efficient level of production of X?

(c) Suggest a Pigouvian tax that would lead to the efficient level of production.

(d) What is the producer surplus in this market with the optimal Pigouvian tax?

(e) If some of the government revenue is spent compensating taxed producers for their lost surplus, how much remains?