The inverse demand curve associated with a product is P = 2250 − 2QD, and the in

The inverse demand curve associated with a product is P = 2250 − 2QD, and the inverse supply curve associated with its production is P = 8QS.

a. What is the free market level of production?

b. Suppose that the marginal damages of production from this good are MD = 70. What is the socially optimal level of production? What is the deadweight loss?

c. To correct the externality, the government decides to impose a tax of t per unit sold. What should t be to achieve the social optimum?

d. Now suppose the marginal damages are not constant with MD = 5Q. Now what is the socially optimal level of production? What is the deadweight loss?

e. What tax t should the government set to achieve the social optimum if MD = 5Q?