Suppose the market demand function (expressed in dollars) for a normal product is P = 80 – q, and the marginal cost (in dollars) of producing it is MC = 1q, where P is the price of the product and q is the quantity demanded and/or supplied.

a. How much would be supplied by a competitive market?

b. Compute the consumer surplus and producer surplus. Show that their sum is maximized.

c. Compute the consumer surplus and the producer surplus assuming this same product was supplied by a monopoly. (Hint: the marginal revenue curve has twice the slope of the demand curve.)

d. Show that, when this market is controlled by a monopoly, producer surplus is larger, consumer surplus is smaller, and the sum of the two surpluses is smaller than when the market is controlled by competitive industry.