Suppose the market demand function (expressed in dollars) for a normal product i

Question

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) 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)

(b) 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.

Explanation / Answer

revenue = pq = 80p-p^2 slope = 80 - 2q q = 80-p slp = 1 1(2) = 80-p so p= 78 Q = 2

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