Suppose that market demand for a good is Q = 480 – 2p. The marginal co

Suppose that market demand for a good is Q = 480 – 2p. The marginal cost is MC = 2Q. Calculate the deadweight loss resulting from a monopoly in this market.

What will be an ideal response?

ANSWER

First, solve for the competitive equilibrium by substituting MC for p in the demand equation and solve for Q. Q = 480 – 2(2Q) = 480 – 4Q. Rearranging yields 5Q = 480, or Q = 96. Since price equals marginal cost, p = 2(96 ) = 192. Second, solve the monopoly output by setting marginal revenue equal to marginal cost. Rewrite the demand curve as p = 240 – 1/2Q so that MR = 240 – Q. Setting MR = MC yields 240 – Q = 2Q or Q = 80. For this quantity, a monopoly can charge a price of 200 and the marginal cost at that output level is 160. The deadweight loss is [(200 – 160 ) ∗ (96 – 80 )]/2 = 320.