Question

Under patent protection, a firm has a monopoly in the production of a high-tech component. Market demand is estimated to be P = 100 – 1.4Q. The firm’s economic costs are given by AC = MC = $30 per component. The deadweight loss from the monopoly of this patent compared to the perfectly competitive outcome is

Answer 1

Answer : For monopoly :

Given, P = 100 - 1.4Q

TR (Total Revenue) = P * Q = (100 - 1.4Q) * Q

=> TR = 100Q - 1.4Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 100 - 2.8Q

MC = $30 (Given)

At monopoly equilibrium, MR = MC.

=> 100 - 2.8Q = 30

=> 100 - 30 = 2.8Q

=> 70 = 2.8Q

=> Q = 70 / 2.8

=> Q = 25

Now, P = 100 - 1.4Q = 100 - (1.4 * 25)

=> P = 65

Therefore, the monopoly price is, P = $65 and quantity is, Q = 25 units.

For perfect competition :

At equilibrium for perfectly competitive firm, P = MC.

=> 100 - 1.4Q = 30

=> 100 - 30 = 1.4Q

=> 70 = 1.4Q

=> Q = 70 / 1.4

=> Q = 50

Now, P = 100 - 1.4Q = 100 - (1.4 * 50)

=> P = 30

Therefore, the perfectly competitive firm's price level is, P = $30 and quantity is, Q = 50 units.

Deadweight loss for monopoly = 0.5 * (Pm - Pc) * (Qc - Qm)

Here Pm = Monopoly price; Pc = Competitive price; Qc = Competitive quantity; Qm = Monopoly quantity.

=> Deadweight loss for monopoly = 0.5 * (65 - 30) * (50 - 25)

=> Deadweight loss for monopoly = 0.5 * 35 * 25 = 437.5

Therefore, the monopoly deadweight loss is $437.5 .