Question

Consider a single-price monopolist (i.e. the monopolist cannot price discriminate) facing the following market demand curve: P = 120 − Q. The monopolist has constant marginal cost of $20 and zero fixed cost.

(a) Determine the monopolist’s profit maximizing quantity, denoted QM, and profit maximizing price, denoted PM.

(b) Determine the quantity and price that would result in the market if this instead were a competitive market, denoted QC and PC, respectively.

(c) Draw a picture of the market demand and marginal cost curves. Label the intercepts of the two curves, the monopoly outcome, and the competitive outcome. Determine the deadweight loss resulting from market power.

Answer 1

a) Use MR = MC where MR = 120 - 2Q and MC = 20.

This gives 120 - 2Q = 20 or Q = (120 - 20)/2 = 50 units and P = 120 - 50 = $70 per unit.

Hence, PM = $70 per unit and QM = 50 units

b) In competitive market P = MC or 120 - Q = 20 or Q = 100 units and Price P = $20 per unit.

Hence, PC = $20 per unit and QC = 100 units

c) Graph is shown below

DWL = 0.5*(PM - MC)*(QC - QM)

= 0.5*(70 - 20)*(100 - 50)

= $1250

Monopoly and profit maximiziation Dollars QC 90 100 0 10 20 70 80 110 120 QM 30 40 50 60 Quantity --Demand MR -MC