Question

A monopolist has a cost function given by C(Q)=Q2 and faces the demand curve p=120-q
a. what is the profit maximizing monopolist output and price
b. what is the consumer surplus ? Monopoly profit?
c. now suppose the monopolist has to follow the narginal cost pricing policy in other word she has to charge competitive prices what is her output and price?

Answer 1

C(Q) = Q^²

MC = 2Q

p = 120 - q

TR = p * q = 120q - q^²

MR = 120 - 2q

a) Monopolist operate at a point when MR = MC when 120 - 2q = 2q

q = 30

At this q, P = 90

b) Consumer surplus would be shaded portion whose sum is (1/2) * (120 - 90) * (30 - 0) = 450

Total cost of producing 30 unit is 900

Total revenue of producing 30 unit is 120 * 30 - 30^² = 2,700

Profit = Total revenue - Total cost = 2,700 - 900 = 1,800

c) If they were to follow perfectly competitive price or at a point when D = MC

120 - q = 2q

q = 40

At this q, p = 80