Question

A monopolist faces the demand curve Q=60-P/2. The cost function is C=Q² . Find the output that maximizes this monopolist's profit. What are the prices at point and that output? Find the elasticity of demand at the profit maximizing output.

Answer 1

Q = 60 - P/2 or P = 120 - 2Q.

Monopolist profit-maximizing quantity is produced, when MR = MC.

$MR = TR' = (P*Q)' = (120Q - 2Q^{2})' = 120 - 4Q,$

$MC = C' = (Q^{2})' = 2Q.$

120 - 4Q = 2Q,

Q = 20 units.

P = 120 - 2*20 = 80.

$Ed = -b*P/Q = -0.5*80/20 = -2,$

so the demand is elastic.