Question

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

Answer 1

Q = 60 - $\frac{P}{2}$ 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.

$Ed = -b×P/Q = -0.5×\frac{80} {20} = -2,$

so the demand is elastic.