Question

A monopolist faces the demand curve Q= 60-p/2. The cost function is C=Q

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.