If a monopolist faces a constant-elasticity demand curve given by Q = 400P ^-² and has total costs given by TC = 0.625Q²,its profit-maximizing level of output is:

Question

Quizplus · Accepted Answer

To find the profit-maximizing output, set marginal revenue (MR) equal to marginal cost (MC). The demand curve is Q = 400P^-2, so P = (400/Q)^0.5. Total revenue (TR) is P*Q = Q*(400/Q)^0.5 = 20Q^0.5. MR is the derivative of TR with respect to Q, which is 10Q^-0.5. MC is the derivative of TC = 0.625Q^2, which is 1.25Q. Setting MR = MC gives 10Q^-0.5 = 1.25Q, solving for Q gives Q = 4.

If a Monopolist Faces a Constant-Elasticity Demand Curve Given by Q