Suppose that a monopolist's inverse demand curve can be expressed as: P = 20,000 - Q².
The monopolist's total cost curve is: TC = 8,000Q.
The monopolist's profit-maximizing level of output is Q = ____.

Question

Quizplus · Accepted Answer

The profit-maximizing level of output is found by setting marginal revenue equal to marginal cost. Marginal revenue is the derivative of total revenue with respect to quantity, and marginal cost is the derivative of total cost with respect to quantity. In this case, total revenue is given by TR = P*Q = (20,000 - Q^2)*Q = 20,000Q - Q^3, so marginal revenue is MR = dTR/dQ = 20,000 - 3Q^2. Total cost is given by TC = 8,000Q, so marginal cost is MC = dTC/dQ = 8,000. Setting MR = MC, we get 20,000 - 3Q^2 = 8,000, which simplifies to Q^2 = 4,000. Taking the square root of both sides, we get Q = 63.25.

Suppose That a Monopolist's Inverse Demand Curve Can Be Expressed