A single price monopoly that faces the demand curve P = 10 - Q and profit maximizes by reducing price from $6 to $5 must have a marginal cost of
A)1
B)5
C)6
D)10

Question

Quizplus · Accepted Answer

The monopolist maximizes profit where marginal revenue (MR) equals marginal cost (MC). The demand curve is P = 10 - Q, so total revenue (TR) is P*Q = (10-Q)Q = 10Q - Q^2. Marginal revenue is the derivative of TR, MR = 10 - 2Q. At P = $6, Q = 4, and at P = $5, Q = 5. The change in MR from Q = 4 to Q = 5 is MR = 10 - 2(5) = 0. Since the monopolist reduces price to $5, MC must equal MR at Q = 5, so MC = 0. However, since the question asks for the MC when reducing price from $6 to $5, we consider the MC at Q = 4, which is MR = 10 - 2(4) = 2. But the closest option to this calculation is 1, considering the context of the problem.

A Single Price Monopoly That Faces the Demand Curve P