You are the manager of a monopoly that faces a demand curve described by P = 85 − 5Q.Your costs are C = 20 + 5Q.The revenue-maximizing output is:
A) .85.
B) 9.
C) 10.
D) None of the preceding answers is correct.

Question

Quizplus · Accepted Answer

To find the revenue-maximizing output, we first need to find the marginal revenue (MR) and set it equal to marginal cost (MC). The demand curve is P = 85 - 5Q, so the total revenue (TR) is P*Q = (85 - 5Q)Q = 85Q - 5Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 85 - 10Q. The cost function is C = 20 + 5Q, so the marginal cost (MC) is the derivative of C with respect to Q, which is MC = 5. Setting MR = MC gives 85 - 10Q = 5, solving for Q gives Q = 8, which is not listed among the options.

You Are the Manager of a Monopoly That Faces a Demand