You are the manager of a monopoly that faces a demand curve described by P = 230 − 20Q.Your costs are C = 5 + 30Q.The profit-maximizing output for your firm is:
A) 4.
B) 5.
C) 6.
D) 7.

Question

Quizplus · Accepted Answer

To find the profit-maximizing output for a monopoly, we first need to determine the marginal revenue (MR) and marginal cost (MC) and then set MR = MC. The demand curve is given by P = 230 - 20Q. To find the marginal revenue, we need to find the derivative of the total revenue (TR), which is P*Q. Since TR = (230 - 20Q)Q, the derivative with respect to Q (which gives us MR) is MR = 230 - 40Q. The marginal cost (MC) is the derivative of the total cost (C) with respect to Q, which is MC = dC/dQ = 30 (since C = 5 + 30Q, and the derivative of a constant is 0, and the derivative of 30Q is 30). Setting MR = MC gives us 230 - 40Q = 30. Solving for Q, we get 200 = 40Q, or Q = 5.

You Are the Manager of a Monopoly That Faces a Demand