You are the manager of a monopoly that faces an inverse demand curve described by P = 200 − 15Q.Your costs are C = 15 + 20Q.The profit-maximizing price is:
A) $20.
B) $110.
C) $135.
D) $290.

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, first, we need to determine the quantity where marginal revenue (MR) equals marginal cost (MC). The inverse demand curve is P = 200 - 15Q, so the total revenue (TR) is P*Q = (200 - 15Q)Q = 200Q - 15Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 200 - 30Q. The total cost (TC) is C = 15 + 20Q, so the marginal cost (MC) is the derivative of TC with respect to Q, which is MC = 20. Setting MR equal to MC to find the profit-maximizing quantity: 200 - 30Q = 20, solving for Q gives Q = 6. Substituting Q = 6 back into the inverse demand equation to find the price: P = 200 - 15*6 = 200 - 90 = $110.

You Are the Manager of a Monopoly That Faces an Inverse