-Suppose a monopolist has TC = 40 + 10Q + Q²,and the demand curve it faces is p = 130 - 2Q.What is the profit-maximizing price and output? A) P = 50; Q = 20 B) P = 110; Q = 40 C) P = 90; Q = 40 D) P = 90; Q = 20

Question

Quizplus · Accepted Answer

To find the profit-maximizing price and output for the monopolist, we first need to determine the marginal cost (MC) and marginal revenue (MR). The total cost (TC) is given as 40 + 10Q + Q^2, so the marginal cost (MC) is the derivative of TC with respect to Q, which is MC = 10 + 2Q. The demand curve is p = 130 - 2Q, so to find the marginal revenue (MR), we first find the inverse demand function to express Q in terms of p, and then differentiate revenue (R = p*Q) with respect to Q. However, a quicker way since MR has the same intercept as the demand curve but twice the slope, MR = 130 - 4Q. Setting MC equal to MR to find the profit-maximizing output: 10 + 2Q = 130 - 4Q, solving this gives Q = 20. Substituting Q = 20 into the demand curve to find the price: p = 130 - 2*20 = 90. Therefore, the profit-maximizing price and output are P = 90; Q = 20.

-Suppose a Monopolist Has TC = 40 + 10Q