-Suppose a monopolist has TC = 40 + 10Q + Q²,and the demand curve it faces is p = 130 - 2Q.What is the maximum profit achieved by this monopoly? A) Profit = 1160 B) Profit = 1240 C) Profit = 1450 D) Profit = 1800

Question

Quizplus · Accepted Answer

To find the maximum profit, we first need to find the monopolist's marginal cost (MC) and marginal revenue (MR), and then set MR = MC to find the quantity (Q) that maximizes profit. The total cost (TC) is given by TC = 40 + 10Q + Q^2, and the demand curve is p = 130 - 2Q.1. Marginal Cost (MC) is the derivative of TC with respect to Q, which is MC = d(TC)/dQ = 10 + 2Q.2. To find Marginal Revenue (MR), we first need the total revenue (TR), which is TR = P*Q = (130 - 2Q)Q. The MR is the derivative of TR with respect to Q, which gives MR = d(TR)/dQ = 130 - 4Q.Setting MR = MC to find the profit-maximizing quantity:130 - 4Q = 10 + 2Q120 = 6QQ = 20To find the maximum profit, we substitute Q = 20 into the demand equation to find the price:P = 130 - 2(20) = 90Then, we calculate total revenue (TR) and total cost (TC) at this quantity:TR = P*Q = 90*20 = 1800TC = 40 + 10(20) + (20)^2 = 40 + 200 + 400 = 640Finally, profit (π) is TR - TC:π = 1800 - 640 = 1160

-Suppose a Monopolist Has TC = 40 + 10Q