Question

AREC 326 Section 0101 Homework 8 Due May 14,2019 Na 1 , A monopolist faces a demand curve of P = 190-5Q and a short run total cost curve of TC-980+30*Q. (Ipt each) How much output will the monopolist produce while maximizing profit? a. b. What is the maximum profit the monopolist can make? How much revenue will the government make from implementing a tax of S10 per unit? c. Extra Credit (3 points): What should Dr. J ask as an extra credit question on the final? These are free points. Please answer the question so I can give them to you

Answer 1

A monopolist faces a demand curve of p = 190 - 5Q and a short run total cost curve of TC = 980 + 30Q. For a profit maximizing monopolist, p) MR = MC So, total revenue (TR) = p * Q = (190 - 5Q) times Q. Marginal revenue (MR) = delta TR/delta Q = delta (190 - 5Q) Q/delta Q = 190 - 5 times 2Q = 190 - 10Q. Marginal cost (MC) = delta TC/delta Q = 30Q Thus the equilibrium output at which MR is equal to MC satisfies 190 - 10Q = 30Q or, 30Q + 10Q = 190 or, 40Q = 190 or, q* = 190/40 = 4.75. A. The monopolist will produce 4.75 units to maximum profit b. If the monopolist is charging a single price, then the profit of the monopolist is given by: profit (pi) = TR - Tc or, pi = (P * Q) - (980 - 30Q) = {(190 - 5Q) * Q}