Answer to Question #178900 in Microeconomics for Sedy

Question

 18. The market demand for the output of a monopolist is Q = 125 - 0.25P. The monopolist’s total cost equation is TC = 1,000 + 200Q +Q2. In this case: MC = 200+2Q. A revenue-maximizing monopolist would charge a price of:  [1] R350.00. [2] R275.50. [3] R380.00. [4] R475.00. 

Answer 1

A revenue-maximizing monopolist would charge a price, at which $TR'(Q) = (P×Q)' = MR = 0.$

P = 500 - 4Q,

MR = 500 - 8Q = 0,

8Q = 500,

Q = 62.5,

P = 500 - 4×62.5 = 250.