Question

Demand for good X is X = 100 – 4P, where P is the market price of X. A monopolist
supplies this market and has a cost function 5X. If the monopolist selects his profit
maximizing level of X, what is the price he will charge?
(a.) 9.5
(b.) 11.5
(c.) 15
(d.) 18.6

Could you draw the graph with curves?

Answer 1

The correct answer is (c) 15

In order to Maximize profit a monopolist produces that quantity at which MR(Marginal Revenue) = MC(Marginal cost)

X = 100 – 4P => P = (1/4)(100 - X) Total revenue(TR) = PX => MR = d(TR)/dQ = d(X((1/4)(100 - X))/dX = (1/4)(100 - 2X)

MC = d(TC)/dX and TC = Total cost = 5X => MC = 5

MR = MC => (1/4)(100 - 2X) = 5 => X = 40

=> P = (1/4)(100 - 40) = 15

Hence he should charge Price = 15

Hence, the correct answer is (c) 15