Question

You are given the​ following:

C = 1.0Q² + 40Q +75

and

p = 160 - 1Q

where Q is​ output, p is​ price, and C is the total cost of production. Determine the profit-maximizing price and output for a monopoly.

Answer 1

A monopolist maximizes profit according to the rule: MR = MC

MC = dC/dQ = 2(1Q) + 40 = 2Q + 40

p = 160 - Q
So, Total Revenue, TR = P*Q = (160 - Q)*Q = 160Q - Q²
So, Marginal Revenue, MR = d(TR)/dQ = 160 - 2Q

Now, MR = MC gives,
160 - 2Q = 2Q + 40
So, 2Q + 2Q = 160 - 40
So, 4Q = 120
So, Q = 120/4
So, Q = 30

P = 160 - Q = 160 - 30 = 130
Thus, P = 130