Question

The manufacturer of high-quality flatbed scanners is trying to decide what price to set for its product. The costs of production and the demand for the product are assumed to be as follows:

TC = 500,000 + 0.85Q + 0.015Q 2

Q = 14,166 - 16.6P

a. Determine the short-run profit-maximizing price.

b. Explain why the demand curve facing a monopolist is less elastic than one facing a firm that operates in a monopolistically competitive market (all other factors held constant).

Answer 1

a. Profit maximizing price is determined where MR = MC

MC = d(TC)/dQ = 0.85 + 2(0.015Q) = 0.85 + 0.03Q

Q = 14,166 - 16.6P
So, 16.6P = 14,166 - Q
So, P = (14,166/16.6) - (Q/16.6)
TR = P*Q = [(14,166/16.6) - (Q/16.6)]*Q = (14,166Q/16.6) - (Q2/16.6)
MR = d(TR)/dQ = (14,166/16.6) - (2Q/16.6) = (14,166 - 2Q)/16.6

So, MR = MC gives,
(14,166 - 2Q)/16.6 = 0.85 + 0.03Q
So, 14,166 - 2Q = 16.6*(0.85 + 0.03Q)
So, 14,166 - 2Q = 14.11 + 0.498Q
So, 2Q + 0.498Q = 2.498Q = 14,166 - 14.11 = 14,151.89
So, Q = 14,151.89/2.498
So, Q = 5,665.29

P = (14,166/16.6) - (Q/16.6) = (14,166-Q)/16.6 = (14,166-5665.29)/16.6 = 8500.71/16.6
So, P = 512.09

b. Demand curve facing a monopolist is less elastic than one facing a firm that operates in a monopolistically competitive market because a monopolist is the only seller so he can raise price without losing customers because there are no substitutes for his product. Thus demand is inelastic. While under monopolistic competition, there are many sellers. Such a firm can also increase price without losing all of its customers but there are substitutes available for his product so demand is elastic.