Question

PFS manufactures specialized athletic performance equipment that is protected by patents. These patents give PFS a monopoly position in the marketplace. The demand curve for athletic performance equipment is given by Q = 100 − P—this implies a marginal revenue curve of MR = 100 − 2Q, where Q is the monthly sales of athletic performance equipment. The average and marginal cost curves curves for PFS are: AC = Q + (2000/Q) MC = 2Q (a) Determine the monopolist’s profit-maximizing quantity of monthly sales for PFS. (b) What uniform price (same for all units sold) can PFS charge for its equipment? (c) What is the price elasticity of demand at that price?(d) What is the markup over marginal cost at the profit-maximizing quantity, expressed as a percentage of price?

Answer 1

a)

Given

MR=100-2Q

MC=2Q

Set MR=MC for profit maximization

100-2Q=2Q

4Q=100

Q=25

Profit maximizing monthly sale for PFS is 25 units.

b)

Price can be determined by using demand function at profit maximizing quantity

Q=100-P

25=100-P

P=75

Uniform price is 75

c)

Given Q=100-P

So, dQ/dP=-1

We have calculated in earlier parts that P=75 at Q=25

So,

Price elasticity of demand=(dQ/dP)*(P/Q)=-1*(75/25)=-3

d)

MC=2Q

At Q=25, MC=2*25=50

Markup over marginal Cost=(P-MC)/P=(75-50)/50=50%