Question

A firm serving a market operates with total variable cost TVC = Q^2. The corresponding marginal cost is MC = 2Q. The firm faces a market demand represented by P = 40 - 3Q.

a) Suppose the firm sets the uniform price that maximizes profit. What would that price be?

(b) Suppose the firm were able to act as a perfect first degree price-discriminating monopolist. How much would the firm’s profit increase compared with the uniform profit-maximizing price you found in (a)?

Answer 1

Q1)

Uniform price policy

MONOPOLY solution,

At eqm, MR = MC

40-6Q = 2Q

40= 8Q

Q*= 5

from demand curve, P*= 40-3*5 = 25

π= 5*25 - 25

= 100

.

​​​​​​Q2) IN PERFECT PRICE DISCRIMINATION

at eqm, P = MC

40-3Q = 2Q

40= 5Q

Q"= 8,

P"= 2*8= 16

So CS = .5*(40-16)*8

= 4*24

= 96

π= PQ- 64

= 16*8-64

= 128-64

= 64

So total π , under Perfect price DISCRIMINATION =

96+64

= 160

(Monopolist extracts entire consumer surplus as his profit in perfect price discrimination)

rise in profits = 160-100

= 60