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)?
Uniform price policy
At eqm, MR = MC
40-6Q = 2Q
from demand curve, P*= 40-3*5 = 25
π= 5*25 - 25
Q2) IN PERFECT PRICE DISCRIMINATION
at eqm, P = MC
40-3Q = 2Q
P"= 2*8= 16
So CS = .5*(40-16)*8
π= PQ- 64
So total π , under Perfect price DISCRIMINATION =
(Monopolist extracts entire consumer surplus as his profit in perfect price discrimination)
rise in profits = 160-100
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