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

Ans. Total revenue, TR = P*Q = 40Q - 3Q^2

=> Marginal Revenue, MR = dTR/dQ = 40 - 6Q

At Equilibrium,

MC = MR

=> 2Q = 40 - 6Q

=> Q = 5 units

From the demand curve we get,

P = $25

And

Profit = TR - TC (TVC = TC as fixed cost is not given)

=> P = P*Q - Q^2

=> P = 25*5 - 5^2 = $100

b) If the person price discriminates, then

P = MC

=> 40 - 3Q = 2Q

=> Q = 8 units

And P = $16

The profit is the entire consumer surplus,

Profit = 0.5*(40 - 0)*8 = $160

Thus, profit increases by $60 when the firm price discriminates.

*Please don’t forget to hit the thumbs up button, if you find the answer helpful.