Question

A monopolist faces the following demand curve: P = 400 - 3Q, its total cost is given by: TC = 3000 + Q² and its marginal cost is given by: MC = 2Q.

(a) If it is a single price monopolist, what is its profit maximizing price and quantity? Show your work. How much is the profit? How much are consumer surplus and producer surplus?

(b) Suppose it is a first degree price discriminator instead of a single price monopolist. What is the lowest price that the monopolist will charge? How much will be the profit (loss) of the firm? Show your work. How much are consumer surplus and producer surplus?

Answer 1

(a)

Profit is maximized when MR = MC.

TR = P x Q = 400Q - 3Q²

MR = dTR/dQ = 400 - 6Q

400 - 6Q = 2Q

8Q = 400

Q = 50

P = 400 - 3 x 50 = 400 - 150 = 250

TR = 250 x 50 = 12,500

TC = 3,000 + 50 x 50 = 3,000 + 2,500 = 5,500

Profit = TR - TC = 12,500 - 5,500 = 7,000

From demand function, when Q = 0, P = 400 (vertical intercept)

Consumer surplus (CS) = Area between demand curve & price = (1/2) x (400 - 250) x 50 = 25 x 150 = 3,750

From MC function, when Q = 0, MC = 0 (vertical intercept)

Producer surplus (PS) = Area between MC curve & price = (1/2) x (250 - 0) x 50 = 25 x 250 = 6,250

(b)

With 1st degree price discrimination, P = MC and Profit = Consumer surplus.

400 - 3Q = 2Q

5Q = 400

Q = 80

P = 2 x 80 = 160

Profit = CS = (1/2) x (400 - 160) x 80 = 40 x 240 = 9,600

Since P = MC, producer surplus is zero.