Question

Suppose that the demand for a monopolist's product is estimated to be Qd = 100 − 2P and its total costs are C = 10Q.

a. How does the number of units sold with first-degree price discrimination compare to the number sold if the firm charged its optimal single price?

b. How do the profits earned with first-degree price discrimination compare to profits earned if the firm charged its optimal single price?

c. How does consumer surplus with first-degree price

Answer 1

Qd = 100 - 2P

P = (100 - Qd)/2

P = 50 - 0.5Qd

MC = dTC/dQ = 10

(a) With first degree price discrimination, P = MC.

50 - 0.5Qd = 10

0.5Qd = 40

Qd = 80

P = MC = 10

With single price monopoly, MR = MC.

TR = P c Qd = 50Q - 0.5Qd²

MR = dTR/dQd = 50 - Qd

50 - Qd = 10

Qd = 40

P = 50 - (0.5 x 40) = 50 - 20 = 30

So number sold with first-degree price discrimination is higher by (80 - 40) = 40.

(b) With first degree price discrimination, Profit = Consumer surplus (CS) = Area between demand curve and price.

From demand function, when Qd = 0, P = 50 (Vertical intercept).

CS = Profit = (1/2) x (50 - 10) x 80 = 40 x 40 = 1600

With single pricing,

Profit = Q x (P - MC) = 40 x (30 - 10) = 40 x 20 = 800

So profit with first-degree price discrimination is higher by (1600 - 800) = 800.

(c) With single pricing, CS = (1/2) x (50 - 30) x 40 = 20 x 20 = 400

So CS with first-degree price discrimination is higher by (1600 - 400) = 1200.