Question

Suppose a monopoly sells to two identifiably different types of customers, A and B. The inverse demand curve for group A is PA= 20-QA, and the inverse demand curve for group B is PB= 20-2QB. The monopolist is able to produce the good for either type of customer at a constant marginal cost of 4, and the monopolist has no fixed costs. If the monopolist is unableto price discriminate (no reselling), (1) what arethe profit maximizing price and quantity, and (2) what arethe consumer surplus, profit, and deadweight loss? SHOW WORK

Answer 1

Demand functions are QA = 20 - PA and QB = 10 - 0.5PB

Combined demand is Q = 30 - 1.5P for Q < 10

This gives inverse demand is 1.5P = 30 - Q and so P = 30/1.5 - Q/1.5

P = 20 - Q/1.5

MR = 20 - 2Q/1,5

Use MR = MC for profit maximizing quantity

20 - 2Q/1.5 = 4

Q = 12 units.

Single price = 20 - 12/1.5 = $12

At this price, for customers A

QA = 20 - 12 = 8 units

CS = 0.5*(Max price - current price)*current qty = 0.5*(20 - 12)*8 = $32

Profit = (P - AC)*Q = (12 - 4)*8 = $64.

DWL = 0.5*(12 - 4)*(16 - 8) = $32

At this price, for customers B

QB = 10 - 0.5*12 = 4 units

CS = 0.5*(Max price - current price)*current qty = 0.5*(20 - 12)*4 = $16

Profit = (P - AC)*Q = (12 - 4)*4 = $32

DWL = 0.5*(12 - 4)*(8 - 4) = $16