Question

A seller produces output with a constant marginal cost MC = 2. Suppose there is one group of consumers with the demand curve P1 = 16 - Q1, and another with the demand curve P2 = 10 - (1/2)Q2.

a) If the seller can discriminate between the two markets, what prices would she charge to each group of consumers?

b) If the seller cannot discriminate, but instead must charge the same price P1 = P2 = P to each consumer group, what will be her profit-maximizing price?

c) Which, if any, consumer group benefits from price discrimination?

d) If instead P1 = 10 - Q1, does either group benefit from price discrimination?

Answer 1

a) If seller discriminates by charging different prices to two separate markets. In market one, P1=16-Q1

MR1=16-2Q1

MC=2

At profit maximization, MR1=MC

16-2Q1=2

Q1=7

P1=9

in market two, P2=10-(1/2)Q2

MR2=10-Q2

At profit maximization

MR2=MC

10-Q2=2

Q2=8

P2=6

Among the two separate markets, price discriminating monopolist charges more price in the market which is more price inelastic.

b) If there is no price discrimination then P1=P2=P then monopolist will maximize profit at MR=MC and when P1=P2 then

16-Q=10-(1/2)Q

6= (1/2)Q

Q=12

P= 4

c) The consumer group which benefits from price discrimination is the one which is more price elastic and responds to change in price while inelastic consumers pay the high discriminated price charged by the monopolist.

d) if P1=10-Q1 then MR1= 10-2Q1 implies Q1= 4 and P1= 6 then P1=P2 and each consumer are benefited.