A seller produces output with a constant marginal cost MC = 2. Suppose there is

Question

A seller produces output with a constant marginal cost MC = 2. Suppose there is one group of consumers with the demand curve P1 = 42 1Q1, and another with the demand curve P2 = 34 1Q2.

(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 a uniform price to consumers in both markets, what will be her profit-maximizing price?

(c) Which, if any, consumer group benefits from price discrimination? (Compare consumer surplus of groups)

(d) If instead P1 = 34 4Q1, does either group benefit from price discrimination?

Explanation / Answer

a) P1 = 42-Q1

TR1 = 42Q1- Q12

MR1 = 42-2Q1

Since MR = MC

42-2Q1 = 2

Q1 = 20

P1 = 42-20 = 22

Similarly, P2 = 34-Q2

TR2 = 34Q2- Q22

MR2= 34-2Q2

Since MR = MC

34-2Q2 = 2

Q2 = 16

P2 = 34-16 = 18

B) the seller will charge the price 22+18 = 40

C) the second group will benefit from the price discrimination as price is relatively lower.

D) if P1 = 34-4Q1

TR1 = 34Q1- 4Q12

MR1 = 34-8Q1

Since MR = MC

34-8Q1 = 2

Q1 = 4

P1 = 34-16

P1 = 18

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