Question

Suppose a manufacturer creates a product with MC=18. The manufacturer sells the product both domestically and abroad. There is no difference in marginal cost and all conditions necessary to practice price discrimination have been met. The manufacturer is interest in maximizing profits by charging a higher price to consumers abroad. Demand abroad (A) is characterized by the inverse demand curve P = 50 - 2Q. Demand domestically (D) is characterized by the inverse demand curve P = 20.7 - 3Q. What is the difference in prices between consumers abroad versus those at home ( PA- PD )?

Answer 1

With price discrimination, profit is maximized when MRA = MC and MRD = MC.

For market abroad,

PA = 50 - 2QA

Total revenue (TRA) = PA x QA = 50QA - 2QA²

Marginal revenue (MRA) = dTRA/dQA = 50 - 4QA

50 - 4QA = 18

4QA = 32

QA = 8

PA = 50 - (2 x 8) = 50 - 16 = 34

For domestic market,

PD = 20.7 - 3QD

Total revenue (TRD) = PD x QD = 20.7QD - 3QD²

Marginal revenue (MRD) = dTRD/dQD = 20.7 - 6QD

20.7 - 6QD = 18

6QD = 2.7

QD = 0.45

PD = 20.7 - (3 x 0.45) = 20.7 - 1.35 = 19.35

Therefore,

PA - PD = 34 - 19.35 = 14.65