Firm C&D; is a monopolist both in The US market and in The international market.

Question

Firm C&D; is a monopolist both in The US market and in The international market. The demand curve for The US market is Qus = 10 - Pus and The demand curve for The international market is Q1 = 20 - P1. The firm's cost function is C(Q) = 2Q + 2. Suppose The firm is restricted to set a single price for both markets (i.e., no price discrimination). What price does The firm set? How much profit does The firm collect? Suppose The firm is able to set a different price for each market (i.e., third-degree price discrimination). What prices does The firm set? How much profit does The firm collect? Discuss The overall effects of price discrimination (relative to no discrimination) on profit, consumer surplus, and total welfare.

Explanation / Answer

(a) With no price discrimination the monopoly would charge a single price for combined market.

P = 10-Qus+20-Qi

P= 30-Q

Monopooly produces where MR is equal to MC

p =30-Q

PQ = 30Q-Q2

MR = 30-2Q

MC = 2

Mr = MC

30-2Q =2

28 = 2Q

Q =14

P =30-14 = $16

P=$16

(b) MRus = MRi = MC

MR us = 10-2Qus

MR i = 20-2Qi

MC = 2

MRus =MC

10-2Qus = 2

Qus = 4 units

Pus = 10-4 = 6

MRi=MC

20-2Q1 = 2

Qi =9

P=20-9 =$11

profit = TRus+TRi-MC

=9x11 + 6x4 -2(6+9) -2

=$91

profit with single price = 14x16 -2x16 -2=190

(c) Here the profits are higher with single pricing. However the prfoits are higher with price discrimination. The consumer surplus is lower with price discrimination.

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