(10 points) A monopolist sells in two adjacent countries and has a constant marg
ID: 1125469 • Letter: #
Question
(10 points) A monopolist sells in two adjacent countries and has a constant marginal cost of 20. The demand in country 1 is Q 90- P, and the demand in country 2 is Q-150 -P2. Resale is not prohibited so the monopolist must deal with the two countries as one market. practices price discrimination by charging different prices in each country. The monopolist produces at constant marginal cost MC- 10. Demand in country 1 is -80-p. Country 2 demand is Q2- 100 - 2p. a. What is the equilibrium quantity, price, and profit? b. What is the price elasticity at the equilibrium price? c. Suppose resale is now prohibited so the monopolist can now practice price discrimination. What is the equilibrium quantity, price, and profit in each country? d. What is the price elasticity at the equilibrium price in each of the two countries?Explanation / Answer
a) Single market has single demand function
Q = 90 - P + 150 - P
Q = 240 - 2P
Inverse demand function is P = 120 - 0.5Q
MR = 120 - Q. MC = 20
Profit maximizing quantity is 120 - Q = 20
Q* = 100,
Profit maximizing Price P = 120 - 100*0.5 = 70
Profit = TR - TC = (70 - 20)*100 = $5000
b) Elasticity = -1/lerner index = -P/P-MC = -70/70 - 20 = -1.4.
c) MR1 = MC and MR2 = MC
80 - 2Q1 = 10 and 50 - Q2 = 10
Q1* = 35 and Q2* = 40
Price P1* = 45 and price P2* = 30
Profits = (45*35 + 30*40) - 10*(40 + 35) = 2025
d) Market 1
ed = -1 x 45/35 = -1.28
Market 2
ed = -2 x 30/40 = - 1.5
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