Answer to Question #274085 in Microeconomics for Haru

Question

A monopoly that sells internationally will often try to sell its product at different prices in different countries. Consider distributors for a monopoly that are located in two countries that are adjacent to each other. The inverse demand curves in the two coun tries are P₁ = 40 - 20₁ and P₂ = 1,000 - Q₂. For simplicity, the monopoly's marginal cost is constant at MC = 20. What is the profit-maximizing price and quantity in each country? Will the monopolist necessarily be able to sell its output at those prices if shipping costs between the two countries are low? Explain.

Answer 1

First country:

$P_1=40-20Q$

$TR=PQ$

$TR=(40-20Q)Q$

$=40Q-20Q^2$

$MR=40-40Q$

$MR=MC$

$40-40Q=20$

$Q=\frac{1}{2}$

$P=40-20(\frac{1}{2})=30$

Second country:

$P_2=1000-Q^2$

$TR=1000Q-Q^2$

$MR=1000-2Q$

At maximum profit:

$MR=MC$

$1000-2Q=20$

$Q=490$

$P=1000-(490^2)=-239,100$

If shipping costs between the two countries are low, the monopoly will have to sell its output at those prices because they are the quantity and prices at which profit is maximized.