Question

A monopoly sells its good in the U.S. and Japanese markets. The American inverse demand function is:

Pa=100-Q_a

and the Japanese inverse demand function is

pj=90-2Q_j

where both​ prices, Pa and Pj​, are measured in dollars. The​ firm's marginal cost of production is m​ = $25 in both countries. If the firm can prevent​ resales, what price will it charge in both​ markets? ​(Hint​: The monopoly determines its optimal​ (monopoly) price in each country separately because customers cannot resell the​ good.)

The equilibrium price in Japan is $___?

Answer 1

Firm will maximize its profit in each market according to the rule MR = MC

America
Total Revenue, TRa = Pa*Qa = (100 - Qa)*Qa = 100Qa - Qa²
Marginal Revenue, MRa = d(TRa)/dQa = 100 - 2Qa
So, MRa = MC gives,
100 - 2Qa = 25
So, 2Qa = 100 - 25 = 75
So, Qa = 75/2 = 37.5
Pa = 100 - Qa = 100 - 37.5 = 62.5

Japan
Total Revenue, TRj = Pj*Qj = (90 - 2Qj)*Qj = 90Qj - 2Qj²
Marginal Revenue, MRj = d(TRj)/dQj = 90 - 4Qj
So, MRj = MC gives,
90 - 4Qj = 25
So, 4Qj = 90 - 25 = 65
So, Qj = 65/4 = 16.25
Pj = 90 - 2Qj = 90 - 16.25 = 73.75

The equilibrium price in Japan is $73.75
The equilibrium price in America is $62.5