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

Question

A monopoly sells its good in the U.S. and Japanese markets. The American inverse demand function is pa = 110-Qa, and the Japanese inverse demand function is P, 90-20, where both prices, pa and pi, 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 $(round your answer to the nearest penny)

Explanation / Answer

Japan:

Pj = 90 - 2Qj

TR = Pj * Qj = 90Pj - 2Q2j

MR = 90 - 4Qj

MC = 25

The equilibrium. Condition is

MR = MC

90 - 4Qj =25

4Qj = 65

Qj = 65 / 4 = 16.25

Pj = 90 - 2(16.25) = $57.50 (we can round it as $58)

So. the equilibrium price in Japan is $58.

America:

Pa = 110 - Qa

TR = 110Qa - Qa2

MR = 110 - 2Qa

MR = MC

110 - 2Qa = 25

2Qa = 85

Qa = 85 / 2 = 42.5

Pa = 110 - 42.5 = $67.50

So, the equilibrium price in America is $67.50

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