A U.S. company and a Japanese company sells an identical product in the U.S. market. The inverse demand equation for this product is P_US = 8 !0.4(Q_USUS + Q_{US J}). Suppose that the best-response functions of the U.S. and Japanese companies are Q_USUS = 7.5 !0.5Q_{US J} and Q_{US J} = 9.375 !0.5Q_USUS, respectively. The Cournot-Nash equilibrium {Q_USUS, Q_{US J} } in the U.S. market is:

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Quizplus · Accepted Answer

To find the Cournot-Nash equilibrium, we substitute one best-response function into the other and solve the system of equations. Substituting the Japanese company's best-response function into the U.S. company's gives us $Q_{US} = 7.5 - 0.5(9.375 - 0.5Q_{US})$. Solving this equation gives us $Q_{US} = 3.75$. Substituting $Q_{US} = 3.75$ into the Japanese company's best-response function gives us $Q_{J} = 9.375 - 0.5(3.75) = 7.5$. Therefore, the Cournot-Nash equilibrium quantities are {3.75, 7.50}.

A US Company and a Japanese Company Sells an Identical Product