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 = 5 !0.2(Q_USUS + Q_{US J}). Suppose that the best-response functions of the U.S. and Japanese companies are Q_USUS = 10 !0.5Q_{US J} and Q_{US J} = 7.5 !0.5Q_USUS, respectively. The Cournot-Nash equilibrium {Q_USUS, Q_{US J} } in the U.S. market is:

Question

Quizplus · Accepted Answer

To find the Cournot-Nash equilibrium, we substitute one best-response function into the other. Substituting the Japanese company's best-response function into the U.S. company's gives: QS_US = 10 - 0.5(7.5 - 0.5QS_US), which simplifies to QS_US = 8.33. Substituting this value into the Japanese company's best-response function gives QS_JP = 7.5 - 0.5(8.33), which simplifies to QS_JP = 3.33. Therefore, the Cournot-Nash equilibrium is {8.33, 3.33}.

A US Company and a Japanese Company Sells an Identical Product