Question
Consider two of Nike's best-selling shoe models: Air Jordan 11 Retros and LeBron 18s. Demand for these shoes is governed by the following symmetric system:
Consider two of Nike's best-selling shoe models: Air Jordan 11 Retros and LeBron 18s. Demand for these shoes is governed by the following symmetric system:
QA(pA,pL)=10504pA+pL,
QL(pA,pL)=10504pL+pA,
wherepAis the Air Jordan price, andpLis the LeBron price. Both prices are in dollars, and quantities are measured in thousands of pairs of shoes. The marginal cost of producing either kind of shoes is $50 per pair.Assume the divisions that price the two models are playing theCooperation Game. Are each of the following statements true or false?
1. The Air Jordan division's best-response function ispA(pL)=150+pL/4.
2.At Nash equilibrium, the Air Jordan division sets its price to $200.
3.At Nash equilibrium, the LeBron division sets its price to $150.
4.The joint-profit-maximizing prices will not be Nash-equilibrium prices in the Cooperation Game.
5.If the Air Jordan division sets its price to $50, then the LeBron division would best-respond with the same price in theCompetition Gameas it would in theCooperation Game.
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