Two stores are located side by side. They attract customers to each other and to themselves by advertising. The profit functions of the two stores are (45 + x₂)x₁ - 2x²₁ for store 1 and (90 + x₁)x₂ - 2x²₂ for store 2, where x₁ and x₂ are total advertising expenditures by stores 1 and 2 respectively. If each store sets its advertising expenditures independently (as in Nash equilibrium), how much would store 1 spend on advertising? A) $18 B) $20 C) $15 D) $23 E) None of the above.

Question

Quizplus · Accepted Answer

In Nash equilibrium, each store maximizes its profit given the other store's expenditure. For store 1, the first-order condition is derived from the profit function: (45 + x2) - 4x1 = 0. Solving this with the similar condition for store 2 gives x1 = 18.

Two Stores Are Located Side by Side