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 (75 + x₂)x₁ - 2x²₁ for store 1 and (105 + 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)$27 B)$29 C)$32 D)$24 E)None of the above.

Question

Quizplus · Accepted Answer

In Nash equilibrium, each store maximizes its profit given the advertising expenditure of the other store. For store 1, the first-order condition for maximizing profit is derived by taking the derivative of its profit function with respect to x1 and setting it to zero: (75 + x2) - 4x1 = 0. Solving this for x1 when x2 is also optimized gives x1 = 27.

Two Stores Are Located Side by Side