Question

A clothing store and a jewelry store are located side by side in a small shopping mall. The number of customers who come to the shopping mall intending to shop at either store depends on the amount of money that the store spends on advertising per day. Each store also attracts some customers who came to shop at the neighboring store. If the clothing store spends $xC per day on advertising, and the jeweler spends $xJ on advertising per day, then the total profits per day of the clothing store are ??(??, ??) = 60?? + ???? − 2?? 2 , and the total profits per day of the jeweler are ??(??, ??) = 105?? + ???? − 2?? 2 . (In each case, these are profits net of all costs, including advertising.)

a) Find the equilibrium amount of advertising for each store if each of them believes that the other store’s amount of advertising is independent of its own advertising expenditure. (Hint: calculate a derivative of each store’s profits with respect to its own advertising and set it equal to zero.)

Answer 1