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 $x, on advertising per day, then the total profits per day of the clothing store are Пc(x,x₁) = (60+x₁)xc-2xc², and the total profits per day of the jewelry store are ₁(x,x₁) = (105 + xc)X₁ -2x;². (In each case, these are profits net of all costs, including advertising.) (a) If each store believes that the other store's amount of advertising is independent of its own advertising expenditure, find the equilibrium amount of advertising for each store by solving two equations in two unknowns. Find also corresponding profits of both stores. (b) Suppose that the owners of both stores know the profit functions of each other, and suppose they choose their advertising level taking into account each others reaction. What would be optimal x, and xc and the corresponding profits? (c) Suppose that the clothing store and the jewelry store have the same profit functions as before but are owned by a single firm that chooses the amounts of advertising so as to maximize the sum of the two stores' profits. Without calculating actual profits, can you determine whether total profits will be higher, lower, or the same as total profits would be when they made their decisions independently?
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 $x, on advertising per day, then the total profits per day of the clothing store are Пc(x,x₁) = (60+x₁)xc-2xc², and the total profits per day of the jewelry store are ₁(x,x₁) = (105 + xc)X₁ -2x;². (In each case, these are profits net of all costs, including advertising.) (a) If each store believes that the other store's amount of advertising is independent of its own advertising expenditure, find the equilibrium amount of advertising for each store by solving two equations in two unknowns. Find also corresponding profits of both stores. (b) Suppose that the owners of both stores know the profit functions of each other, and suppose they choose their advertising level taking into account each others reaction. What would be optimal x, and xc and the corresponding profits? (c) Suppose that the clothing store and the jewelry store have the same profit functions as before but are owned by a single firm that chooses the amounts of advertising so as to maximize the sum of the two stores' profits. Without calculating actual profits, can you determine whether total profits will be higher, lower, or the same as total profits would be when they made their decisions independently?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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 $x, on advertising per day, then the total profits per day of the clothing store are
Пc(x,x₁) = (60+x₁)xc-2xc², and the total profits per day of the jewelry store are П(x,x₁) = (105 + x)x₁
-2x;². (In each case, these are profits net of all costs, including advertising.)
(a) If each store believes that the other store's amount of advertising is independent of its
own advertising expenditure, find the equilibrium amount of advertising for each store by
solving two equations in two unknowns. Find also corresponding profits of both stores.
(b) Suppose that the owners of both stores know the profit functions of each other, and
suppose they choose their advertising level taking into account each others reaction.
What would be optimal x, and xc and the corresponding profits?
(c) Suppose that the clothing store and the jewelry store have the same profit functions as
before but are owned by a single firm that chooses the amounts of advertising so as to
maximize the sum of the two stores' profits. Without calculating actual profits, can you
determine whether total profits will be higher, lower, or the same as total profits would
be when they made their decisions independently?
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