Your firm competes with a close rival for shares of a $20 million per year market. Your main decision concerns how much to spend on advertising each year. Your rival is currently spending $8 million on advertising. The best estimate of your profit is given by the equation

???? = 20[A ∕ (A + 8)] − A,

Where A is your firm’s advertising expenditure (in millions of dollars). According to this equation, the firms’ shares of the $20 million market are in proportion to their advertising spending. (If the firms spend equal amounts, A = 8, they have equal shares of the market, and so on.)

This chapter’s special appendix reviews the basics of creating, using, and optimizing spreadsheets.

a. Create a spreadsheet modeled on the example shown. Determine the firm’s optimal advertising expenditure. Refer to the appendix of this chapter, if you are unsure about finding MR—that is, taking the derivative of the quotient, A / (A + 8).

b. Use your spreadsheet’s optimizer to confirm your answer in part a. Is matching your rival’s spending your best policy?

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A. D 2 AN OPTIMAL ADVERTISING BUDGET 3 |Advertising Revenue 5 Cost Profit 2.00 8.00 10.00 8.00 10 MR MC Мл 11 12 0.625 1.000 -0.375 13