The profit-maximizing level of advertising expenditures

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A producer estimated the dependence of sales volume on advertising expenditures and priced as follow: Q = 35,000 - 5,000 P + 0.8 A - 0.000025 A2 where Q is the monthly quantity sold, P the price and A the monthly level of advertising. The average cost is constant at $2.65 (and hence equal to marginal cost) between 5,000 and 20,000 units produced per month and there is no fixed cost other than the ? ?where Q = output, P = the market price, and S = the amount of advertising, where the unit cost of advertising ?is constant and equal to 1. 2 advertising expenditures. Right now, the price is fixed by a 60% mark-up over average cost or P = 1.60 * 2.65 = $4.24 and the advertising expenditures amount to $9,000 per month.

a) At the actual level of advertising of $ 9,000 is the $ 4.24 price profit-maximizing? If not, determine the profit-maximizing price and the maximum amount of profit.

b) At the actual price of $4.24 what would be the profit-maximizing level of advertising expenditures and what would be the maximum amount of profit?

c) Verify if the Dorfman-Steiner condition is satisfied for a level of advertising of $ 8.524 and a price of $ 5.33.

Reference no: EM132243526

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