Consider a consumer products firm that must decide not only what price to set for its product but also how much to spend on advertising. At a given price, spending on advertising will raise sales to some extent. We can write the demand function Q(P,A) to indicate that demand depends both on price and advertising expenditure. Profit is therefore ? = P*Q(P,A) – C[Q(P,A)] – A

That is, profit is equal to revenue minus the cost of production C(Q) minus the cost of advertising. The trade-off with advertising is that it increases revenue but also imposes a cost on the firm. As always, the firm should optimize by setting the marginal profit with respect to A equal to zero:

M?A = ??/?A = P(?Q/?A) – (dC / dQ) (?Q/?A) – 1 = 0

Which can be written as: (P – MC)(?Q/?A) = 1

Note that the left hand side represents the marginal profit from an extra dollar of advertising.

a) Show that an equivalent condition for the optimal level of advertising is (P – MC)(Q/A) = 1/EA where EA = (?Q/Q)/(?A/A) is the elasticity of demand with respect to advertising. In words, the ratio of advertising spending on operating profit should be equal to EA. Other things being equal, the greater this elasticity, the greater the spending on advertising.

b) Use the markup rule and the equation in part (a) to show that A/(PQ) = -EA/EP.

c) In 1986, General Motors Corporation was ranked 5th of all U.S. firms in advertising expenditure, and Kellogg Co. was ranked 30th. But advertising expenditure constituted 17% of total sales for Kellogg and only 1% for GM. Given the result in part (b), what must be true about the firms’ respective price and advertising elasticity’s to explain this difference?

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a The marginal condition given in the text is Multiply and d... View the full answer