a. Using the marginal condition in Equation, 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 to operating profit should equal EA. Other things being equal, the greater this elasticity, the greater the spending on advertising.
b. Use the markup rule, (P - MC)/P = -1/EP, and the equation in part (a) to show that A/(PQ) = -EA/EP. Divide the former by the latter. According to this result, the ratio of advertising spending to dollar sales is simply the ratio of the respective elasticities.
c. Recently, General Motors Corporation was ranked fifth of all U.S. firms in advertising expenditure, and Kellogg Co. was ranked thirtieth. But advertising spending constituted 17 percent of total sales for Kellogg and only 1 percent for GM. Given the result in part (b), what must be true about the firms’ respective price and advertising elasticities to explain this difference?