c. Using the results in part (b), write the firm’s profit expression in
terms of A alone. Find the firm’s optimal level of advertising. Find its
optimal quantity and price.
*14. a. Using the marginal condition in Equation 9.7, 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. Hint: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?Discussion Question Choose a good or service that is supplied by a small
number of oligopoly firms. (Examples range from athletic shoes to aircraft to
toothpaste, or choose a product from the industry list in Table 9.1.) Gather
information on the good from public sources (business periodicals, the Inter-
net, or government reports) to answer the following questions.
a. Who are the leading firms and what are their market shares? Compute
the concentration ratio for the relevant market.
b. What are the most important dimensions (price, technological innovation,
advertising and promotion, and so on) on which firms compete?
c. What has been the history of entry into the market? What kinds of
barriers to entry exist?Spreadsheet Problems
S1. A dominant firm in an industry has costs given by C 70 5qL. The dom-
inant firm sets the market price, and the eight “small” firms coexisting in
the market take this price as given. Each small firm has costs given by C
25 q^2 4q. Total industry demand is given by Qd 400 20P.
a. Create a spreadsheet similar to the example to model price setting by
the dominant firm. (If you completed Problem S1 of Chapter 7, you
need only make slight modifications in that spreadsheet.)388 Chapter 9 Oligopoly*Starred problems are more challenging.c09Oligopoly.qxd 9/29/11 1:32 PM Page 388