9781118041581

Other Dimensions of Competition 379

Profit is simply revenue minus production cost minus total advertising cost. We

see that determining the level of advertising involves a basic trade-off: Raising

A increases sales and profits (the net value of the first two terms) but is itself

costly (the third term). As always, the optimal level of advertising is found

where marginal profit with respect to A is zero. Taking the derivative of

Equation 9.6 and setting this equal to zero, we find

or

[9.7]

The left-hand side of this equation is the marginal profit of an extra dollar of

advertising, computed as the increase in quantity ( Q/ A) times the profit

contribution per unit. The right-hand side is the MC of advertising ($1).

Optimal advertising spending occurs when its marginal benefit (in terms of

profit) equals its marginal cost.

EXAMPLE Let the demand for a good be given by Q 10,000P^5 A.5and

let MC $.80. Let’s use marginal analysis to find the firm’s optimal price,

output, and level of advertising. Noting that EP5, we can solve for price

using the markup rule: P [EP/(1 EP)]MC (5/4)(.8) $1.00. For

the constant elasticity demand function, optimal price does not depend on

the level of advertising expenditure. (This markup is relatively low, because

demand is quite price elastic.) With P 1.00 and MC  .8, the firm’s con-

tribution is $.20 per unit. Thus, net profit is

In turn, we find MA1,000A.5 1 0. A rearrangement gives A.51,000.

Therefore, A (1,000)^2 $1,000,000. Finally, substituting A $1,000,000

into the demand equation yields Q 10,000,000.

ADVERTISING WITHIN OLIGOPOLY To consider the impact of advertising in

an oligopoly, we must move from a single firm’s point of view and ask: What is

the effect when a small number of oligopolists simultaneously pursue optimal

strategies? To illustrate the possibilities, we briefly consider two polar cases.

1.Product Differentiation.One role of advertising is to underscore real or

perceived differences between competing products, that is, to

promote product differentiation and brand-name allegiance. Thus,

the aim of a firm’s advertising is to convince consumers that its

product is different and better than competing goods, for example,

(.2)(10,000A.5)A.

.2Q(P, A)A

(PMC)( Q/ A)1.

MA    / AP( Q/ A)(dC/dQ)( Q/ A) 1  0

c09Oligopoly.qxd 9/29/11 1:32 PM Page 379