amortization becomes more difficult the smaller the expected market share of any individual brand and the higher the fixed costs of brand introduction. Brand proliferation reduces the former and heavy advertising raises the latter. That some firms will drop out and that other firms will not replace them is not surprising, nor are our statistical results.
In fact, the model is a plausible explanation for Joe Bain's lament:19
We are at loss to explain, for example, in terms of the preced
ing argument [i.e. the expectation of substantial selling outlays
for prestige, complex, or durable goods], the very high level
of selling costs that persists in the soap industry.
Our data show that the soap firms, for each of the time periods examined, had the largest or second largest value for the "new products per firm" variable. It is clear that any public policy concerned with intense oligopolistic advertisers should start with those factors that promote advertising. Brand proliferation looks like a good place to start.
Schmalensee's model starts with the profit function:
π = P Q (A, A + ̅,P) - C[Q(A,A + ̅,P) - AT
where P = price, C = cost, Q = quantity, A = "number of advertising messages . . . purchased by the firm at a constant cost of T per message," and A + ̅ = "number of advertising messages purchased by competitors."
The first order condition is:
The term (dA + ̅/dA) indicates the reaction expected from one's competitors if advertising is increased. Multiplying this expression by A + ̅/PQ,
the second expression in the second parentheses by A + ̅/A and setting T = 1, we obtain:
E meaning elasticity, and the expression (EA + EA + ̅ Econj A) measuring net advertising elasticity of demand.
Therefore, A/PQ depends upon the price-cost margin and the elasticities of Q with respect to A and A + ̅, and the reaction of competitors. Assuming CQ, long-run marginal cost, is constant, it follows that when P rises, so does A/PQ. Interpreting P - CQ/P as the Lerner index of monopoly, it follows that profitability rises with P and therefore A/PQ rises with profitability.____________________