Stochastically optimal advertising policies under dynamic conditions: The ratio rule

There has been considerable debate among marketing researchers about the optimality of popularly used advertising policies. In particular, the ratio rule has aroused much interest. This paper analyses its optimality under the expected profit maximization criterion for a general class of models. The optimality of the ratio rule extends to the stochastic case provided that the conditions which ensure its optimality for the deterministic case are enlarged by an additional restriction. This additional restriction has the effect of transforming the stochastic evolution of goodwill and sales to log-normal processes. Advertising dynamics, the nature of the response function and unexplained error variance all interact to determine whether the ratio rule is exactly optimal, approximately optimal or not optimal at all.