A generalization that makes useful the dorfman–steiner theorem with respect to advertising

Dorfman and Steiner's theorem is trivial with respect to advertising because it deals with only one period. It simply says that a firm should stop with that volume of advertising at which an additional dollar of advertising just produces an additional dollar of net revenue. This note generalizes the theorem to the meaningful multi-period situation in which the effect of advertising is lagged. The optimizing decision rule is to advertise up to the point at which f′(A_t) = 1 - bd, where A stands for advertising, b for the customer-rentention factor, and d for the cost-of capital discount factor.