Technical Note—A Pure Birth Model of Optimal Advertising with Word-of-Mouth

A stochastic, dynamic model of advertising, which incorporates both advertising and word-of-mouth effects, is formulated. The time between the acquisition of new customers is assumed to be random. The distribution of the time until the firm obtains a new customer depends upon the rate of advertising expenditures and upon a word-of-mouth parameter. The problem of choosing the rate of advertising expenditures so as to maximize long-run expected profit is formulated as a continuous-time Markov decision chain. The impact of changes in various parameters of the model on optimal advertising decisions is studied.