Advertising Frequency Decisions in a Discrete Markov Process under a Budget Constraint

Abstract

The author studies the optimality of advertising pulsing under the assumption that demand follows a discrete and interpretable Markov process and that the advertising budget is constrained. The author develops two main results. First, when pulsing is optimal, the prevalence of advertising effects on switching or repurchasing affects the length of the pulse (shorter versus longer, respectively), as well as the optimal level of advertising. Second, the author identifies the functional forms of the short- and long-term effects of advertising in the discrete Markov process and shows that pulsing can be optimal if the transition probabilities are concave in advertising. As an alternative to a pure Markov carryover (if any), the author considers that carryover effects of advertising also might be caused by accumulation of memory for the advertisement. Although general results are difficult to obtain, the author analyzes one case of the compound dynamics of the Markov process and memory effects for advertising with results similar to the pure Markov process. Similarities and differences with continuous-time models, as well as managerial implications, are discussed.