Stochastic Models of a Price Promotion

Stochastic models of a commonly used consumer marketing tool—a price off or price promotion—are developed. Two cases are considered: first, when the duration of the promotion is unknown to customers, and second, when it is known. The optimal duration is derived in both cases as a function of the probability of purchasers of competitive brands switching to the promoted brand, the increased quantity purchased due to the “bargain” and the possible increase in the consumption rate as a consequence. A numerical illustration and a discussion of promotion desirability at different times is presented. Finally, a procedure for estimating model parameters and testing model assumptions is discussed.