The paper proposes a dynamic optimization model for a retailer's price promotions of two brands in a product category. There is no general concensus in empirical marketing literature on what are the impacts of a promotion on intertemporal consumer behavior. This paper will focus on three effects: (1) The immediate, and positive, impact of a price deal on the sales of a promoted brand; (2) Brand substitution, where some consumers switch from a nonpromoted brand to a lower priced promoted brand; and (3) Consumers stockpile a promoted brand during a deal period, which affects postpromotional demand. The paper characterizes the magnitude of discounts as well as the timing and durations of promotions. Optimal policies for a myopic and a forward looking retailer are identified. We also provide comparative statics that identify the dependence of discounts and durations upon key model parameters
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