Optimal Category Pricing with Endogenous Store Traffic

Abstract

We propose a dynamic programming framework for retailers of frequently purchased consumer goods in which the prices affect both the profit per visit in the current period and the number of visitors (i.e., store traffic) in future periods. We show that optimal category prices in the infinite-horizon problem also maximize the closed form sum of a geometric series, allowing us to derive meaningful analytical results. Modeling the linkage between category prices and future store traffic fundamentally changes optimal pricing policy. Optimal pricing must balance current profits against future traffic; under general conditions, optimal long-run prices are uniformly lower across all categories than those that maximize current profits. This result explains the empirical generalization that category demand in grocery stores is inelastic. Parameterizing profit per visit and store traffic reveals that, as future traffic becomes more sensitive to price, retailers should increasingly lower current prices and sacrifice current profits. We also determine how the burden of drawing future traffic to the store should be distributed across categories; this is the foundation for a new taxonomy of category roles.