Rational shopping behavior and the option value of variable pricing

When a product's price fluctuates at a store, how should rational, cost-minimizing shoppers shop for it? Specifically, how frequently should they visit the store, and how much of the product should they buy when they get there? Would this rational shopping behavior differ across Every Day Low Price (EDLP) and Promotional Pricing (HILO) stores? If shoppers are rational, which retail price format is more profitable, EDLP or HILO? To answer these questions, we develop a normative model that shows how rational customers should shop when the price of the product is random. We derive a closed-form expression for the optimal purchasing policy and show that the optimal quantity to purchase under a given price scenario is linearly decreasing in the difference between the price under that scenario and the average price. This purchase flexibility due to price variability has a direct impact on shopping frequency. Indeed, the benefit of this purchase flexibility can be captured via an "option value" that implicitly reduces the fixed cost associated with each shopping trip. Consequently, rational shoppers should shop more often and buy fewer units per trip when they face higher price variability. Our results suggest that if two stores charge the same average price for a product, rational shoppers incur a lower level of expenditure at the store with a higher price variability. Since stores with different price variabilities coexist in practice, we expect stores with higher price variability to charge a higher average price. Thus, given two stores, a higher relative mean price for a given item should be indicative of higher price variability, and vice versa. These model implications are tested using multicategory scanner panel data from 513 households and pricing data for three stores (two EDLP stores and one HILO store) and 33 product categories over a two-year period. We find strong empirical support for the model implications.