Rational shopping behavior and the option value of variable pricing

When a product's price fluctuates at a store, how should rational, cost-min imizing shoppers shop for it? Specifically, how frequently should they visi t the store, and how much of the product should they buy when they get ther e? Would this rational shopping behavior differ across Every Day Low Price (EDLP) and Promotional Pricing (HILO) stores? If shoppers are rational, whi ch retail price format is more profitable, EDLP or HILO? To answer these qu estions, we develop a normative model that shows how rational customers sho uld shop when the price of the product is random. We derive a closed-form expression for the optimal purchasing policy and sh ow that the optimal quantity to purchase under a given price scenario is li nearly decreasing in the difference between the price under that scenario a nd the average price. This purchase flexibility due to price variability ha s a direct impact on shopping frequency. Indeed, the benefit of this purcha se flexibility can be captured via an "option value" that implicitly reduce s the fixed cost associated with each shopping trip. Consequently, rational shoppers should shop more often and buy fewer units per trip when they fac e 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 variabil ities coexist in practice, we expect stores with higher price variability t o charge a higher average price. Thus, given two stores, a higher relative mean price for a given item should be indicative of higher price variabilit y, 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 ana one HILO store) and 33 product categories over a two-year period. We find s trong empirical support for the model implications.