We investigate the impact of store capacity and extent of inter-product substitution in a retailer's assortment on the optimal timing and depth of price promotions. We develop a stylized model of a monopolistic retailer selling two substitutable products over time, where demand for each product in each period is a function of the price of the product in that and earlier periods, the price of the other product in that and earlier periods, and the degree of substitution between the two periods. We present closed-form solutions to limiting cases of the model, and observe the following: When retailers optimize profits, (1) price promotions are relatively deeper in both absolute and relative terms at higher capacity stores than at low capacity stores, (2) price promotions for expensive products are relatively deeper (shallower) in both absolute and relative terms than price promotions for cheaper products if the degree of substitution is low (high) and (3) the products are sequentially promoted if the degree of substitution is low, and simultaneously promoted if the degree of substitution is high. To confirm that these insights from a simple stylized two-product model are relevant in practice, we survey price promotions within the shampoo and detergent assortments of four mass-market retailers, and observe behavior corresponding to the results from our stylized model.
Published November 2014 , 32 pages