The impact of product substitution and retail capacity on the timing and depth of price promotions: theory and evidence

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 stylised model of a monopolistic retailer selling two substitutable products over time, where demand for each product in each period is a function of the prices of both products in that and earlier periods as well as 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 optimise 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 more 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 stylised two-product model are relevant in practice, we survey price promotions within the shampoo and detergent assortments of four mass-market retailers, and observe behaviour corresponding to the results from our stylised model.