Pricing a Product Line

Abstract

Many firms confront the recurring problem of pricing strategy for a line of products that are partial substitutes for each other. The difficulty of this problem stems from the complex interactions among the pricing decisions on the several products. A low price for one product may siphon demand away from another as customers realize the advantages of substituting one for the other. Or quantity discounts may induce customers to switch products. Confronting the problem in its full complexity, one realizes that all of the prices and terms must be set jointly to take full account simultaneously of the many interactions. In this paper we address a special case of the product-line pricing problem in which the prices of successively higher products can be determined sequentially. Our aims are quite practical. For example, for one class of models an explicit computational procedure has been programmed for a computer so that a pricing manager sitting at an interactive terminal with a visual display can readily explore the implications of a variety of assumptions. Alternatively, market data generated by a current pricing strategy can be used as input to predict ways in which profits might be improved by altering the array of We study the problem of setting prices for a line of products that are partial substitutes for each other. The main innovation is an application of nonlinear pricing to capture the role of price breaks designed to achieve market segmentation. We focus on products interpreted as machines that differ along a single dimension of quality interpreted as marginal operating cost. The pricing problem is, How should the terms of leases be designed to maximize the lessor's total profit? The net price to the customer may be a nonlinear function of the usage rate. Our results show how to compute an optimal price schedule.