Product Line Selection and Pricing Under the Multinomial Logit Choice Model

In this paper we consider a retailer's product line selection and pricing problem. We use a consumer choice model in which individuals have stochastic utility for each product and act to maximize their consumer surplus. We consider three basic problems: (1) A retailer who has a current product line with xed prices and who is considering the addition of a new model to the product line. The retailer must determine whether or not to o er the new model and, if so, at what price. (2) A retailer who has a pre-selected set of n models that she will o er. The retailer must jointly determine the optimal prices of these n models. (3) A retailer who may select any subset of models from a set of potential models. The retailer must determine how many and which products to select, and then determine the optimal price for each model. We obtain several insights into these problems by considering the case in which the consumers' reservation prices have a Gumbel distribution (i.e., under a multinomial logit (MNL) choice model). This paper provides a basis that can be built upon in order to gain a better understanding of the retailer's problem of selecting and pricing a product line under cannibalization.