Pricing and composition of bundles with constrained multinomial logit

Abstract

In this paper, we propose an extension of the problem of bundling with multinomial logit, making an explicit inclusion of the consumers’ maximum willingness to pay (MWTP) by means of the constrained multinomial logit (CMNL). In the bundling problem, we determine the price and the composition of bundles offered for a single segment of consumers by a firm, which is competing with others in the market, and we compare this result to a base case in which the consumers’ MWTP is not considered. We assume these consumers as rational since they choose the bundle that maximise their utility and the bundle price is within their MWTP. The resulting model is a non-linear mixed integer programme which is solved in two steps: (i) pricing is the first step; the prices are numerically determined in a fixed point equations system and (ii) in the second step the composition of the bundle is determined by explicit enumeration. The results show that the price obtained is less than the one got in the case without CMNL (and bigger than the costs), and the composition of the offered bundle is different as well. It is possible to conclude that not considering the consumers’ MWTP in the context of the problem of bundling will imply an overestimation of the firm’s profit. We have analysed as well the results for a Chilean telecommunications company. These results show the importance of including the MWTP in the pricing and composition process.