Optimal pricing and composition of multiple bundles: A two-step approach

Abstract

This paper analyzes the problem facing a firm that must determine the optimal composition and pricing of multiple bundles it supplies to a single market segment. It is assumed the firm’s competitors does not react in the short run to its decisions and that their bundles’ prices and characteristics are known. It is further assumed that potential consumers of bundles are rational and maximize a random utility function. The problem is modeled as a mixed integer non-linear program. Though such programs are normally hard to solve using traditional methods, the difficulties are circumvented here by taking advantage of the problem’s mathematical structure to develop a novel two-phase solution approach. Two aspects of the solution are particularly worthy of note: (1) we demonstrate that the optimal price of a bundle marketed by a firm depends on the composition of all the firm’s bundles, and not on their prices, and on the composition and price of all the competitors’ bundles in the market, and (2) that if the consumer choice behavior is described by a logit model, then the firm’s bundles should be very similar to each other.