Selecting Valuation Distributions: Non-Price Decisions of Multi-Product Firms

This paper analyzes decisions of multi-product firms regarding product selection, innovation and advertising as choices of consumer valuation distributions. We show that a profit-maximizing monopolist chooses these distributions so as to maximize the dispersion of the valuation differences between goods across consumers. By contrast, she chooses the willingness-to-pay to be maximally or minimally dispersed, depending on the set of available distributions. In our benchmark model with uniform valuation differences, prices are increasing in valuation difference heterogeneity, but in more general settings this is not necessarily true. Moreover, the relation between willingness-to-pay heterogeneity and prices may well be non-monotone. Over wide parameter ranges, the firm's choice of valuation distribution does not maximize net consumer surplus. This problem is exacerbated when the firm has access to strategies that distort valuation heterogeneity or willingness-to-pay heterogeneity.