We formulate a family of direct utility functions for the consumption of a differentiated good. The family is based on a generalization of the Shannon entropy and includes dual representations of all additive random utility discrete choice models.

This leads to a family of demand systems with flexible substitution patterns. Demand models for market shares can be estimated by regression enabling the use of instrumental variables. Models for microdata can be estimated by maximum likelihood.

Keywords: market shares; product differentiation; discrete choice; duality; generalized entropy