A micro foundation for discrete choice models with multiple categories of goods

Discrete choice models are well suited to describing consumer choice. However, conventional discrete choice models depart from standard utility maximization models in two important respects. First, in typical discrete choice models, the total demand for a choice set is exogenously fixed. Second, conventional discrete choice models have a limited ability to describe the unrestricted substitutionary or complementary relationships between multiple categories of goods. Both suggest that conventional discrete choice models correspond to a special utility maximization problem that we can develop to incorporate endogenous change in the total demand for a choice set and multiple categories of goods in an unrestrictive way. The purpose of this paper is to clarify the theoretical foundation of such discrete choice models in the context of standard deterministic utility maximization, derive the elasticities of the implied demand functions, and obtain a method for the calculation of welfare change. The framework in this paper is most useful for considering complementary relationships across categories, which is generally intractable in conventional discrete choice models in the absence of restrictive assumptions. The analysis demonstrates that the results of discrete choice models are perfectly consistent with standard deterministic utility maximization, even if the total demand for a choice set changes endogenously or with multiple categories of goods. Thus, discrete choice models are intrinsically more applicable across a much broader range of consumer choices.