# SFB 303 Discussion Paper No. A - 470

**Author**: Peitz, Martin

**Title**: Utility Maximization in Models of Discrete Choice

**Abstract**: In various common models of discrete choice it is assumed that consumers either choose one variant of a
good of which they consume one unit and none of the other variants or they choose the outside option. Articles
analyzing this class of models usually commence with an evaluation function which is called a conditional
indirect utility function. A consumer chooses the variant with the highest value: if for some variant the value is
positive a consumer buys one unit of the variant which gives him the maximal value. Otherwise, he chooses the
outside option. Duality theory suggests that there is an associated direct utility function. However, the results of
duality theory cannot be applied to this problem because continuity is not satisfied. Therefore, there are some
doubts whether the evaluation function is indeed an indirect utility function and whether it is consistent with
utility maximization. I will construct a direct utility function such that the underlying preference relation satisfies
reflexivity, transitivity, completeness, and local nonsatiation. I will then show that this direct utility function has
as its counterpart the indirect utility function I was looking for. Hence consumer behavior in discrete choice
models of the type presented can be derived from utility maximization.

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**JEL-Classification-Number**:

**Creation-Date**: January 1995

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