Revealed preference and revealed preference cycles: a survey

TL;DR

This survey reviews the extensions and applications of Afriat's Theorem, emphasizing how datasets consistent with utility maximization can be characterized by modified versions of GARP, highlighting its theoretical and practical significance.

Contribution

It provides a comprehensive overview of how Afriat's Theorem and GARP have been extended and applied across various contexts in revealed preference theory.

Findings

Extensions of Afriat's Theorem are numerous and diverse.

Modified GARP conditions characterize dataset consistency with utility maximization.

The survey highlights practical applications in economic data analysis.

Abstract

Afriat's Theorem (1967) states that a dataset can be thought of as being generated by a consumer maximizing a continuous and increasing utility function if and only if it is free of revealed preference cycles containing a strict relation. The latter property is often known by its acronym, GARP (for generalized axiom of revealed preference). This paper surveys extensions and applications of Afriat's seminal result. We focus on those results where the consistency of a dataset with the maximization of a utility function satisfying some property can be characterized by a suitably modified version of GARP.