Samuelson’s Approach to Revealed Preference Theory: Some Recent Advances

Abstract

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A Rationalization of the Weak Axiom of Revealed Preference

“…In other words, separate violations of any of these properties cannot be detected in finite data sets. Varian (1982) shows that the numbers U t and λ t in statement (iii) can be interpreted as measures of the utility level and marginal utility level of income at observation t ∈ T. Analogously, Demuynck and Hjertstrand (2019) shows that the numbers V t in statement (iv) can be interpreted as measures of the utility levels at the observed demands. Matzkin and Richter (1991) provides an analogous result for strict rationalization, by showing that SARP is a necessary and sufficient condition for a data set O T to be strictly rationalized by a continuous, strictly increasing, and strictly concave utility function:…”

The Theory of Weak Revealed Preference

“…There are several interesting features of Afriat's theorem. 11 Statements (ii), (iii), and (iv) give testable conditions that are easy to implement in practice (See, e.g., Demuynck and Hjertstrand 2019). Perhaps the most interesting theoretical implication of Afriat's theorem is that statements (i) and (v) are equivalent, which means that continuity, monotonicity, and concavity are nontestable properties.…”

“…Varian (1982) shows that the numbers U t and λ t in statement (iii) can be interpreted as measures of the utility level and marginal utility level of income at observation t ∈ T. Analogously, Demuynck and Hjertstrand (2019) shows that the numbers V t in statement (iv) can be interpreted as measures of the utility levels at the observed demands. Matzkin and Richter (1991) provides an analogous result for strict rationalization, by showing that SARP is a necessary and sufficient condition for a data set O T to be strictly rationalized by a continuous, strictly increasing, and strictly concave utility function:…”

“…Statement (iv) is rather new to the revealed preference literature. SeeDemuynck and Hjertstrand (2019) for a motivation and intuition of the Varian inequalities in statement (iv).…”