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Econometrica
Article
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Article
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Econometrica
Article . 1977 . Peer-reviewed
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EconStor
Research . 1974
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Revealed Preference and Aggregation

Revealed preference and aggregation
Authors: Shafer, Wayne J;

Revealed Preference and Aggregation

Abstract

This paper studies conditions under which aggregate demand behavior will satisfy the usual revealed preference axioms. Assuming a fixed distribution of income and the hypothesis that individual demand is homogeneous in income, it is shown that the weak axiom of revealed preference or the congruence axiom will hold in the aggregate if each individual demand satisfies the corresponding axiom. It is also shown that the hypothesis of homogeneity in income is not necessary for the weak axiom to hold in the aggregate. 1. INTRODUCrION THE PURPOSE OF THIS PAPER is to establish conditions under which aggregate demand behavior will have properties normally associated with individual demand when the distribution of income remains fixed. The best-known result of this type is that if each individual has a homogeneous concave utility function, and the distribution of income is fixed, then the aggregate demand correspondence will be one derived from a homogeneous concave utility function. This was first established by Eisenberg [4], though not in the context of demand theory, who employed duality theory of concave programming. More recently Chipman [1] interpreted Eisenberg's results from the point of view of demand theory and gave a proof of the aggregation theorem based in part on earlier work of Chipman and Moore [2 and 3]. In this paper utility functions will not be employed; instead, a revealed preference approach is taken. Strengthened forms of the weak axiom of revealed preference, the strong axiom of revealed preference, and the congruence axiom are used which are preserved in aggregation, and it is shown that demand correspondences homogeneous of degree one in income which satisfy the regular revealed preference axioms will also satisfy the strengthened versions. One advantage of this approach is that it shows the Eisenberg-Chipman aggregation theorem is a purely algebraic problem and does not require continuity or convexity assumptions. It will also be shown that there are demand functions not homogeneous of degree one in income which satisfy the strengthened form of the

Keywords

Convex programming, ddc:330, Utility theory, Decision theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
13
Average
Top 10%
Average
bronze