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Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint

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Date
1999
Dewey
Probabilités et mathématiques appliquées
Sujet
Microeconomics; consumer theory; aggregation; market demand
JEL code
D11
Journal issue
Econometrica
Volume
67
Number
6
Publication date
1999
Article pages
1435-1457
Publisher
Wiley
DOI
http://dx.doi.org/10.1111/1468-0262.00085
URI
https://basepub.dauphine.fr/handle/123456789/6427
Collections
  • CEREMADE : Publications
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Author
Chiappori, Pierre-André
Ekeland, Ivar
Type
Article accepté pour publication ou publié
Abstract (EN)
We analyze under which conditions a given vector field can be disaggregated as a linear combination of gradients. This problem is typical of aggregation theory, as illustrated by the literature on the characterization of aggregate market demand and excess demand. We argue that exterior differential calculus provides very useful tools to address these problems. In particular, we show, using these techniques, that any analytic mapping in Rn satisfying Walras Law can be locally decomposed as the sum of n individual, utility-maximizing market demand functions. In addition, we show that the result holds for arbitrary (price-dependent) income distributions, and that the decomposition can be chosen such that it varies continuously with the mapping. Finally, when income distribution can be freely chosen, then decomposition requires only n/2 agents.

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