Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 1999, Volume 67, Issue 6

Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint
p. 1435-1457

P. A. Chiappori, I. Ekeland

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 satisfying Walras Law can be locally decomposed as the sum of 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 /2 agents.

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