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Equilibria in networks

By K Hendricks, Michele Piccione and G Tan

Abstract

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

Topics: HB Economic Theory
Publisher: Wiley-Blackwell on behalf of the Econometric Society
Year: 1999
DOI identifier: 10.1111/1468-0262.00085
OAI identifier: oai:eprints.lse.ac.uk:1324
Provided by: LSE Research Online
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