Hendricks, K, Piccione, Michele and Tan, G
(1999)
*Equilibria in networks.*
Econometrica, 67 (6).
pp. 1407-1434.
ISSN 0012-9682

## 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.

Item Type: | Article |
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Official URL: | http://eu.wiley.com/WileyCDA/WileyTitle/productCd-... |

Additional Information: | © 1999 The Econometric Society |

Divisions: | Economics |

Subjects: | H Social Sciences > HB Economic Theory |

JEL classification: | D - Microeconomics > D5 - General Equilibrium and Disequilibrium |

Sets: | Departments > Economics Collections > Economists Online |

Date Deposited: | 27 Apr 2007 |

Last Modified: | 20 Feb 2021 01:13 |

URI: | http://eprints.lse.ac.uk/id/eprint/1324 |

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