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Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint

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  • Chiappori, Pierre-André
  • Ekeland, Ivar
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    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.

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    Bibliographic Info

    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/6427.

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    Date of creation: 1999
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    Publication status: Published in Econometrica, 1999, Vol. 67, no. 6. pp. 1435-1457.Length: 22 pages
    Handle: RePEc:dau:papers:123456789/6427

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    Related research

    Keywords: Microeconomics; consumer theory; aggregation; market demand;

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    Cited by:
    1. Martin Browning & Pierre-Andre Chiappori, 2006. "Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power," Economics Series Working Papers 289, University of Oxford, Department of Economics.
    2. Carvajal, Andres, 2004. "Testable restrictions on the equilibrium manifold under random preferences," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 121-143, February.
    3. Andrés Carvajal, 2003. "Testable Restrictions og General Equilibrium Theory in Exchange Economies with Externalities," BORRADORES DE ECONOMIA 003556, BANCO DE LA REPÚBLICA.
    4. POLEMARCHAKIS, Heracles M. & CHIAPPORI, P. A. & KUBLER, F. & EKELAND, I., 2000. "The identification of preferences from equilibrium prices under uncertainty," Les Cahiers de Recherche 689, HEC Paris.
    5. Aloqeili, Marwan, 2004. "The generalized Slutsky relations," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 71-91, February.
    6. Chiappori, P. -A. & Ekeland, I. & Kubler, F. & Polemarchakis, H. M., 2004. "Testable implications of general equilibrium theory: a differentiable approach," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 105-119, February.
    7. Michael Jerison, 2001. "Demand Dispersion, Metonymy and Ideal Panel Data," Discussion Papers 01-11, University at Albany, SUNY, Department of Economics.
    8. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    9. Chiappori, P. A. & Ekeland, I., 2004. "Individual excess demands," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 41-57, February.
    10. Pierre-André Chiappori & Ivar Ekeland & Martin Browning, 2005. "Local Disaggregation of Negative Demand and Excess Demand Functions," CAM Working Papers 2005-09, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    11. Dorofeenko, Victor & Shorish, Jamsheed, 2005. "Partial differential equation modelling for stochastic fixed strategy distributed systems," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 335-367, January.
    12. Snyder, Susan K., 2004. "Observable implications of equilibrium behavior on finite data," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 165-176, February.
    13. Bellaïche, Joël, 2010. "On the path-dependence of economic growth," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 163-178, March.

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