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Local Disaggregation of Negative Demand and Excess Demand Functions

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  • Pierre-André Chiappori

    (Department of Economics, Columbia University)

  • Ivar Ekeland

    (University of British Columbia)

  • Martin Browning

    (Institute of Economics, University of Copenhagen)

Abstract

The literature on the characterization of aggregate excess and market demand has generated three types of results: global, local, or ’at a point’. In this note, we study the relationship between the last two approaches. We prove that within the class of functions satisfying standard conditions and whose Jacobian matrix is negative semi-definite, only n/2 + 1 agents are needed for the ’at’ decomposition. We ask whether, within the same class, the ’around’ decomposition also requires only n/2 + 1 agents.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics in its series CAM Working Papers with number 2005-09.

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Length: 7 pages
Date of creation: May 2005
Date of revision:
Handle: RePEc:kud:kuieca:2005_09

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Keywords: aggregation; market demand functions;

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  1. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August.
  2. Martin Browning & P.A. Chiappori, 1996. "Efficient Intra-Household Allocations - A General Characterization and Empirical Tests," Discussion Papers 96-10, University of Copenhagen. Department of Economics.
  3. Chiappori, Pierre-André & Ekeland, Ivar, 1999. "Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint," Economics Papers from University Paris Dauphine 123456789/6427, Paris Dauphine University.
  4. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
  5. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-31, March.
  6. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
  7. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
  8. Hugo Sonnenschein, 1973. "The Utility Hypothesis and Market Demand Theory," Discussion Papers 51, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. P. A. Chiappori & I. Ekeland, 1999. "Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint," Econometrica, Econometric Society, vol. 67(6), pages 1435-1458, November.
  10. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
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