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Local disaggregation of negative demand and excess demand functions

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  • Chiappori, Pierre-Andre
  • Ekeland, Ivar
  • Browning, Martin

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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Suggested Citation

  • Chiappori, Pierre-Andre & Ekeland, Ivar & Browning, Martin, 2007. "Local disaggregation of negative demand and excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 764-770, August.
  • Handle: RePEc:eee:mateco:v:43:y:2007:i:6:p:764-770
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    References listed on IDEAS

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    1. Hugo Sonnenschein, 1973. "The Utility Hypothesis and Market Demand Theory," Discussion Papers 51, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    3. M. Browning & P. A. Chiappori, 1998. "Efficient Intra-Household Allocations: A General Characterization and Empirical Tests," Econometrica, Econometric Society, vol. 66(6), pages 1241-1278, November.
    4. 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.
    5. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August.
    6. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    7. 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.
    8. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    9. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-331, March.
    10. repec:dau:papers:123456789/6427 is not listed on IDEAS
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    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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