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Engel Curves Leading to the Weak Axiom in the Aggregate

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  • Freixas, Xavier
  • Mas-Colell, Andreu

Abstract

For every range of admissible incomes, the authors characterize the class of Engel curves with the property that if an economy has, first, a price independent distribution of income and, second, preferences which are identical across consumers and generate Engel curves in the class, then the corresponding aggregate demand function satisfies the Weak Axiom of Revealed Preference. This class is defined by two simple conditions. The no-torsion condition says that, in the relevant range of income, the Engel curve is contained in a plane through the origin. The uniform-curvature condition says that, in addition, the Engel curve is either convex or concave to the origin. Copyright 1987 by The Econometric Society.

Suggested Citation

  • Freixas, Xavier & Mas-Colell, Andreu, 1987. "Engel Curves Leading to the Weak Axiom in the Aggregate," Econometrica, Econometric Society, vol. 55(3), pages 515-531, May.
  • Handle: RePEc:ecm:emetrp:v:55:y:1987:i:3:p:515-31
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    References listed on IDEAS

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    1. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    2. Jerison, Michael, 1984. "Aggregation and pairwise aggregation of demand when the distribution of income is fixed," Journal of Economic Theory, Elsevier, vol. 33(1), pages 1-31, June.
    3. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
    4. Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-978, September.
    5. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
    6. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Oxford University Press, vol. 42(4), pages 525-543.
    7. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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    Cited by:

    1. Jerison, Michael, 1999. "Dispersed excess demands, the weak axiom and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 15-48, February.
    2. Brighi, Luigi, 2004. "A stronger criterion for the Weak Weak Axiom," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 93-103, February.
    3. Fousekis, Panos & Lazaridis, Panagiotis, 2001. "Food Expenditure Patterns of the Urban and the Rural Households in Greece. A Kernel Regression Analysis," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 2(1), January.
    4. Laisney, François, 1991. "Mikroökonometrische Untersuchung von Aggregationsproblemen: Eine partielle Übersicht," ZEW Discussion Papers 91-03, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    5. Andrea Mantovi, 2014. "On Luxury and Equilibrium," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 6(2), pages 87-118, December.
    6. Krysiak, Frank C. & Krysiak, Daniela, 2002. "Aggregation of Dynamic Systems and the Existence of a Regeneration Function," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 517-539, November.
    7. Alexis Akira Toda & Kieran James Walsh, 2017. "Edgeworth box economies with multiple equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 65-80, April.
    8. Lilia Maliar & Serguei Maliar, 2005. "An Analytical Construction Of Constantinides¿ Social Utility Function," Working Papers. Serie AD 2005-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Masao Ogaki, 2003. "Aggregation under Complete Markets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 977-986, October.
    10. Neary, J Peter, 2000. "True Multilateral Indexes for International Comparisons of Real Income: Theory and Empirics," CEPR Discussion Papers 2590, C.E.P.R. Discussion Papers.
    11. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.

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