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Transformations of the Commodity Space, Behavioral Heterogeneity and the Aggregation Problem

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  • Jean-Michel Grandmont

    (Cowles Foundation, Yale University)

Abstract

The aggregation problem in demand analysis and exchange equilibrium is studied by putting restrictions on the shape of the distribution of the agents' characteristics. This is done by exploiting the finite dimensional linear structure induced on demand functions by affine transformations of the commodity space (or household equivalence scales). Increasing the degree of behavioral heterogeneity in the household sector or more specifically, making the conditional distributions in each equivalence class of demand functions fiat enough, has an important regularizing influence on aggregate budget shares: market demand has a negative dominant diagonal Jacobian matrix, aggregate excess demand has the gross substitutability property, on a large set of prices. These facts have strong consequences for the unicity and stability of equilibrium as well as for the prevalence of the weak axiom of revealed preference in the aggregate in a private ownership Walrasian exchange model.

Suggested Citation

  • Jean-Michel Grandmont, 1991. "Transformations of the Commodity Space, Behavioral Heterogeneity and the Aggregation Problem," Cowles Foundation Discussion Papers 987, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:987
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    References listed on IDEAS

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    1. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    2. Deaton, Angus, 1986. "Demand analysis," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 30, pages 1767-1839, Elsevier.
    3. Grandmont, Jean-Michel, 1987. "Distributions of Preferences and the 'Law of Demand.'," Econometrica, Econometric Society, vol. 55(1), pages 155-161, January.
    4. Hildenbrand, Werner, 1989. "Facts and ideas in microeconomic theory," European Economic Review, Elsevier, vol. 33(2-3), pages 251-276, March.
    5. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
    6. Muellbauer, John, 1980. "The Estimation of the Prais-Houthakker Model of Equivalence Scales," Econometrica, Econometric Society, vol. 48(1), pages 153-176, January.
    7. Jorgenson, Dale W & Slesnick, Daniel T, 1987. "Aggregate Consumer Behavior and Household Equivalence Scales," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 219-232, April.
    8. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
    9. Debreu, Gerard, 1993. "Existence of competitive equilibrium," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 15, pages 697-743, Elsevier.
    10. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    11. HILDENBRAND, Werner, 1971. "Random preferences and equilibrium analysis," LIDAM Reprints CORE 100, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. 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.
    13. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    14. Hildegard DIERKER, 1989. "Existence of Nash Equilibrium in Pure Strategies in an Oligopoly With Price Setting Firms," Vienna Economics Papers vie8902, University of Vienna, Department of Economics.
    15. Dierker, Egbert & Dierker, Hildegard & Trockel, Walter, 1984. "Price-dispersed preferences and C1 mean demand," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 11-42, April.
    16. Mas-Colell, Andreu & Neuefeind, Wilhelm, 1977. "Some Generic Properties of Aggregate Excess Demand and an Application," Econometrica, Econometric Society, vol. 45(3), pages 591-599, April.
    17. Trockel, Walter, 1989. "Classification of budget-invariant monotonic preferences," Economics Letters, Elsevier, vol. 30(1), pages 7-10.
    18. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
    19. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    20. Shafer, Wayne & Sonnenschein, Hugo, 1993. "Market demand and excess demand functions," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 14, pages 671-693, Elsevier.
    21. Gordon Tullock, 1967. "The General Irrelevance of the General Impossibility Theorem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(2), pages 256-270.
    22. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
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    More about this item

    Keywords

    Aggregation; demand functions; revealed preferences;
    All these keywords.

    JEL classification:

    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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