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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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 987.

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Length: 48 pages
Date of creation: Jul 1991
Date of revision:
Handle: RePEc:cwl:cwldpp:987

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Aggregation; demand functions; revealed preferences;

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References

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  1. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  2. Jean-Michel Grandmont, 1984. "Distribution of Preferences and the 'Law of Demand'," Working papers 356, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. 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.
  4. Hildenbrand, Werner, 1989. "Facts and ideas in microeconomic theory," European Economic Review, Elsevier, vol. 33(2-3), pages 251-276, March.
  5. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Social Choice: A Mean Voter Theorem," Cowles Foundation Discussion Papers 938, Cowles Foundation for Research in Economics, Yale University.
  6. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
  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 219-32, April.
  8. 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.
  9. 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.
  10. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  11. 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.
  12. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
  13. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  14. Mas-Colell, Andreu & Neuefeind, Wilhelm, 1977. "Some Generic Properties of Aggregate Excess Demand and an Application," Econometrica, Econometric Society, vol. 45(3), pages 591-99, April.
  15. Muellbauer, John, 1980. "The Estimation of the Prais-Houthakker Model of Equivalence Scales," Econometrica, Econometric Society, vol. 48(1), pages 153-76, January.
  16. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-57, January.
  17. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
  18. 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.
  19. 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.
  20. Trockel, Walter, 1989. "Classification of budget-invariant monotonic preferences," Economics Letters, Elsevier, vol. 30(1), pages 7-10.
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