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Transformation of the commodity space, behavioral heterogeneity and the aggregation problem

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  • Grandmont Jean-michel

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 CEPREMAP in its series CEPREMAP Working Papers (Couverture Orange) with number 9114.

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Length: 47 pages
Date of creation: 1991
Date of revision:
Handle: RePEc:cpm:cepmap:9114

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  1. Mas-Colell, Andreu & Neuefeind, Wilhelm, 1977. "Some Generic Properties of Aggregate Excess Demand and an Application," Econometrica, Econometric Society, Econometric Society, vol. 45(3), pages 591-99, April.
  2. Jean-Michel Grandmont, 1984. "Distribution of Preferences and the 'Law of Demand'," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 356, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Muellbauer, John, 1980. "The Estimation of the Prais-Houthakker Model of Equivalence Scales," Econometrica, Econometric Society, Econometric Society, vol. 48(1), pages 153-76, January.
  4. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, Elsevier, vol. 3(4), pages 414-429, December.
  5. Deaton, Angus, 1986. "Demand analysis," Handbook of Econometrics, Elsevier, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 30, pages 1767-1839 Elsevier.
  6. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, Econometric Society, vol. 59(1), pages 1-23, January.
  7. Trockel, Walter, 1989. "Classification of budget-invariant monotonic preferences," Economics Letters, Elsevier, Elsevier, vol. 30(1), pages 7-10.
  8. Dierker, Egbert & Dierker, Hildegard & Trockel, Walter, 1984. "Price-dispersed preferences and C1 mean demand," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 13(1), pages 11-42, April.
  9. Hildenbrand, Werner, 1989. "Facts and ideas in microeconomic theory," European Economic Review, Elsevier, Elsevier, vol. 33(2-3), pages 251-276, March.
  10. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, Econometric Society, vol. 56(4), pages 787-814, July.
  11. Hildegard DIERKER, 1989. "Existence of Nash Equilibrium in Pure Strategies in an Oligopoly With Price Setting Firms," Vienna Economics Papers, University of Vienna, Department of Economics vie8902, University of Vienna, Department of Economics.
  12. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, Econometric Society, vol. 46(2), pages 317-30, March.
  13. Jorgenson, Dale W & Slesnick, Daniel T, 1987. "Aggregate Consumer Behavior and Household Equivalence Scales," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 5(2), pages 219-32, April.
  14. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A, University of Bonn, Germany 244, University of Bonn, Germany.
  15. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 1(1), pages 51-62, March.
  16. Shafer, Wayne & Sonnenschein, Hugo, 1993. "Market demand and excess demand functions," Handbook of Mathematical Economics, Elsevier, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 14, pages 671-693 Elsevier.
  17. Debreu, Gerard, 1993. "Existence of competitive equilibrium," Handbook of Mathematical Economics, Elsevier, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 15, pages 697-743 Elsevier.
  18. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, Elsevier, vol. 6(4), pages 345-354, August.
  19. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, Econometric Society, vol. 40(1), pages 147-57, January.
  20. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 997-1019, July.
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