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

  • Grandmont Jean-michel

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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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. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Social Choice: A Mean Voter Theorem," Discussion Papers 1989_31, Columbia University, Department of Economics.
  2. 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.
  3. 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.
  4. 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.
  5. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  6. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  7. 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.
  8. Muellbauer, John, 1980. "The Estimation of the Prais-Houthakker Model of Equivalence Scales," Econometrica, Econometric Society, vol. 48(1), pages 153-76, January.
  9. 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.
  10. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
  11. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
  12. 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.
  13. Grandmont, Jean-Michel, 1987. "Distributions of Preferences and the 'Law of Demand.'," Econometrica, Econometric Society, vol. 55(1), pages 155-61, January.
  14. Trockel, Walter, 1989. "Classification of budget-invariant monotonic preferences," Economics Letters, Elsevier, vol. 30(1), pages 7-10.
  15. Hildenbrand, Werner, 1989. "Facts and ideas in microeconomic theory," European Economic Review, Elsevier, vol. 33(2-3), pages 251-276, March.
  16. 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.
  17. 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.
  18. 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.
  19. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  20. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
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