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

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Author Info
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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File URL: http://cowles.econ.yale.edu/P/cd/d09b/d0987.pdf
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Publisher Info
Paper provided by Cowles Foundation, 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
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Aggregation; demand functions; revealed preferences;

Find related papers by 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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  1. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March. [Downloadable!] (restricted)
  2. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December. [Downloadable!] (restricted)
  3. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  6. Muellbauer, John, 1980. "The Estimation of the Prais-Houthakker Model of Equivalence Scales," Econometrica, Econometric Society, vol. 48(1), pages 153-76, January. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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.
  9. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July. [Downloadable!] (restricted)
  10. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  12. Grandmont, Jean-Michel, 1987. "Distributions of Preferences and the 'Law of Demand.'," Econometrica, Econometric Society, vol. 55(1), pages 155-61, January. [Downloadable!] (restricted)
  13. Hildenbrand, Werner, 1989. "Facts and ideas in microeconomic theory," European Economic Review, Elsevier, vol. 33(2-3), pages 251-276, March. [Downloadable!] (restricted)
  14. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March. [Downloadable!] (restricted)
  15. Trockel, Walter, 1989. "Classification of budget-invariant monotonic preferences," Economics Letters, Elsevier, vol. 30(1), pages 7-10. [Downloadable!] (restricted)
  16. Mas-Colell, Andreu & Neuefeind, Wilhelm, 1977. "Some Generic Properties of Aggregate Excess Demand and an Application," Econometrica, Econometric Society, vol. 45(3), pages 591-99, April. [Downloadable!] (restricted)
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