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Approximately Rational Consumer Demand

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  • Jerison, David
  • Jerison, Michael

Abstract

We define measures of violations of Slutsky symmetry and negative semidefiniteness and relate them to measures of revealed preference inconsistencies exhibited by nonoptimizing demand behavior. The degree of Slutsky asymmetry is shown to restrict the rate at which real income can rise everywhere along smooth loops in income and price space. The largest eigenvalue of the quadratic form of the Slutsky matrix is used to bound violations of the weak axiom. The sizes of the violations of either Slutsky condition are used to bound the distance between the given demand function and approximating functions that satisfy that Slutsky condition exactly.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 3 (1993)
Issue (Month): 2 (April)
Pages: 217-41

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Handle: RePEc:spr:joecth:v:3:y:1993:i:2:p:217-41

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References

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  1. Polemarchakis, H. M., 1979. "Is there an income effect?," Journal of Economic Theory, Elsevier, vol. 21(3), pages 380-388, December.
  2. Richter, Marcel K., 1979. "Duality and rationality," Journal of Economic Theory, Elsevier, vol. 20(2), pages 131-181, April.
  3. Jerison, David & Jerison, Michael, 1992. "Approximately rational consumer demand and ville cycles," Journal of Economic Theory, Elsevier, vol. 56(1), pages 100-120, February.
  4. Koch,Karl-Josef, 1987. "Revealed preference theory and mean demand," Discussion Paper Serie A 103, University of Bonn, Germany.
  5. Shafer, Wayne J., 1977. "Revealed preference cycles and the slutsky matrix," Journal of Economic Theory, Elsevier, vol. 16(2), pages 293-309, December.
  6. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
  7. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-31, March.
  8. Russell, Thomas & Thaler, Richard, 1985. "The Relevance of Quasi Rationality in Competitive Markets," American Economic Review, American Economic Association, vol. 75(5), pages 1071-82, December.
  9. Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-78, September.
  10. Hurwicz, Leonid & Richter, Marcel K., 1979. "An integrability condition with applications to utility theory and thermodynamics," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 7-14, March.
  11. Koo, Anthony Y C & Hasenkamp, Georg, 1972. "Structure of Revealed Preference: Some Preliminary Evidence," Journal of Political Economy, University of Chicago Press, vol. 80(4), pages 724-44, July-Aug..
  12. Kehoe, Timothy J, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, MIT Press, vol. 100(1), pages 119-47, February.
  13. Hildenbrand, Werner, 1989. "The Weak Axiom of Revealed Preference for Market Demand Is Strong," Econometrica, Econometric Society, vol. 57(4), pages 979-85, July.
  14. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
  15. Jerison, Michael, 1984. "Aggregation and pairwise aggregation of demand when the distribution of income is fixed," Journal of Economic Theory, Elsevier, vol. 33(1), pages 1-31, June.
  16. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  17. Akerlof, George A & Yellen, Janet L, 1985. "Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?," American Economic Review, American Economic Association, vol. 75(4), pages 708-20, September.
  18. Hurwicz, Leonid & Richter, Marcel K, 1979. "Ville Axioms and Consumer Theory," Econometrica, Econometric Society, vol. 47(3), pages 603-19, May.
  19. Afriat, S N, 1973. "On a System of Inequalities in Demand Analysis: An Extension of the Classical Method," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 460-72, June.
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Citations

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Cited by:
  1. Russell, Thomas, 1997. "How quasi-rational are you?: A behavioral interpretation of a two form which measures non-integrability of a system of demand equations," Economics Letters, Elsevier, vol. 56(2), pages 181-186, October.
  2. Michael Jerison, 2001. "Demand Dispersion, Metonymy and Ideal Panel Data," Discussion Papers 01-11, University at Albany, SUNY, Department of Economics.
  3. Victor H. Aguiar & Roberto Serrano, 2013. "Slutsky Matrix Norms and the Size of Bounded Rationality," Working Papers 2013-16, Brown University, Department of Economics.
  4. Reinhard Sippel, 1995. "An Experiment on the Pure Theory of Consumer's Behaviour," Discussion Paper Serie B 274, University of Bonn, Germany.

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