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Approximately Rational Consumer Demand

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  • Michael Jerison
  • David Jerison

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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Suggested Citation

  • Michael Jerison & David Jerison, 1991. "Approximately Rational Consumer Demand," Discussion Papers 92-02, University at Albany, SUNY, Department of Economics.
  • Handle: RePEc:nya:albaec:92-02
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    References listed on IDEAS

    as
    1. Jerison, David & Jerison, Michael, 1992. "Approximately rational consumer demand and ville cycles," Journal of Economic Theory, Elsevier, vol. 56(1), pages 100-120, February.
    2. 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.
    3. Hildenbrand, Werner, 1989. "The Weak Axiom of Revealed Preference for Market Demand Is Strong," Econometrica, Econometric Society, vol. 57(4), pages 979-985, July.
    4. 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.
    5. Russell, Thomas & Thaler, Richard, 1985. "The Relevance of Quasi Rationality in Competitive Markets," American Economic Review, American Economic Association, vol. 75(5), pages 1071-1082, December.
    6. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-331, March.
    7. 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 708-720, September.
    8. Shafer, Wayne J., 1977. "Revealed preference cycles and the slutsky matrix," Journal of Economic Theory, Elsevier, vol. 16(2), pages 293-309, December.
    9. 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.
    10. Richter, Marcel K., 1979. "Duality and rationality," Journal of Economic Theory, Elsevier, vol. 20(2), pages 131-181, April.
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    12. Lionel McKenzie, 1957. "Demand Theory Without a Utility Index," Review of Economic Studies, Oxford University Press, vol. 24(3), pages 185-189.
    13. Hurwicz, Leonid & Richter, Marcel K, 1979. "Ville Axioms and Consumer Theory," Econometrica, Econometric Society, vol. 47(3), pages 603-619, May.
    14. 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 724-744, July-Aug..
    15. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    16. 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 460-472, June.
    17. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, Oxford University Press, vol. 100(1), pages 119-147.
    18. Koch,Karl-Josef, 1987. "Revealed preference theory and mean demand," Discussion Paper Serie A 103, University of Bonn, Germany.
    19. Polemarchakis, H. M., 1979. "Is there an income effect?," Journal of Economic Theory, Elsevier, vol. 21(3), pages 380-388, December.
    20. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
    21. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
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    1. repec:eee:jetheo:v:172:y:2017:i:c:p:163-201 is not listed on IDEAS
    2. 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.
    3. Reinhard Sippel, 1995. "An Experiment on the Pure Theory of Consumer's Behaviour," Discussion Paper Serie B 274, University of Bonn, Germany.
    4. Victor H. Aguiar & Roberto Serrano, 2013. "Slutsky Matrix Norms and the Size of Bounded Rationality," Working Papers 2013-16, Brown University, Department of Economics.
    5. Halevy, Yoram & Persitz, Dotan & Zrill, Lanny, 2012. "Parametric Recoverability of Preferences," Microeconomics.ca working papers yoram_halevy-2012-20, Vancouver School of Economics, revised 28 Aug 2015.
    6. Michael Jerison, 2001. "Demand Dispersion, Metonymy and Ideal Panel Data," Discussion Papers 01-11, University at Albany, SUNY, Department of Economics.

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    Keywords

    Consumption; Demand;

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