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Violation of the Law of Demand

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  • Yakar Kannai
  • Larry Selden

Abstract

Following the classic work of Mitjuschin, Polterovich and Milleron, necessary and sufficient as well as sufficient conditions have been developed for when the multicommodity Law of Demand holds. We show when the widely cited Mitjuschin and Polterovich sufficient condition also becomes necessary. Using this result, violation regions for the very popular Modified Bergson (or hyperbolic absolute risk aversion) class of utility functions are fully characterized in terms of preference parameters. For a natural extension of the constant elasticity of substitution member of the Modified Bergson family that is neither homothetic nor quasihomothetic, we create the first simple, explicit example of which we are aware that (i) fully characterizes violation regions in both the preference parameter and commodity spaces and (ii) analyzes the range of relative income and price changes within which violations occur. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Yakar Kannai & Larry Selden, 2014. "Violation of the Law of Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 1-28, January.
    • Handle: RePEc:spr:joecth:v:55:y:2014:i:1:p:1-28
    DOI: 10.1007/s00199-013-0742-6
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    References listed on IDEAS

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    Cited by:

    1. Franks, Edwin & Bryant, William D.A., 2017. "The Uncompensated Law of Demand: A ‘Revealed Preference’ approach," Economics Letters, Elsevier, vol. 152(C), pages 105-111.
    2. Lanier, Joshua, 2020. "Risk, ambiguity, and Giffen assets," Journal of Economic Theory, Elsevier, vol. 186(C).
    3. Kannai, Yakar & Selden, Larry & Kang, Minwook & Wei, Xiao, 2016. "Risk neutrality regions," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 75-89.
    4. Franks, Edwin & Bryant, William D.A., 2018. "The Uncompensated Law of Demand in an exchange economy," Economics Letters, Elsevier, vol. 168(C), pages 127-131.
    5. Kazuyuki Sasakura, 2021. "Calculating a Giffen Good," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 7(3), pages 349-369, November.

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    More about this item

    Keywords

    Law of Demand; Monotonicity; Violation region; Minimum concavity point; D01; D11;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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