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Violation of the Law of Demand

  • Yakar Kannai

    ()

  • Larry Selden

    ()

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    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

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    File URL: http://hdl.handle.net/10.1007/s00199-013-0742-6
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    Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

    Volume (Year): 55 (2014)
    Issue (Month): 1 (January)
    Pages: 1-28

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    Handle: RePEc:spr:joecth:v:55:y:2014:i:1:p:1-28
    DOI: 10.1007/s00199-013-0742-6
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    Web page: http://saet.uiowa.edu/

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    1. Hurwicz, Leonid & Jordan, James & Kannai, Yakar, 1987. "On the demand generated by a smooth and concavifiable preference ordering," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 169-189, April.
    2. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    3. Quah, J-K-H, 1996. "The Monotonicity of Individual and Market Demand," Economics Papers 127, Economics Group, Nuffield College, University of Oxford.
    4. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
    5. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
    6. Felix Kubler & Larry Selden & Xiao Wei, 2013. "Inferior Good and Giffen Behavior for Investing and Borrowing," American Economic Review, American Economic Association, vol. 103(2), pages 1034-53, April.
    7. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, Junio.
    8. Kannai, Yakar, 1989. "A characterization of monotone individual demand functions," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 87-94, February.
    9. Pollak, Robert A, 1970. "Habit Formation and Dynamic Demand Functions," Journal of Political Economy, University of Chicago Press, vol. 78(4), pages 745-63, Part I Ju.
    10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, December.
    11. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    12. Rubinstein, Mark, 1976. "The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets," Journal of Finance, American Finance Association, vol. 31(2), pages 551-71, May.
    13. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Oxford University Press, vol. 38(4), pages 401-414.
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