IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v55y2014i1p1-28.html
   My bibliography  Save this article

Violation of the Law of Demand

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-013-0742-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-013-0742-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
    2. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. 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 551-571, May.
    5. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, January.
    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 1034-1053, April.
    7. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
    8. Kannai, Yakar, 1989. "A characterization of monotone individual demand functions," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 87-94, February.
    9. Hosoya, Yuhki, 2011. "An existence result and a characterization of the least concave utility of quasi-linear preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 251-252, March.
    10. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    11. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    12. Barnett,William A. & Cornet,Bernard & D'Aspremont,Claude & Gabszewicz,Jean & Mas-Colell,Andreu (ed.), 1991. "Equilibrium Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521392198, January.
    13. 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.
    14. Pollak, Robert A, 1970. "Habit Formation and Dynamic Demand Functions," Journal of Political Economy, University of Chicago Press, vol. 78(4), pages 745-763, Part I Ju.
    15. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.
    2. 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.
    3. Kannai, Yakar & Selden, Larry & Wei, Xiao, 2014. "Myopic separability," Journal of Economic Behavior & Organization, Elsevier, vol. 103(C), pages 125-144.
    4. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Papers 2001-W3, Economics Group, Nuffield College, University of Oxford.
    5. Kannai, Yakar & Selden, Larry & Kang, Minwook & Wei, Xiao, 2016. "Risk neutrality regions," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 75-89.
    6. Chavas, Jean-Paul, 2013. "On Demand Analysis and Dynamics: A Benefit Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149683, Agricultural and Applied Economics Association.
    7. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    8. Lanier, Joshua, 2020. "Risk, ambiguity, and Giffen assets," Journal of Economic Theory, Elsevier, vol. 186(C).
    9. Ole Boysen, 2019. "When does specification or aggregation across consumers matter for economic impact analysis models? An investigation into demand systems," Empirical Economics, Springer, vol. 56(1), pages 137-172, January.
    10. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, October.
    11. Simas Kucinskas, 2015. "Liquidity creation without banks," DNB Working Papers 482, Netherlands Central Bank, Research Department.
    12. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
    13. Simas Kucinskas, 2015. "Liquidity Creation without Banks," Tinbergen Institute Discussion Papers 15-101/VI, Tinbergen Institute.
    14. Apartsin, Yevgenia & Kannai, Yakar, 2006. "Demand properties of concavifiable preferences," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 36-55, December.
    15. repec:eee:labchp:v:1:y:1986:i:c:p:3-102 is not listed on IDEAS
    16. John Quah, 2004. "The aggregate weak axiom in a financial economy through dominant substitution effects," Economics Papers 2004-W18, Economics Group, Nuffield College, University of Oxford.
    17. repec:spo:wpmain:info:hdl:2441/vbu6kd1s68o6r34k5bcm3iopv is not listed on IDEAS
    18. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
    19. Alexander Zimper, 2023. "Belief aggregation for representative agent models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(2), pages 309-342, June.
    20. Susanne Fuchs-Seliger, 2016. "Axiomatic Models of Rational Behavior and Interpretations," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(4), pages 385-401, December.
    21. Florin O. Bilbiie, 2011. "Nonseparable Preferences, Frisch Labor Supply, and the Consumption Multiplier of Government Spending: One Solution to a Fiscal Policy Puzzle," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(1), pages 221-251, February.
    22. Javier Hervés-Estévez & Emma Moreno-García, 2018. "A limit result on bargaining sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 327-341, August.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:55:y:2014:i:1:p:1-28. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.