IDEAS home Printed from https://ideas.repec.org/p/uea/aepppr/2011_31.html
   My bibliography  Save this paper

Mirror utility functions and reflexion properties of various classes of goods

Author

Listed:
  • Peter Moffatt

    (School of Economics, University of East Anglia)

  • Keith Moffatt

    (Trinity College, Cambridge)

Abstract

Any 2-good direct utility function satisfying standard axioms may be transformed into an indirect utility function, also satisfying standard axioms, by a straightforward change of sign. The reverse is also true. We shall refer to one such function as the `mirror' of the other. It is sometimes the case that the demand function for one of the goods, arising from one utility function, exhibits a particular feature if and only if the mirror utility function exhibits the same feature for the other good. When this occurs, we say that the demand feature in question has the `reflexion property'. It is shown that Giffen behaviour and the necessity/luxury dichotomy are two features of demand that do have this reflexion property. However, it is also shown that the normality/inferiority dichotomy is one feature that does not.

Suggested Citation

  • Peter Moffatt & Keith Moffatt, 2011. "Mirror utility functions and reflexion properties of various classes of goods," University of East Anglia Applied and Financial Economics Working Paper Series 031, School of Economics, University of East Anglia, Norwich, UK..
    • Handle: RePEc:uea:aepppr:2011_31
    as

    Download full text from publisher

    File URL: https://ueaeco.github.io/working-papers/papers/afe/UEA-AFE-031.pdf
    Download Restriction: no
    ---><---

    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. Kohli, Ulrich, 1985. "Inverse demand and anti-giffen goods," European Economic Review, Elsevier, vol. 27(3), pages 397-404.
    3. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, October.
    4. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
    5. Junko Doi & Kazumichi Iwasa & Koji Shimomura, 2012. "Giffen Behavior Independent of the Wealth Level," Lecture Notes in Economics and Mathematical Systems, in: Wim Heijman & Pierre Mouche (ed.), New Insights into the Theory of Giffen Goods, pages 105-126, Springer.
    6. Moffatt, Peter G., 2002. "Is Giffen behaviour compatible with the axioms of consumer theory?," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 259-267, July.
    7. Christian E. Weber, 1997. "The Case of a Giffen Good: Comment," The Journal of Economic Education, Taylor & Francis Journals, vol. 28(1), pages 36-44, March.
    8. repec:bla:manchs:v:69:y:2001:i:6:p:616-22 is not listed on IDEAS
    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. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).

    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. Sproule, Robert A., 2020. "The delimitation of Giffenity for the Wold-Juréen (1953) utility function using relative prices: A note," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 14, pages 1-8.
    2. Massimiliano Landi, 2014. "A Class of Symmetric and Quadratic Utility Functions Generating Giffen Demand," Working Papers 21-2014, Singapore Management University, School of Economics.
    3. Landi, Massimiliano, 2015. "A class of symmetric and quadratic utility functions generating Giffen demand," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 50-54.
    4. 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.
    5. Peter G. Moffatt, 2012. "A Class of Indirect Utility Functions Predicting Giffen Behaviour," Lecture Notes in Economics and Mathematical Systems, in: Wim Heijman & Pierre Mouche (ed.), New Insights into the Theory of Giffen Goods, pages 127-141, Springer.
    6. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, September.
    7. P. G. Moffatt & H. K. Moffatt, 2014. "Giffen Goods and their Reflexion Property," Manchester School, University of Manchester, vol. 82(2), pages 129-142, March.
    8. Junko Doi & Kazumichi Iwasa & Koji Shimomura, 2012. "Giffen Behavior Independent of the Wealth Level," Lecture Notes in Economics and Mathematical Systems, in: Wim Heijman & Pierre Mouche (ed.), New Insights into the Theory of Giffen Goods, pages 105-126, Springer.
    9. Peter Sørensen, 2007. "Simple Utility Functions with Giffen Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 367-370, May.
    10. 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.
    11. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.
    12. 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.
    13. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    14. Miller, Anne, 2023. "Demand Theory for Poverty and Affluence: A Contribution to Utility Theory," MPRA Paper 117618, University Library of Munich, Germany, revised 13 Jun 2023.
    15. Biederman, Daniel K., 2015. "A strictly-concave, non-spliced, Giffen-compatible utility function," Economics Letters, Elsevier, vol. 131(C), pages 24-28.
    16. Sproule, Robert, 2023. "The Anomalies Of The Wold-Juréen (1953) Functional Form In Overview," MPRA Paper 117835, University Library of Munich, Germany.
    17. Robert SPROULE & Michael KARRAS, 2022. "Two conditions which induce Giffen behavior in any numerical analysis if applied to the Wold-Juréen (1953) utility function," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(633), W), pages 197-204, Winter.
    18. Kazuyuki Sasakura, 2016. "Slutsky Revisited: A New Decomposition of the Price Effect," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 2(2), pages 253-280, July.
    19. Miller, Anne, 2024. "The Concept of Separate needs in Cardinal Utility Theory: A Functional Form for Added Leaning-S-shaped Utlities," MPRA Paper 121455, University Library of Munich, Germany.
    20. Miller, Anne, 2022. "Demand theory for poverty and affluence," MPRA Paper 116144, University Library of Munich, Germany.

    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:uea:aepppr:2011_31. 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: Cara Liggins (email available below). General contact details of provider: https://edirc.repec.org/data/esueauk.html .

    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.