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Mirror utility functions and reflexion properties of various classes of goods


  • Peter Moffatt

    (School of Economics, University of East Anglia)

  • Keith Moffatt

    (Trinity College, Cambridge)


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

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    References listed on IDEAS

    1. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
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    4. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.
    5. 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.
    6. 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.
    7. Junko Doi & Kazumichi Iwasa & Koji Shimomura, 2009. "Giffen behavior independent of the wealth level," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 247-267, November.
    8. Weber, Christian E, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-622, December.
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