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Mirror utility functions and reflexion properties of various classes of goods

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  • Peter Moffatt

    (School of Economics, University of East Anglia)

  • Keith Moffatt

    (Trinity College, Cambridge)

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    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.

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    File URL: http://www.uea.ac.uk/menu/depts/eco/research/RePEc/uea/papers_pdf/UEA-AFE-031.pdf
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    Bibliographic Info

    Paper provided by School of Economics, University of East Anglia, Norwich, UK. in its series University of East Anglia Applied and Financial Economics Working Paper Series with number 031.

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    Date of creation: 11 Nov 2011
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    Handle: RePEc:uea:aepppr:2011_31

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    Related research

    Keywords: Reflexion theorems; Giffen behaviour; normal/inferior; necessity/luxury;

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    1. Kohli, Ulrich, 1985. "Inverse demand and anti-giffen goods," European Economic Review, Elsevier, vol. 27(3), pages 397-404.
    2. 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.
    3. Quah, J-K-H, 1996. "The Monotonicity of Individual and Market Demand," Economics Papers 127, Economics Group, Nuffield College, University of Oxford.
    4. Weber, Christian E, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-22, December.
    5. Junko Doi & Kazumichi Iwasa & Koji Shimomura, 2009. "Giffen behavior independent of the wealth level," Economic Theory, Springer, vol. 41(2), pages 247-267, November.
    6. John Quah, 2002. "The Law of Demand and Risk Aversion," Economics Series Working Papers 2002-W03, University of Oxford, Department of Economics.
    7. 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.
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