Mirror utility functions and reflexion properties of various classes of goods
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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- 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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2002-W3, Economics Group, Nuffield College, University of Oxford.
- Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, October.
- 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.
- Kohli, Ulrich, 1985. "Inverse demand and anti-giffen goods," European Economic Review, Elsevier, vol. 27(3), pages 397-404.
- 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.
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