Mirror utility functions and reflexion properties of various classes of goods
AbstractAny 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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Bibliographic InfoPaper 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.
Date of creation: 11 Nov 2011
Date of revision:
Postal: Helen Chapman, School of Economics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK
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