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Mirror utility functions and reflexion properties of various classes of goods

Peter Moffatt and Keith Moffatt
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Keith Moffatt: Trinity College, Cambridge

No 31, University of East Anglia Applied and Financial Economics Working Paper Series from School of Economics, University of East Anglia, Norwich, UK.

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.

Keywords: Reflexion theorems; Giffen behaviour; normal/inferior; necessity/luxury (search for similar items in EconPapers)
Date: 2011-11-11
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