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.
|Date of creation:||11 Nov 2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 44 1603 591131
Fax: +44(0)1603 4562592
Web page: http://www.uea.ac.uk/economics
More information through EDIRC
|Order Information:|| Postal: Jessica Pointer, School of Economics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, October.
- 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.
- John Quah, 2002.
"The Law of Demand and Risk Aversion,"
Economics Series Working Papers
2002-W03, University of Oxford, Department of Economics.
- Junko Doi & Kazumichi Iwasa & Koji Shimomura, 2009. "Giffen behavior independent of the wealth level," Economic Theory, Springer, vol. 41(2), pages 247-267, November.
- John K.-H. Quah, 2000.
"The Monotonicity of Individual and Market Demand,"
Econometric Society, vol. 68(4), pages 911-930, July.
- Kohli, Ulrich, 1985. "Inverse demand and anti-giffen goods," European Economic Review, Elsevier, vol. 27(3), pages 397-404.
- Weber, Christian E, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-22, December.
When requesting a correction, please mention this item's handle: RePEc:uea:aepppr:2011_31. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alasdair Brown)
If references are entirely missing, you can add them using this form.