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A Class of Indirect Utility Functions Predicting Giffen Behaviour

In: New Insights into the Theory of Giffen Goods

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  • Peter G. Moffatt

    (University of East Anglia)

Abstract

The problem of recognising Giffen behaviour is approached from the standpoint of the indirect utility function (IUF) from which the Marshallian demands are easily obtained via Roy’s identity. It is shown that, for the two-good situation, downward convergence of the contours of the IUF is necessary for giffenity, and sufficient if this downward convergence is strong enough, in a sense that is geometrically determined. A family of IUFs involving hyperbolic contours convex to the origin, and having this property of (locally) downward convergence is constructed. The Marshallian demands are obtained, and the region of Giffen behaviour determined. For this family, such regions exist for each good, and are non-overlapping. Finally, it is shown by geometric construction that the family of Direct Utility Functions having the same pattern of hyperbolic contours also exhibits giffenity in corresponding subregions of the positive quadrant.

Suggested Citation

  • Peter G. Moffatt, 2012. "A Class of Indirect Utility Functions Predicting Giffen Behaviour," Lecture Notes in Economics and Mathematical Systems, in: Wim Heijman & Pierre Mouche (ed.), New Insights into the Theory of Giffen Goods, pages 127-141, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-21777-7_10
    DOI: 10.1007/978-3-642-21777-7_10
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    References listed on IDEAS

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    1. Henry Keith Moffatt & Peter Moffatt, 2010. "Giffen Goods: A Duality Theorem," University of East Anglia Applied and Financial Economics Working Paper Series 012, School of Economics, University of East Anglia, Norwich, UK..
    2. 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.
    3. 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.
    4. Weber, Christian E, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-622, December.
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    Cited by:

    1. Massimiliano Landi, 2014. "A Class of Symmetric and Quadratic Utility Functions Generating Giffen Demand," Working Papers 21-2014, Singapore Management University, School of Economics.
    2. Landi, Massimiliano, 2015. "A class of symmetric and quadratic utility functions generating Giffen demand," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 50-54.
    3. Miller, Anne, 2023. "Demand Theory for Poverty and Affluence: A Contribution to Utility Theory," MPRA Paper 117618, University Library of Munich, Germany, revised 13 Jun 2023.
    4. Miller, Anne, 2022. "Demand theory for poverty and affluence," MPRA Paper 116144, University Library of Munich, Germany.
    5. Biederman, Daniel K., 2015. "A strictly-concave, non-spliced, Giffen-compatible utility function," Economics Letters, Elsevier, vol. 131(C), pages 24-28.
    6. Zhu, Drew, 2016. "The Mechanism of Giffen Behaviour," MPRA Paper 75707, University Library of Munich, Germany.

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