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A strictly-concave, non-spliced, Giffen-compatible utility function

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  • Biederman, Daniel K.

Abstract

We propose a new bivariate utility function for the analysis of Giffen behavior. The function is strictly concave and twice continuously differentiable, with marginal utilities that are strictly positive. The function is defined by a single equation, rather than by two or more “spliced” functional forms. We contend that, in the search for Giffen-compatible utility functions, it is helpful to consider explicitly the elasticities of the consumer’s marginal rate of substitution with respect to the quantities of the two goods.

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  • Biederman, Daniel K., 2015. "A strictly-concave, non-spliced, Giffen-compatible utility function," Economics Letters, Elsevier, vol. 131(C), pages 24-28.
    • Handle: RePEc:eee:ecolet:v:131:y:2015:i:c:p:24-28
    DOI: 10.1016/j.econlet.2015.03.024
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    References listed on IDEAS

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    1. 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.
    2. Peter Sørensen, 2007. "Simple Utility Functions with Giffen Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 367-370, May.
    3. Robert T. Jensen & Nolan H. Miller, 2008. "Giffen Behavior and Subsistence Consumption," American Economic Review, American Economic Association, vol. 98(4), pages 1553-1577, September.
    4. Bilancini, Ennio & Boncinelli, Leonardo, 2010. "Preferences and normal goods: An easy-to-check necessary and sufficient condition," Economics Letters, Elsevier, vol. 108(1), pages 13-15, July.
    5. Landi, Massimiliano, 2015. "A class of symmetric and quadratic utility functions generating Giffen demand," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 50-54.
    6. Junko Doi & Kazumichi Iwasa & Koji Shimomura, 2012. "Giffen Behavior Independent of the Wealth Level," Lecture Notes in Economics and Mathematical Systems, in: Wim Heijman & Pierre Mouche (ed.), New Insights into the Theory of Giffen Goods, pages 105-126, Springer.
    7. 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.
    8. Chipman, John S., 1977. "An empirical implication of Auspitz-Lieben-Edgeworth-Pareto complementarity," Journal of Economic Theory, Elsevier, vol. 14(1), pages 228-231, February.
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    Cited by:

    1. Le Van, Cuong & Pham, Ngoc-Sang, 2020. "Demand and equilibrium with inferior and Giffen behaviors," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 45-50.
    2. 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.
    3. Franks, Edwin & Bryant, William D.A., 2017. "The Uncompensated Law of Demand: A ‘Revealed Preference’ approach," Economics Letters, Elsevier, vol. 152(C), pages 105-111.
    4. Zhu, Drew, 2016. "The Mechanism of Giffen Behaviour," MPRA Paper 75707, University Library of Munich, Germany.
    5. Miller, Anne, 2024. "The Concept of Separate needs in Cardinal Utility Theory: A Functional Form for Added Leaning-S-shaped Utlities," MPRA Paper 121455, University Library of Munich, Germany.
    6. Miller, Anne, 2022. "Demand theory for poverty and affluence," MPRA Paper 116144, University Library of Munich, Germany.
    7. Sproule, Robert A., 2020. "The delimitation of Giffenity for the Wold-Juréen (1953) utility function using relative prices: A note," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 14, pages 1-8.

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    More about this item

    Keywords

    Utility function; Giffen behavior; Elasticity of marginal rate of substitution;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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