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Calculating a Giffen Good

Author

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  • Kazuyuki Sasakura

    (Waseda University)

Abstract

This paper provides a simple example of the utility function with two consumption goods which can be calculated by hand to produce a Giffen good. It is based on the theoretical result by Kubler et al. (Am Econ Rev 103:1034–1053, 2013). Using a model of portfolio selection with a risk-free asset and a risky asset, they showed that there always exists a parameter set which assures that the risk-free asset becomes a Giffen good if the utility function belongs to the HARA (hyperbolic absolute risk aversion) family with decreasing absolute risk aversion (DARA) and decreasing relative risk aversion (DRRA). This paper investigates their result further in a usual microeconomic setting where the risk-free asset and the risky asset are changed to the first and second consumption goods, respectively. It is organized as follows. First, a standard utility maximization problem of a consumer is directly solved to obtain the conditions for the first good to be a Giffen good. Second, the same problem is analyzed by means of decompositions of the price effect due to Slutsky and Sasakura (Italian Econ J 2:258–280, 2016). As is well known, the former decomposition consists of the substitution effect and the income effect, while the latter implies the decomposition into the ratio effect and the unit-elasticity effect. Lastly these analyses are compared and summarized. It should be added that the utility function proposed in this paper can also be used for the analysis of a normal good mutatis mutandis.

Suggested Citation

  • Kazuyuki Sasakura, 2021. "Calculating a Giffen Good," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 7(3), pages 349-369, November.
    • Handle: RePEc:spr:italej:v:7:y:2021:i:3:d:10.1007_s40797-020-00140-1
    DOI: 10.1007/s40797-020-00140-1
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    References listed on IDEAS

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    1. Masuda, Etsusuke & Newman, Peter, 1981. "Gray and Giffen Goods," Economic Journal, Royal Economic Society, vol. 91(364), pages 1011-1014, December.
    2. Meyer, Donald J. & Meyer, Jack, 2005. "Risk preferences in multi-period consumption models, the equity premium puzzle, and habit formation utility," Journal of Monetary Economics, Elsevier, vol. 52(8), pages 1497-1515, November.
    3. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    4. Kazuyuki Sasakura, 2016. "Slutsky Revisited: A New Decomposition of the Price Effect," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 2(2), pages 253-280, July.
    5. Yakar Kannai & Larry Selden, 2014. "Violation of the Law of Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 1-28, January.
    6. Masaki Fujimoto, 2018. "A Geometrical Approach to Giffen Behavior: The Epstein and Spiegel Utility Function Revisited," Manchester School, University of Manchester, vol. 86(5), pages 681-694, September.
    7. 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.
    8. Felix Kubler & Larry Selden & Xiao Wei, 2013. "Inferior Good and Giffen Behavior for Investing and Borrowing," American Economic Review, American Economic Association, vol. 103(2), pages 1034-1053, April.
    9. 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.
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    More about this item

    Keywords

    HARA family; Decreasing relative risk aversion; Giffen good; Slutsky equation; Ratio effect;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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