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Preferences and Normal Goods: An Easy-to-Check Necessary and Sufficient Condition

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  • Ennio Bilancini
  • Leonardo Boncinelli

Abstract

We provide a necessary and sufficient condition for goods to be normal when utility functions are differentiable and strongly quasi-concave. Our condition is equivalent to the condition proposed by Alarie et al. (1990), but it is easier to check: it only requires to compute the minors associated with the border column (or row) of the bordered Hessian matrix of the utility function.

Suggested Citation

  • Ennio Bilancini & Leonardo Boncinelli, 2010. "Preferences and Normal Goods: An Easy-to-Check Necessary and Sufficient Condition," Center for Economic Research (RECent) 042, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    • Handle: RePEc:mod:recent:042
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    References listed on IDEAS

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    1. Alarie, Yves & Bronsard, Camille & Ouellette, Pierre, 1990. "Preferences and normal goods: A necessary and sufficient condition," Journal of Economic Theory, Elsevier, vol. 51(2), pages 423-430, August.
    2. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    3. Leroux, Alain, 1987. "Preferences and normal goods: A sufficient condition," Journal of Economic Theory, Elsevier, vol. 43(1), pages 192-199, October.
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    Cited by:

    1. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Normality of demand in a two-goods setting," Journal of Economic Theory, Elsevier, vol. 173(C), pages 361-382.
    2. Biederman, Daniel K., 2015. "A strictly-concave, non-spliced, Giffen-compatible utility function," Economics Letters, Elsevier, vol. 131(C), pages 24-28.
    3. Lanot, Gauthier, 2016. "The Marginal Rate of Substitution and the Specification of Labour Supply Models," Umeå Economic Studies 922, Umeå University, Department of Economics.
    4. Annie Liang & Xiaosheng Mu & Vasilis Syrgkanis, 2022. "Dynamically Aggregating Diverse Information," Econometrica, Econometric Society, vol. 90(1), pages 47-80, January.
    5. Annie Liang & Xiaosheng Mu & Vasilis Syrgkanis, 2021. "Dynamically Aggregating Diverse Information," Working Papers 2021-43, Princeton University. Economics Department..

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    More about this item

    Keywords

    normal goods; bordered hessian;

    JEL classification:

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

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