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Welfare variations and the comparative statics of demand

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  • Koji Shirai

Abstract

By employing order-theoretic comparative statics, we provide necessary and sufficient conditions on the direct utility function (alternatively, on the indirect utility function) to guarantee that the compensating and equivalent variations are monotonically increasing in income. We also show that these conditions are sufficient to guarantee normal demand. Our results do not depend on the smoothness or strict quasiconcavity of the utility function, and can be extended to a setting with non-linear prices. Copyright Springer-Verlag 2013

Suggested Citation

  • Koji Shirai, 2013. "Welfare variations and the comparative statics of demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 315-333, June.
    • Handle: RePEc:spr:joecth:v:53:y:2013:i:2:p:315-333
    DOI: 10.1007/s00199-011-0681-z
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    References listed on IDEAS

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    1. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
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    3. Leonard J. Mirman & Richard Ruble, 2008. "Lattice Theory and the Consumer's Problem," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 301-314, May.
    4. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847.
    5. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
    6. 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.
    7. Elena Antoniadou, 2007. "Comparative Statics for the Consumer Problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 189-203, April.
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    Cited by:

    1. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    2. Koch, Caleb M., 2019. "Index-wise comparative statics," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 35-41.
    3. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    Monotone comparative statics; Equivalent variation; Compensating variation; Complementarity; Value order; Indirect utility; D11; C61;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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