IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v53y2013i2p315-333.html
   My bibliography  Save this article

Welfare variations and the comparative statics of demand

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-011-0681-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-011-0681-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, September.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Olivier Morand & Kevin Reffett & Suchismita Tarafdar, 2018. "Generalized Envelope Theorems: Applications to Dynamic Programming," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 650-687, March.
    2. Koji Shirai, 2008. "A generalization of monotone comparative statics," Economics Bulletin, AccessEcon, vol. 3(39), pages 1-9.
    3. Elena Antoniadou & Leonard J Mirman & Richard Ruble, 2014. "Lattices and Lotteries," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 445-463, May.
    4. Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
    5. Edward E. Schlee & M. Ali Khan, 2022. "Money Metrics In Applied Welfare Analysis: A Saddlepoint Rehabilitation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 189-210, February.
    6. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    7. Wang, Jianli & Li, Jingyuan, 2016. "Lattice-based monotone comparative statics on saving with Selden/Kreps–Porteus preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 132-138.
    8. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    9. Paweł Dziewulski, 2011. "On Time-to-Build Economies with Multiple-Stage Investments," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 9, pages 23-49.
    10. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.
    11. Brunner, Christoph & Hu, Audrey & Oechssler, Jörg, 2014. "Premium auctions and risk preferences: An experimental study," Games and Economic Behavior, Elsevier, vol. 87(C), pages 467-484.
    12. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    13. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    14. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    15. Prokopovych, Pavlo & Yannelis, Nicholas C., 2017. "On strategic complementarities in discontinuous games with totally ordered strategies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 147-153.
    16. Natalia Lazzati, 2013. "Comparison of equilibrium actions and payoffs across players in games of strategic complements," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 777-788, November.
    17. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    18. repec:kan:wpaper:201412 is not listed on IDEAS
    19. Anne-Christine Barthel & Eric Hoffmann, 2020. "Characterizing monotone games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1045-1068, November.
    20. John Quah, 2016. "Supermodular Correspondences," Economics Series Working Papers 795, University of Oxford, Department of Economics.
    21. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:53:y:2013:i:2:p:315-333. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.