IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/11293.html
   My bibliography  Save this paper

Quasi-Linear Integrability

Author

Listed:
  • Nocke, Volker
  • Schutz, Nicolas

Abstract

Applied researchers often work with demand systems that do not depend on income, with the implicit assumption that preferences are quasi-linear and income sufficiently large. The classic approach to the integrability of demand does not readily apply in this case. Adopting a much simpler approach that is based on Poincaré's Lemma and duality, we provide necessary and sufficient conditions for the quasi-linear integrability of such demand systems. We also derive results on the associated utility function and its domain.

Suggested Citation

  • Nocke, Volker & Schutz, Nicolas, 2016. "Quasi-Linear Integrability," CEPR Discussion Papers 11293, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:11293
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP11293
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
    3. József Sákovics, 2013. "Revealed cardinal preference," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 39-45, May.
    4. Jackson, Matthew O., 1986. "Integration of demand and continuous utility functions," Journal of Economic Theory, Elsevier, vol. 38(2), pages 298-312, April.
    5. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
    6. Donald J. Brown & Caterina Calsamiglia, 2008. "The Nonparametric Approach to Applied Welfare Analysis," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 41-46, Springer.
    7. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.
    8. Pawel Dziewulski & John Quah, 2014. "Testing for production with complementarities," Economics Series Working Papers 722, University of Oxford, Department of Economics.
    9. Amir, Rabah & Erickson, Philip & Jin, Jim, 2017. "On the microeconomic foundations of linear demand for differentiated products," Journal of Economic Theory, Elsevier, vol. 169(C), pages 641-665.
    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. Thomas Favory, 2020. "Multiproduct Firms and Discrete Choice Models of Demand: Existence and Uniqueness of the Bertrand-Nash Equilibrium," Economics Discussion / Working Papers 20-24, The University of Western Australia, Department of Economics.
    2. Jeon, Doh-Shin & Lefouili, Yassine & Li, Yaxin & Simcoe, Timothy, 2023. "Ecosystems and Complementary Platforms," TSE Working Papers 23-1468, Toulouse School of Economics (TSE), revised Apr 2024.
    3. Marco Castillo & Mikhail Freer, 2023. "A general revealed preference test for quasilinear preferences: theory and experiments," Experimental Economics, Springer;Economic Science Association, vol. 26(3), pages 673-696, July.
    4. Nocke, Volker & Schutz, Nicolas, 2018. "Quasi-linear integrability: Addendum," Journal of Economic Theory, Elsevier, vol. 175(C), pages 1-2.
    5. Choné, Philippe & Linnemer, Laurent, 2020. "Linear demand systems for differentiated goods: Overview and user’s guide," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    6. Yang, Erya & Kopylov, Igor, 2023. "Random quasi-linear utility," Journal of Economic Theory, Elsevier, vol. 209(C).
    7. Thibault Fally, 2018. "Integrability and Generalized Separability," NBER Working Papers 25025, National Bureau of Economic Research, Inc.
    8. Amir, Rabah & Erickson, Philip & Jin, Jim, 2017. "On the microeconomic foundations of linear demand for differentiated products," Journal of Economic Theory, Elsevier, vol. 169(C), pages 641-665.
    9. Mikhail Freer & Marco Castillo, 2021. "A General Revealed Preference Test for Quasilinear Preferences: Theory and Experiments," Papers 2111.01248, arXiv.org, revised Dec 2022.
    10. Simona Bigerna & Carlo Andrea Bollino & Maria Chiara D’Errico, 2020. "A general expenditure system for estimation of consumer demand functions," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 37(3), pages 1071-1088, October.
    11. Fally, Thibault, 2022. "Generalized separability and integrability: Consumer demand with a price aggregator," Journal of Economic Theory, Elsevier, vol. 203(C).

    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. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    2. Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.
    3. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev.2, Osaka University, Graduate School of Economics, revised Aug 2016.
    4. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    5. Richard Blundell & Martin Browning & Ian Crawford, 2008. "Best Nonparametric Bounds on Demand Responses," Econometrica, Econometric Society, vol. 76(6), pages 1227-1262, November.
    6. Alfred Galichon & John Quah, 2013. "Symposium on revealed preference analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 419-423, November.
    7. Laurens CHERCHYE & Ian CRAWFORD & Bram DE ROCK & Frederic VERMEULEN, 2011. "Aggregation without the aggravation? Nonparametric analysis of the representative consumer," Working Papers of Department of Economics, Leuven ces11.36, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    8. Laurens CHERCHYE & Ian CRAWFORD & Bram DE ROCK & Frederic VERMEULEN, 2013. "Gorman revisited: nonparametric conditions for exact linear aggregation," Working Papers of Department of Economics, Leuven ces13.05, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    9. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    10. Chambers, Christopher P. & Rehbeck, John, 2018. "Note on symmetric utility," Economics Letters, Elsevier, vol. 162(C), pages 27-29.
    11. Mikhail Freer & César Martinelli, 2023. "An algebraic approach to revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 717-742, April.
    12. Chambers, Christopher P. & Liu, Ce & Rehbeck, John, 2020. "Costly information acquisition," Journal of Economic Theory, Elsevier, vol. 186(C).
    13. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    14. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    15. Rahul Deb & Yuichi Kitamura & John K H Quah & Jörg Stoye, 2023. "Revealed Price Preference: Theory and Empirical Analysis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 707-743.
    16. Geoffroy de Clippel & Kareen Rozen, 2018. "Consumer Theory with Misperceived Tastes," Working Papers 2018-10, Brown University, Department of Economics.
    17. Shiozawa, Kohei, 2016. "Revealed preference test and shortest path problem; graph theoretic structure of the rationalizability test," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 38-48.
    18. Chambers, Christopher P. & Echenique, Federico & Shmaya, Eran, 2010. "On behavioral complementarity and its implications," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2332-2355, November.
    19. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17, Osaka University, Graduate School of Economics.
    20. Christopher P Chambers & Federico Echenique, 2021. "Empirical Welfare Economics," Papers 2108.03277, arXiv.org, revised Jun 2024.

    More about this item

    Keywords

    Quasi-linear demand; Integrability; Duality;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cpr:ceprdp:11293. 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: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    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.