IDEAS home Printed from https://ideas.repec.org/p/mpg/wpaper/2008_4.html
   My bibliography  Save this paper

A Maximum Principle for Control Problems with Monotonicity Constraints

Author

Listed:
  • Martin Hellwig

    (Max Planck Institute for Research on Collective Goods, Bonn)

Abstract

The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this variable as a new control variable subject to a nonnegativity constraint, the paper obtains the maximum principle without such an additional assumption. The result is useful for studying incentive problems with hidden characteristics when the type set is a continuum and preferences satisfy a single-crossing constraint.

Suggested Citation

  • Martin Hellwig, 2008. "A Maximum Principle for Control Problems with Monotonicity Constraints," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2008_04, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2008_4
    as

    Download full text from publisher

    File URL: http://www.coll.mpg.de/pdf_dat/2008_04online.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hellwig, Martin F., 2007. "A contribution to the theory of optimal utilitarian income taxation," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1449-1477, August.
    2. Martin Hellwig, 2004. "Risk Aversion in the Small and in the Large. When Outcomes are Multidimensional," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2004_6, Max Planck Institute for Research on Collective Goods.
    3. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    4. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    5. Hellwig, Martin F., 2007. "The undesirability of randomized income taxation under decreasing risk aversion," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 791-816, April.
    6. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    7. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    8. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
    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. Jacquet, Laurence & Lehmann, Etienne & Van der Linden, Bruno, 2013. "Optimal redistributive taxation with both extensive and intensive responses," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1770-1805.
    2. Hellwig, Martin F., 2007. "A contribution to the theory of optimal utilitarian income taxation," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1449-1477, August.
    3. Martin F. Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 361-397, September.
    4. Gerardi, Dino & Hörner, Johannes & Maestri, Lucas, 2014. "The role of commitment in bilateral trade," Journal of Economic Theory, Elsevier, vol. 154(C), pages 578-603.
    5. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    6. Garrett, Daniel F., 2020. "Payoff Implications of Incentive Contracting," TSE Working Papers 20-1140, Toulouse School of Economics (TSE).
    7. Artyom Shneyerov, 2014. "An optimal slow Dutch auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 577-602, November.
    8. Hellwig, Martin, 2004. "Optimal income taxation, public-goods provision and public-sector pricing : a contribution to the foundations of public economics," Papers 04-42, Sonderforschungsbreich 504.
    9. Filip Tokarski, 2024. "Ironing allocations," Papers 2402.11881, arXiv.org.
    10. Hellwig, Martin F., 2010. "A generalization of the Atkinson-Stiglitz (1976) theorem on the undesirability of nonuniform excise taxation," Economics Letters, Elsevier, vol. 108(2), pages 156-158, August.

    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. Hellwig, Martin F., 2007. "A contribution to the theory of optimal utilitarian income taxation," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1449-1477, August.
    2. Martin Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 361-397, September.
    3. Brett, Craig & Weymark, John A., 2016. "Voting over selfishly optimal nonlinear income tax schedules with a minimum-utility constraint," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 18-31.
    4. Martin Hellwig, 2004. "Optimal Income Taxation, Public-Goods Provision and Public-Sector Pricing: A Contribution to the Foundations of Public Economics," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2004_14, Max Planck Institute for Research on Collective Goods.
    5. Jacquet, Laurence & Lehmann, Etienne & Van der Linden, Bruno, 2013. "Optimal redistributive taxation with both extensive and intensive responses," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1770-1805.
    6. Laurence Jacquet & Etienne Lehmann, 2021. "Optimal Income Taxation with Composition Effects," Journal of the European Economic Association, European Economic Association, vol. 19(2), pages 1299-1341.
    7. Brett, Craig & Weymark, John A., 2017. "Voting over selfishly optimal nonlinear income tax schedules," Games and Economic Behavior, Elsevier, vol. 101(C), pages 172-188.
    8. Hellwig, Martin F., 2007. "The undesirability of randomized income taxation under decreasing risk aversion," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 791-816, April.
    9. Konishi, Hideo, 1995. "A Pareto-improving commodity tax reform under a smooth nonlinear income tax," Journal of Public Economics, Elsevier, vol. 56(3), pages 413-446, March.
    10. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    11. Laurent Simula & Alain Trannoy, 2020. "Bunching and Rank-Dependent Optimal Income Taxation," CESifo Working Paper Series 8443, CESifo.
    12. Laurence Jacquet & Etienne lehmann & Bruno Van Der Linden, 2012. "Signing distortions in optimal tax or other adverse selection models with random participation," THEMA Working Papers 2012-27, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Boone, Jan & Bovenberg, Lans, 2004. "The optimal taxation of unskilled labor with job search and social assistance," Journal of Public Economics, Elsevier, vol. 88(11), pages 2227-2258, September.
    14. Laurent Simula & Alain Trannoy, 2023. "Bunching in rank-dependent optimal income tax schedules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 237-263, January.
    15. Laurence Jacquet & Dirk Van de Gaer, 2015. "Politiques fiscales optimales pour les bas revenus et principe de compensation," Revue économique, Presses de Sciences-Po, vol. 66(3), pages 579-600.
    16. Boadway, Robin & Jacquet, Laurence, 2008. "Optimal marginal and average income taxation under maximin," Journal of Economic Theory, Elsevier, vol. 143(1), pages 425-441, November.
    17. Thomas Koch & Javier Birchenall, 2016. "Taking versus taxing: an analysis of conscription in a private information economy," Public Choice, Springer, vol. 167(3), pages 177-199, June.
    18. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 311-321, December.
    19. Oztek, Abdullah Selim, 2019. "A Characterization for Marginal Income Tax Schedules," MPRA Paper 103046, University Library of Munich, Germany, revised 02 Dec 2019.
    20. Fleurbaey, Marc & Gary-Bobo, Robert J. & Maguain, Denis, 2002. "Education, distributive justice, and adverse selection," Journal of Public Economics, Elsevier, vol. 84(1), pages 113-150, April.

    More about this item

    Keywords

    Maximum Principle; Optimal Control; Monotonicity Constraints; Incentive Problems with Hidden Characteristics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:mpg:wpaper:2008_4. 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: Marc Martin (email available below). General contact details of provider: https://edirc.repec.org/data/mppggde.html .

    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.