IDEAS home Printed from https://ideas.repec.org/p/mpg/wpaper/2008_4.html

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 Behavioral Economics 2008_04, Max Planck Institute for Behavioral Economics.
    • 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 Behavioral Economics 2004_6, Max Planck Institute for Behavioral Economics.
    3. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    4. 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.
    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. 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.
    7. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    8. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    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. 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.
    2. 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.
    3. 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.
    4. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    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. 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.
    7. 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.
    8. Filip Tokarski, 2024. "Ironing Without Concavification," Papers 2402.11881, arXiv.org, revised Jan 2026.
    9. 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.
    10. Garrett, Daniel F., 2021. "Payoff implications of incentive contracting," Theoretical Economics, Econometric Society, vol. 16(4), November.

    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 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.
    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. 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.
    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. 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.
    7. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    8. 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.
    9. Laurent Simula & Alain Trannoy, 2020. "Bunching and Rank-Dependent Optimal Income Taxation," CESifo Working Paper Series 8443, CESifo.
    10. 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.
    11. 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), CY Cergy-Paris University, ESSEC and CNRS.
    12. 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.
    13. 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.
    14. 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.
    15. Oztek, Abdullah Selim, 2019. "A Characterization for Marginal Income Tax Schedules," MPRA Paper 103046, University Library of Munich, Germany, revised 02 Dec 2019.
    16. 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.
    17. Florian Hoffmann & Roman Inderst & Ulf Moslener, 2017. "Taxing Externalities Under Financing Constraints," Economic Journal, Royal Economic Society, vol. 127(606), pages 2478-2503, November.
    18. Louis Kaplow, 2007. "Optimal income transfers," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 14(3), pages 295-325, June.
    19. Hirofumi Takikawa, 2026. "Optimal Redistribution with Institutional Reference Points," Discussion Paper Series DP2026-03, Research Institute for Economics & Business Administration, Kobe University.
    20. 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.

    More about this item

    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.