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A Maximum Principle for Control Problems with Monotonicity Constraints

Author

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  • 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
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    File URL: http://www.coll.mpg.de/pdf_dat/2008_04online.pdf
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    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. 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.
    3. Hellwig, Martin, 2004. "Risk aversion in the small and in the large when outcomes are multidimensional," Papers 04-22, Sonderforschungsbreich 504.
    4. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    5. 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.
    6. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    7. 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.
    8. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
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    Citations

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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. Filip Tokarski, 2024. "Ironing Without Concavification," Papers 2402.11881, arXiv.org, revised Jan 2026.
    6. 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.
    7. 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.
    8. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, July.
    9. 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.
    10. Garrett, Daniel F., 2021. "Payoff implications of incentive contracting," Theoretical Economics, Econometric Society, vol. 16(4), November.

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    JEL classification:

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

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