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A Maximum Principle for Control Problems with Monotonicity Constraints

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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.

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File URL: http://www.coll.mpg.de/pdf_dat/2008_04online.pdf
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Bibliographic Info

Paper provided by Max Planck Institute for Research on Collective Goods in its series Working Paper Series of the Max Planck Institute for Research on Collective Goods with number 2008_04.

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Length: 40 pages
Date of creation: Jan 2008
Date of revision:
Handle: RePEc:mpg:wpaper:2008_4

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Related research

Keywords: Maximum Principle; Optimal Control; Monotonicity Constraints; Incentive Problems with Hidden Characteristics;

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References

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  1. Martin Hellwig, 2007. "A Contribution to the Theory of Optimal Utilitarian Income Taxation," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2007_2, Max Planck Institute for Research on Collective Goods.
  2. 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.
  3. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
  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. Martin Hellwig, 2006. "Incentive Problems with Unidimensional Hidden Characteristics: A Unified Approach," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2006_26, Max Planck Institute for Research on Collective Goods, revised Apr 2010.
  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. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Wiley Blackwell, vol. 38(114), pages 175-208, April.
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Citations

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Cited by:
  1. Martin Hellwig, 2007. "A Contribution to the Theory of Optimal Utilitarian Income Taxation," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2007_2, Max Planck Institute for Research on Collective Goods.
  2. Martin F. Hellwig, 2010. "Incentive Problems With Unidimensional Hidden Characteristics: A Unified Approach," Econometrica, Econometric Society, vol. 78(4), pages 1201-1237, 07.
  3. Martin Hellwig, 2004. "Optimal Income Taxation, Public-Goods Provision and Public-Sector Pricing: A Contribution to the Foundations of Public Economics," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2004_14, Max Planck Institute for Research on Collective Goods.
  4. Martin Hellwig, 2009. "Utilitarian Mechanism Design for an Excludable Public Good," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2009_12, Max Planck Institute for Research on Collective Goods.
  5. 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.

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