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A Maximum Principle for Control Problems with Monotonicity Constraints

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Author Info
Martin Hellwig () (Max Planck Institute for Research on Collective Goods, Bonn)

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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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Publisher 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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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October. [Downloadable!] (restricted)
  3. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Blackwell Publishing, vol. 38(114), pages 175-208, April. [Downloadable!] (restricted)
  4. J. A. Mirrlees, 1976. "Optimal Tax Theory: A Synthesis," Working papers 176, Massachusetts Institute of Technology (MIT), Department of Economics.
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  5. Martin Hellwig, 2006. "Incentive Provision with 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. [Downloadable!]
  6. 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. [Downloadable!] (restricted)
    Other versions:
  7. Martin Hellwig, 2005. "A Contribution to the Theory of Optimal Utilitarian Income Taxation," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2005_23, Max Planck Institute for Research on Collective Goods. [Downloadable!]
    Other versions:
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Martin Hellwig, 2005. "A Contribution to the Theory of Optimal Utilitarian Income Taxation," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2005_23, Max Planck Institute for Research on Collective Goods. [Downloadable!]
    Other versions:
  2. Martin Hellwig, 2006. "Incentive Provision with 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. [Downloadable!]
  3. Hellwig, Martin, 2004. "Optimal Income Taxation, Public-Goods Provision," Sonderforschungsbereich 504 Publications 04-42, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  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. [Downloadable!]
  5. 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. [Downloadable!]
  6. Martin Hellwig, 2008. "A Generalization of the Atkinson-Stiglitz (1976) Theorem on the Undesirability of Nonuniform Excise Taxation," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2008_47, Max Planck Institute for Research on Collective Goods. [Downloadable!]
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