IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v122y2026ics0304406825001223.html

Optimal contracts under general mixed constraints: Continuity, structure, and applications

Author

Listed:
  • Simons, Aggey

Abstract

This paper characterizes optimal contracts under adverse selection when the principal faces a general linear constraint involving both the quantity produced and the transfer paid. These constraints capture enforcement limits, budget restrictions, and minimum quality standards. Using optimal control techniques, we establish existence and continuity of the optimal quantity schedule and derive a three-region structure: under regularity conditions, the optimal contract splits the type space into at most three connected intervals (slack and binding intervals), where binding intervals generically induce endogenous bunching of quantities. Our unifying framework, along with novel analytical assumptions, provides rigorous foundations for understanding how optimal mechanisms behave under such smooth constraints and offers a toolkit for analyzing a broad class of constrained contracting problems.

Suggested Citation

  • Simons, Aggey, 2026. "Optimal contracts under general mixed constraints: Continuity, structure, and applications," Journal of Mathematical Economics, Elsevier, vol. 122(C).
    • Handle: RePEc:eee:mateco:v:122:y:2026:i:c:s0304406825001223
    DOI: 10.1016/j.jmateco.2025.103205
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406825001223
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2025.103205?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rochet, Jean-Charles, 1985. "Bilateral monopoly with imperfect information," Journal of Economic Theory, Elsevier, vol. 36(2), pages 214-236, August.
    2. Raj Chetty & John N. Friedman & Tore Olsen & Luigi Pistaferri, 2011. "Adjustment Costs, Firm Responses, and Micro vs. Macro Labor Supply Elasticities: Evidence from Danish Tax Records," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(2), pages 749-804.
    3. Jean-Jacques Laffont & Jean Tirole, 1993. "A Theory of Incentives in Procurement and Regulation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121743, December.
    4. Thomas, Lionel, 2002. "Non-linear pricing with budget constraint," Economics Letters, Elsevier, vol. 75(2), pages 257-263, April.
    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. Michael Kuhn & Luigi Siciliani, 2009. "Performance Indicators for Quality with Costly Falsification," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 18(4), pages 1137-1154, December.
    7. repec:adr:anecst:y:1990:i:18:p:07 is not listed on IDEAS
    8. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    9. Henrik J. Kleven & Mazhar Waseem, 2013. "Using Notches to Uncover Optimization Frictions and Structural Elasticities: Theory and Evidence from Pakistan," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 669-723.
    10. Axel Gautier & Manipushpak Mitra, 2006. "Regulating a monopolist with limited funds," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 705-718, April.
    11. 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.
    12. Martimort, David & Semenov, Aggey & Stole, Lars, 2017. "Optimal stationary contract with two-sided imperfect enforcement and persistent adverse selection," Economics Letters, Elsevier, vol. 159(C), pages 18-22.
    13. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    14. Rey, Patrick & Tirole, Jean, 1986. "The Logic of Vertical Restraints," American Economic Review, American Economic Association, vol. 76(5), pages 921-939, December.
    15. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    16. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    17. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    18. Bernard Salanié, 1990. "Sélection adverse et aversion pour le risque," Annals of Economics and Statistics, GENES, issue 18, pages 131-149.
    Full references (including those not matched with items on IDEAS)

    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. Andersson, Tommy, 2004. "Essays on Nonlinear Pricing and Welfare," MPRA Paper 59446, University Library of Munich, Germany.
    2. Hoppe, Eva I. & Schmitz, Patrick W., 2015. "Do sellers offer menus of contracts to separate buyer types? An experimental test of adverse selection theory," Games and Economic Behavior, Elsevier, vol. 89(C), pages 17-33.
    3. Noldeke, Georg & Samuelson, Larry, 2007. "Optimal bunching without optimal control," Journal of Economic Theory, Elsevier, vol. 134(1), pages 405-420, May.
    4. David Martimort & Aggey Semenov & Lars Stole, 2017. "A Theory of Contracts with Limited Enforcement," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 816-852.
    5. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2020. "Bank monitoring incentives under moral hazard and adverse selection," Post-Print hal-01435460, HAL.
    6. , R., 2008. "Rigidity in bilateral trade with holdup," Theoretical Economics, Econometric Society, vol. 3(1), March.
    7. 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.
    8. Wong, Adam Chi Leung, 2014. "The choice of the number of varieties: Justifying simple mechanisms," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 7-21.
    9. Waldenstrom, Daniel & Bastani, Spencer, 2020. "The Ability Gradient in Bunching," CEPR Discussion Papers 14599, Centre for Economic Policy Research.
    10. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2017. "Bank monitoring incentives under moral hazard and adverse selection," Working Papers hal-01435460, HAL.
    11. Dirk Bergemann & Alessandro Pavan, 2015. "Introduction to JET Symposium Issue on "Dynamic Contracts and Mechanism Design"," Cowles Foundation Discussion Papers 2016, Cowles Foundation for Research in Economics, Yale University.
    12. 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.
    13. Nicol'as Hern'andez Santib'a~nez & Dylan Possamai & Chao Zhou, 2017. "Bank monitoring incentives under moral hazard and adverse selection," Papers 1701.05864, arXiv.org, revised Jan 2019.
    14. Rodrigo Carril, 2021. "Rules Versus Discretion in Public Procurement," Working Papers 1232, Barcelona School of Economics.
    15. B. Caillaud & R. Guesnerie & P. Rey & J. Tirole, 1988. "Government Intervention in Production and Incentives Theory: A Review of Recent Contributions," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 1-26, Spring.
    16. Jorge Paulo De Araújo & Marcelo De Carvalho Griebeler, 2014. "On The Integral Representation Of Thevalue Function," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 118, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    17. Noldeke,G. & Samuelson,L., 2004. "Decomposable principal-agent problems," Working papers 14, Wisconsin Madison - Social Systems.
    18. Carina Neisser, 2021. "The Elasticity of Taxable Income: A Meta-Regression Analysis [The top 1% in international and historical perspective]," The Economic Journal, Royal Economic Society, vol. 131(640), pages 3365-3391.
    19. Alasseur, Clémence & Chaton, Corinne & Hubert, Emma, 2022. "Optimal contracts under adverse selection for staple goods such as energy: Effectiveness of in-kind insurance," Energy Economics, Elsevier, vol. 106(C).
    20. Carmen Camacho & Hye-Jin Cho, 2020. "Sorting in Credit Rationing: An Elementary Survey," PSE Working Papers halshs-03030433, HAL.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L51 - Industrial Organization - - Regulation and Industrial Policy - - - Economics of Regulation
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

    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:eee:mateco:v:122:y:2026:i:c:s0304406825001223. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.