IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v189y2021i3d10.1007_s10957-021-01861-8.html
   My bibliography  Save this article

The Risk-Sharing Problem Under Limited Liability Constraints in a Single-Period Model

Author

Listed:
  • Jessica Martin

    (INSA de Toulouse, IMT UMR CNRS 5219, Université de Toulouse)

Abstract

This work provides analysis of a variant of the Risk-Sharing Principal-Agent problem in a single period setting with additional constant lower and upper bounds on the wage paid to the Agent. The effect of the extra constraints on optimal contract existence is studied and leads to conditions on the underlying utility functions under which an optimum may be attained. Solution characterization is then provided along with the derivation of a Borch rule for Limited Liability. Finally, some applications, including the CARA utility case, are discussed.

Suggested Citation

  • Jessica Martin, 2021. "The Risk-Sharing Problem Under Limited Liability Constraints in a Single-Period Model," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 854-872, June.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01861-8
    DOI: 10.1007/s10957-021-01861-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01861-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-021-01861-8?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Page, Frank Jr., 1987. "The existence of optimal contracts in the principal-agent model," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 157-167, April.
    2. James A. Mirrlees, 1976. "The Optimal Structure of Incentives and Authority Within an Organization," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 105-131, Spring.
    3. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    4. Ohad Kadan & Philip J. Reny & Jeroen M. Swinkels, 2017. "Existence of Optimal Mechanisms in Principal‐Agent Problems," Econometrica, Econometric Society, vol. 85, pages 769-823, May.
    5. Kadan, Ohad & Swinkels, Jeroen M., 2013. "Minimum payments and induced effort in moral hazard problems," Games and Economic Behavior, Elsevier, vol. 82(C), pages 468-489.
    6. Mathias Dewatripont & Patrick Legros & Steven A. Matthews, 2003. "Moral Hazard and Capital Structure Dynamics," Journal of the European Economic Association, MIT Press, vol. 1(4), pages 890-930, June.
    7. Matthews, Steven A., 2001. "Renegotiating Moral Hazard Contracts under Limited Liability and Monotonicity," Journal of Economic Theory, Elsevier, vol. 97(1), pages 1-29, March.
    8. Eun‐Soo Park, 1995. "Incentive Contracting Under Limited Liability," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 477-490, September.
    9. Sappington, David, 1983. "Limited liability contracts between principal and agent," Journal of Economic Theory, Elsevier, vol. 29(1), pages 1-21, February.
    10. Ross, Stephen A, 1973. "The Economic Theory of Agency: The Principal's Problem," American Economic Review, American Economic Association, vol. 63(2), pages 134-139, May.
    11. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    12. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    13. Park, Eun-Soo, 1995. "Incentive Contracting under Limited Liability," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 477-490, Fall.
    14. Son Ku Kim, 1997. "Limited Liability and Bonus Contracts," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(4), pages 899-913, December.
    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. Jessica Martin, 2020. "The Risk-Sharing problem under limited liability constraints in a single-period model," Working Papers hal-02566942, HAL.
    2. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    3. Kadan, Ohad & Swinkels, Jeroen M., 2013. "Minimum payments and induced effort in moral hazard problems," Games and Economic Behavior, Elsevier, vol. 82(C), pages 468-489.
    4. Inés Macho-Stadler & David Pérez-Castrillo, 2018. "Moral hazard: Base models and two extensions," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 16, pages 453-485, Edward Elgar Publishing.
    5. Itza Tlaloc Quetzalcoatl Curiel-Cabral & Sonia Giannatale & Giselle Labrador-Badía, 2024. "Risk Aversion, Reservation Utility and Bargaining Power: An Evolutionary Algorithm Approximation of Incentive Contracts," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 477-511, February.
    6. Jiajia Cong & Wen Zhou, 2021. "Optimal contract under double moral hazard and limited liability," Journal of Economics, Springer, vol. 134(1), pages 49-71, September.
    7. Jenny Kragl & Anja Schöttner, 2014. "Wage Floors, Imperfect Performance Measures, And Optimal Job Design," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(2), pages 525-550, May.
    8. Hilmer, Michael, 2013. "Fiscal treatment of managerial compensation - a welfare analysis," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79703, Verein für Socialpolitik / German Economic Association.
    9. Jenny Kragl & Anja Schöttner, 2014. "Wage Floors, Imperfect Performance Measures, And Optimal Job Design," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 525-550, May.
    10. Leon Yang Chu & Guoming Lai, 2013. "Salesforce Contracting Under Demand Censorship," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 320-334, May.
    11. Bo Chen & Yu Chen & David Rietzke, 2017. "Simple Contracts under Observable and Hidden Actions," Graz Economics Papers 2017-07, University of Graz, Department of Economics.
    12. Chi, Chang Koo & Choi, Kyoung Jin, 2023. "A dual approach to agency problems," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    13. Fabian Herweg & Daniel Muller & Philipp Weinschenk, 2010. "Binary Payment Schemes: Moral Hazard and Loss Aversion," American Economic Review, American Economic Association, vol. 100(5), pages 2451-2477, December.
    14. Tinglong Dai & Kinshuk Jerath, 2013. "Salesforce Compensation with Inventory Considerations," Management Science, INFORMS, vol. 59(11), pages 2490-2501, November.
    15. Bo Chen & Yu Chen & David Rietzke, 2020. "Simple contracts under observable and hidden actions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1023-1047, June.
    16. Daniel Krv{s}ek & Dylan Possamai, 2023. "Randomisation with moral hazard: a path to existence of optimal contracts," Papers 2311.13278, arXiv.org.
    17. Kragl, Jenny & Schöttner, Anja, 2011. "Wage floors and optimal job design," Bonn Econ Discussion Papers 01/2011, University of Bonn, Bonn Graduate School of Economics (BGSE).
    18. Chang Koo Chi & Kyoung Jin Choi, 2022. "A Dual Approach To Agency Problems: Existence," Working papers 2022rwp-197, Yonsei University, Yonsei Economics Research Institute.
    19. Demougin, Dominique & Fluet, Claude, 2001. "Monitoring versus incentives," European Economic Review, Elsevier, vol. 45(9), pages 1741-1764, October.
    20. Tinglong Dai & Kinshuk Jerath, 2019. "Salesforce Contracting Under Uncertain Demand and Supply: Double Moral Hazard and Optimality of Smooth Contracts," Marketing Science, INFORMS, vol. 38(5), pages 852-870, September.

    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:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01861-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.