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Existence and non-existence in the moral hazard problem

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  • Moroni, Sofia
  • Swinkels, Jeroen

Abstract

We provide a new class of counter-examples to existence in a simple moral hazard problem in which the first-order approach is valid. In contrast to the Mirrlees example, unbounded likelihood ratios on the signal technology are not central. Rather, our examples center around the behavior of the utility function as utility diverges to negative infinity. For any utility function, such as ln(w), in which utility diverges to negative infinity at a finite wealth level, existence will fail for some specifications of the agentʼs cost of effort. When utility diverges to negative infinity only as wealth does as well, existence holds for all specifications of the agentʼs cost of effort if and only if the agent continues to dislike risk as wealth diverges to negative infinity. When there is a finite lower bound on utility, existence is assured. For those cases where existence fails, we characterize the limit of near optimal contracts.

Suggested Citation

  • Moroni, Sofia & Swinkels, Jeroen, 2014. "Existence and non-existence in the moral hazard problem," Journal of Economic Theory, Elsevier, vol. 150(C), pages 668-682.
    • Handle: RePEc:eee:jetheo:v:150:y:2014:i:c:p:668-682
    DOI: 10.1016/j.jet.2013.09.011
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    References listed on IDEAS

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    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. 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.
    6. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 3-21.
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    Citations

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    Cited by:

    1. Chang Koo Chi & Kyoung Jin Choi, 2022. "A Dual Approach To Agency Problems: Existence," Working papers 2022rwp-197, Yonsei University, Yonsei Economics Research Institute.
    2. Roger, Guillaume, 2016. "Participation in moral hazard problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 10-24.
    3. Hector Chade, 2017. "Disentangling Moral Hazard and Adverse Selection," 2017 Meeting Papers 1537, Society for Economic Dynamics.
    4. Rongzhu Ke & Xinyi Xu, 2023. "The existence of an optimal deterministic contract in moral hazard problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 375-416, August.
    5. Hernández-Santibáñez, Nicolás, 2024. "Principal-Multiagents problem under equivalent changes of measure: General study and an existence result," Stochastic Processes and their Applications, Elsevier, vol. 177(C).
    6. 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.
    7. Barron, Daniel & Georgiadis, George & Swinkels, Jeroen M., 2020. "Optimal contracts with a risk-taking agent," Theoretical Economics, Econometric Society, vol. 15(2), May.
    8. Chi, Chang Koo & Choi, Kyoung Jin, 2023. "A dual approach to agency problems," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    9. Jung, Jin Yong, 2022. "Effects of changes in preferences in moral hazard problems," Journal of Economic Theory, Elsevier, vol. 205(C).

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    More about this item

    Keywords

    Moral hazard; Principal–agent models; Optimal contract; Existence; Mirrlees non-existence example;
    All these keywords.

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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