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Existence and non-existence in the moral hazard problem


  • Moroni, Sofia
  • Swinkels, Jeroen


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

    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    2. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 3-21.
    3. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    4. 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.
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    Cited by:

    1. Roger, Guillaume, 2016. "Participation in moral hazard problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 10-24.
    2. Hector Chade, 2017. "Disentangling Moral Hazard and Adverse Selection," 2017 Meeting Papers 1537, Society for Economic Dynamics.
    3. 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.
    4. Barron, Daniel & Georgiadis, George & Swinkels, Jeroen M., 0. "Optimal contracts with a risk-taking agent," Theoretical Economics, Econometric Society.

    More about this item


    Moral hazard; Principal–agent models; Optimal contract; Existence; Mirrlees non-existence example;

    JEL classification:

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


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