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Moral hazard with limited liability: Random-variable formulation and optimal contract structures

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  • Wang, Wenbin
  • Hu, Shanshan

Abstract

This paper studies the optimal contract for a risk-neutral agency with limited liability. We introduce a novel formulation of the model, in which the contract design problem reduces to a problem of constructing the distribution function of a random variable. This formulation directly balances the principal's tradeoff between incentivizing the agent to exert proper effort and minimizing the cost of the agent's compensation. We show that the optimal contract may involve one or two tiers of performance-based bonuses. We obtain new sufficient conditions for the optimality of bonus contracts and provide new insights into the choice of contract parameters.

Suggested Citation

  • Wang, Wenbin & Hu, Shanshan, 2021. "Moral hazard with limited liability: Random-variable formulation and optimal contract structures," Games and Economic Behavior, Elsevier, vol. 126(C), pages 374-386.
    • Handle: RePEc:eee:gamebe:v:126:y:2021:i:c:p:374-386
    DOI: 10.1016/j.geb.2021.01.002
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    References listed on IDEAS

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    1. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, April.
    2. Joaquín Poblete & Daniel Spulber, 2012. "The form of incentive contracts: agency with moral hazard, risk neutrality, and limited liability," RAND Journal of Economics, RAND Corporation, vol. 43(2), pages 215-234, June.
    3. repec:dau:papers:123456789/5371 is not listed on IDEAS
    4. Innes, Robert D., 1990. "Limited liability and incentive contracting with ex-ante action choices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 45-67, October.
    5. Ke, Rongzhu & Ryan, Christopher Thomas, 2018. "A general solution method for moral hazard problems," Theoretical Economics, Econometric Society, vol. 13(3), September.
    6. Kadan, Ohad & Swinkels, Jeroen M., 2013. "On the moral hazard problem without the first-order approach," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2313-2343.
    7. Kirkegaard, René, 2017. "Moral hazard and the spanning condition without the first-order approach," Games and Economic Behavior, Elsevier, vol. 102(C), pages 373-387.
    8. Carlier, G. & Dana, R.-A., 2005. "Existence and monotonicity of solutions to moral hazard problems," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 826-843, November.
    9. Eun‐Soo Park, 1995. "Incentive Contracting Under Limited Liability," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 477-490, September.
    10. Park, Eun-Soo, 1995. "Incentive Contracting under Limited Liability," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 477-490, Fall.
    11. Oyer, Paul, 2000. "A Theory of Sales Quotas with Limited Liability and Rent Sharing," Journal of Labor Economics, University of Chicago Press, vol. 18(3), pages 405-426, July.
    12. 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)

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    More about this item

    Keywords

    Moral hazard; Risk-neutral agency; Limited liability; First-order approach; Pay-for-performance;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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