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A general Lagrangian approach for non-concave moral hazard problems

Author

Listed:
  • Aloisio Araújo
  • Humberto Moreira

    (Department of Economics PUC-Rio)

Abstract

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Aloisio Araújo & Humberto Moreira, 2000. "A general Lagrangian approach for non-concave moral hazard problems," Textos para discussão 425, Department of Economics PUC-Rio (Brazil).
    • Handle: RePEc:rio:texdis:425
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    Cited by:

    1. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
    2. G. Rodriguez, 2007. "On the value of information in the presence of moral hazard," Review of Economic Design, Springer;Society for Economic Design, vol. 10(4), pages 341-361, March.
    3. Christopher S. Armstrong & David F. Larcker & Che-Lin Su, 2010. "Endogenous Selection and Moral Hazard in Compensation Contracts," Operations Research, INFORMS, vol. 58(4-part-2), pages 1090-1106, August.
    4. Gustavo Ferro & Omar O. Chisari, 2010. "Tópicos de Economía de la Regulación de los Servicios Públicos," Working Papers hal-00473038, HAL.
    5. Guillaume Roger, 2013. "Optimal Contract under Moral Hazard with Soft Information," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 55-80, November.
    6. Cysne, Rubens Penha, 2000. "A note on an application of Arrow's theorem: sufficient conditions for Lucas' inflation and welfare," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 397, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    7. Eduardo Azevedo & Ilan Wolff, 2025. "Broad Validity of the First-Order Approach in Moral Hazard," Papers 2506.18873, arXiv.org, revised Dec 2025.
    8. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    9. Bond, Philip & Gomes, Armando, 2009. "Multitask principal-agent problems: Optimal contracts, fragility, and effort misallocation," Journal of Economic Theory, Elsevier, vol. 144(1), pages 175-211, January.
    10. Chaigneau, Pierre & Edmans, Alex & Gottlieb, Daniel, 2019. "The informativeness principle without the first-order approach," Games and Economic Behavior, Elsevier, vol. 113(C), pages 743-755.
    11. Christopher Armstrong & David Larcker & Che-Lin Su, 2007. "Stock Options and Chief Executive Compensation," Discussion Papers 1447, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Kihlstrom, Richard, 2000. "Monopoly power in dynamic securities markets," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 428, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    13. 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.
    14. Philipp Renner, 2020. "An augmented first-order approach for incentive problems," Working Papers 297498586, Lancaster University Management School, Economics Department.

    More about this item

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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