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The First-Order Approach when the Cost of Effort is Money

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  • Marie-Cécile Fagart
  • Claude Fluet

Abstract

We provide sufficient conditions for the first-order approach in the principal-agent problem when the agent’s utility has the non-separable form u(y - c(a)) where y is the contractual payoff and c(a) is the money cost of effort. We first consider a decision-maker facing prospects which cost c(a) with distributions of returns y that depends on a. The decision problem is shown to be concave if the primitive of the cumulative distribution of returns is a convex function, a condition we call Concavity of the Cumulative Quantile (CCQ). Next we apply CCQ to the distribution of outcomes (or their likelihood-ratio transforms) in the principal-agent problem and derive restrictions on the utility function that validate the first-order approach. We also discuss a stronger condition, log-convexity of the distribution, and show that it allows binding limited liability constraints, which CCQ does not.

Suggested Citation

  • Marie-Cécile Fagart & Claude Fluet, 2012. "The First-Order Approach when the Cost of Effort is Money," Cahiers de recherche 1220, CIRPEE.
    • Handle: RePEc:lvl:lacicr:1220
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    References listed on IDEAS

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    Cited by:

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    2. Nicolas Quérou & Antoine Soubeyran & Raphael Soubeyran, 2020. "Contracting under unverifiable monetary costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(4), pages 892-909, October.
    3. Fraser, Clive D., 2021. "Protection in numbers? Self-protection as a local public good," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    4. Richard Peter, 2021. "Who should exert more effort? Risk aversion, downside risk aversion and optimal prevention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1259-1281, June.
    5. Jung, Jin Yong & Kim, Son Ku, 2015. "Information space conditions for the first-order approach in agency problems," Journal of Economic Theory, Elsevier, vol. 160(C), pages 243-279.
    6. Han Bleichrodt, 2022. "The prevention puzzle," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 47(2), pages 277-297, September.
    7. Peter, Richard, 2021. "Prevention as a Giffen good," Economics Letters, Elsevier, vol. 208(C).
    8. Wang, Leran, 2021. "Fertility, Imperfect Labor Market, and Notional Defined Contribution Pension," The Journal of the Economics of Ageing, Elsevier, vol. 20(C).

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    More about this item

    Keywords

    Principal-agent models; moral hazard; stochastic decision problem; quantile function; information systems;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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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