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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.

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Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 1220.

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Date of creation: 2012
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Handle: RePEc:lvl:lacicr:1220

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Keywords: Principal-agent models; moral hazard; stochastic decision problem; quantile function; information systems;

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  1. Donald Meyer & Jack Meyer, 2011. "A Diamond-Stiglitz approach to the demand for self-protection," Journal of Risk and Uncertainty, Springer, vol. 42(1), pages 45-60, February.
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  19. repec:fth:inseep:9812 is not listed on IDEAS
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