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The first-order approach when the cost of effort is money

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  • Fagart, Marie-Cécile
  • Fluet, Claude

Abstract

We provide sufficient conditions for the first-order approach in the principal-agent problem when the agent’s utility has the nonseparable 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) and with distributions of returns y that depend on a. The decision problem is shown to be concave if the primitive of the cdf of returns is jointly convex in a and y, a condition we call Concavity of the Cumulative Quantile (CCQ) and which is satisfied by many common distributions. 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 another 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

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 49 (2013)
Issue (Month): 1 ()
Pages: 7-16

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Handle: RePEc:eee:mateco:v:49:y:2013:i:1:p:7-16

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Principal-agent model; Contract; Moral hazard; Pecuniary effort; Nonseparable utility; Information system;

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