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

*Marie-Cecile Fagart* and
*Claude Fluet* ()

*Journal of Mathematical Economics*, 2013, vol. 49, issue 1, 7-16

**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.

**Keywords:** Principal-agent model; Contract; Moral hazard; Pecuniary effort; Nonseparable utility; Information system (search for similar items in EconPapers)

**Date:** 2013

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**Related works:**

Working Paper: The First-Order Approach when the Cost of Effort is Money (2012)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:49:y:2013:i:1:p:7-16

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