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Title: The First-Order Approach when the Cost of Effort is Money
Authors: Fagart, Marie-Cécile
Fluet, Claude
Keywords: Principal-agent models
Moral hazard
Stochastic decision problem
Quantile function
Information systems
Issue Date: 2012-04
Series/Report no.: Cahiers du CIRPÉE;12-20
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.
URI: https://depot.erudit.org/id/003602dd
Appears in Collections:Cahiers de recherche du CIRPÉE

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