The First-Order Approach when the Cost of Effort is Money
AbstractWe 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 InfoPaper provided by CIRPEE in its series Cahiers de recherche with number 1220.
Date of creation: 2012
Date of revision:
Principal-agent models; moral hazard; stochastic decision problem; quantile function; information systems;
Other versions of this item:
- Fagart, Marie-Cécile & Fluet, Claude, 2013. "The first-order approach when the cost of effort is money," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 7-16.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-23 (All new papers)
- NEP-CTA-2012-04-23 (Contract Theory & Applications)
- NEP-MIC-2012-04-23 (Microeconomics)
- NEP-ORE-2012-04-23 (Operations Research)
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