Bounds on the Welfare Loss from Moral Hazard with Limited Liability

26 Pages Posted: 1 Oct 2012 Last revised: 14 Nov 2015

See all articles by Felipe Balmaceda

Felipe Balmaceda

Diego Portales University

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations

José Correa

University of Chile - Engineering Department

Nicolas E. Stier-Moses

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Date Written: August 28, 2015

Abstract

This article studies a principal-agent problem with discrete outcome and effort level spaces. The principal and the agent are risk neutral and the latter is subject to limited liability. We consider the ratio between the first-best social welfare and the social welfare arising from the principal's optimal pay-for-performance contract, i.e., the welfare loss ratio. In the presence of moral hazard, we provide simple parametric bounds on the welfare loss ratio of a given instance of the problem, and then study the worst-case welfare loss ratio among all problem instances with a fixed number of effort and outcome levels. Key parameters for these bounds are the number of possible effort levels and the likelihood ratio evaluated at the highest outcome. As extensions, we also look at linear contracts and at cases with multiple identical tasks. Our work constitutes an initial attempt to quantify the losses arising from moral hazard problems when the agent is subject to limited liability, and shows that these losses are non-negligible in the worst case (e.g., the welfare loss can approach 100% when the number of possible effort levels is large).

Keywords: Contract Theory, Principal-Agent Problem, Price of Anarchy, First-Order Method

Suggested Citation

Balmaceda, Felipe and Balseiro, Santiago and Correa, José and Stier-Moses, Nicolas E., Bounds on the Welfare Loss from Moral Hazard with Limited Liability (August 28, 2015). Available at SSRN: https://ssrn.com/abstract=2150355 or http://dx.doi.org/10.2139/ssrn.2150355

Felipe Balmaceda

Diego Portales University ( email )

Avda Santa Clara 797
Santiago, RM 8580000
Chile

HOME PAGE: http://https://works.bepress.com/felipe_balmaceda

Santiago Balseiro (Contact Author)

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

José Correa

University of Chile - Engineering Department ( email )

Republica 701 Santiago
Chile

Nicolas E. Stier-Moses

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Menlo Park, CA California 94025
United States

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