Moral Hazard with Limited Liability: The Random-Variable Formulation and Optimal Contract Structures

30 Pages Posted: 6 Nov 2011 Last revised: 10 Nov 2016

See all articles by Wenbin Wang

Wenbin Wang

Shanghai University of Finance and Economics

Shanshan Hu

Indiana University - Kelley School of Business - Department of Operation & Decision Technologies

Date Written: November 1, 2016

Abstract

We consider an important category of agency models: the moral hazard problem between a principal and an agent with limited liability. We introduce a new way of formulating the model, where the contract design problem reduces to a problem of constructing the distribution function of a random variable. This formulation allows to directly balance the central tradeoff in the agency problem: maximizing the principal’s payoff as well as incentivizing the agent to exert effort or take proper risk.

Our new method overcomes the limitation of the standard first-order-approach in solving the moral hazard problems in practice. Several structural results are established about the optimal contracts. We are the first to report that the optimal contract may involve two tiers of performance-based bonuses. In regard to the widely used bonus contract, we obtain new sufficient conditions for its optimality and provide new insights about setting the bonus-triggering threshold and bonus size.

Keywords: moral hazard, risk-neutral agency, limited liability, first-order approach, pay-for-performance

JEL Classification: D82, J33

Suggested Citation

Wang, Wenbin and Hu, Shanshan, Moral Hazard with Limited Liability: The Random-Variable Formulation and Optimal Contract Structures (November 1, 2016). Available at SSRN: https://ssrn.com/abstract=1954916 or http://dx.doi.org/10.2139/ssrn.1954916

Wenbin Wang (Contact Author)

Shanghai University of Finance and Economics ( email )

777 Guoding Road
Shanghai, AK Shanghai 200433
China

Shanshan Hu

Indiana University - Kelley School of Business - Department of Operation & Decision Technologies ( email )

Business 670
1309 E. Tenth Street
Bloomington, IN 47401
United States
812-856-2342 (Phone)

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