Moral Hazard with Limited Liability: Incentive Contracting Under Monotone Ratio Assumptions

Abstract

This paper studies the moral hazard problem between a risk-neutral principal and a risk-neutral agent with limited liability. We contribute to the contract theory by introducing the monotone ratio assumptions that are satisfied by many standard effort-dependent distributions. They allow us to characterize the optimal contract without using the first order approach, the dominant solution method for moral hazard problems. The optimal solution demonstrates the robustness of the fixed-bonus contract as a second-best design and provides new insights about the choice of contract terms. We illustrate that a greater effort may be induced from the agent by reducing the performance threshold and bonus. Motivated by their popularity in practice, we also investigate the design of linear contracts under one relaxed monotone ratio assumption. We show that the widely used debt contract loses its optimality under higher output variability, and a contingent revenue sharing contract should be adopted instead.