Dynamic Contracting: Accidents Lead to Nonlinear Contracts

We consider a dynamic multitask principal-agent model in which the agent allocates his resources on two tasks of different types: effort and accident prevention. We explicitly characterize the optimal contract as well as optimal effort and prevention actions applied by the agent. In contrast to the linear incentive scheme for effort, accident prevention leads to a log-linear punishment scheme if the agent is risk averse, becoming linear only if the agent is risk neutral. Both the sublinearity of the contract and the allocation of resources on the two tasks crucially depend on the risk aversion of the agent. Accident prevention ties up some of the agent’s capacity and induces him to substitute resources away from effort to prevention.