A solvable continuous time dynamic principal-agent model

I study the provision of incentives in a continuous time dynamic moral hazard model with hidden actions and hidden states. I consider a principal-agent model with linear production and exponential utility, whose explicit solution allows me to show how allocations are distorted for incentive reasons, and how access to hidden savings further alters allocations. I solve the model by applying a stochastic maximum principal, where the co-state variables from the agent’s optimization problem become state variables for the principal’s problem of choosing an optimal contract. I show that the main effect of moral hazard is a distortion on the effort margin, with a smaller effect on the intertemporal consumption allocation. Access to hidden savings shuts down the intertemporal distortions and increases the effort distortion. I also show how the optimal contracts can be implemented via a constant equity share, a constant flow payment, and a constant tax on savings.