A Solvable Dynamic Principal-Agent Model with Linear Marginal Productivity

Abstract

We study how to design an optimal contract which provides incentives for agent to put forth the desired effort in a continuous time dynamic moral hazard model with linear marginal productivity. Using exponential utility and linear production, three different information structures, full information, hidden actions and hidden savings, are considered in the principal-agent model. Applying the stochastic maximum principle, we solve the model explicitly, where the agent’s optimization problem becomes the principal’s problem of choosing an optimal contract. The explicit solutions to our model allow us to analyze the distortion of allocations. The main effect of hidden actions is a reduction of effort, but the a smaller effect is on the consumption allocation. In the hidden saving case, the consumption distortion almost vanishes but the effort distortion is expanded. In our setting, the agent’s optimal effort is also reduced with the decline of marginal productivity.