An analytically solvable principal-agent model

Abstract

We analyze a principal-agent model with moral hazard where the principal is risk neutral while the agent is risk averse or risk neutral. The agent is free to choose any probability distribution over outcomes, where some distributions require more effort than others. The agent's effort-cost function is of “Legendre type” and satisfies an axiom of invariance under mergers of outcomes that are equally paid by the principal. We analyze a family of such effort-cost functions. For a canonical subclass of these, and arbitrary outcome spaces, the principal's contract problem allows for closed-form solutions. Optimal contracts then combine debt with a monotonic sharing rule for the surplus above a threshold chosen by the principal. When the agent is risk neutral, the contract boils down to a pure debt contract. For agents with unit degree of relative risk aversion, the surplus is divided in fixed shares.