Simple Optimal Contracts with a Risk-Taking Agent

Abstract

Consider an agent who can costlessly add mean-preserving noise to his output. Then, the principal can do no better than offer weakly concave incentives to deter risk-taking. If the agent is risk-neutral and protected by limited liability, optimal incentives are strikingly simple: linear contracts maximize profit. If the agent is risk averse, we characterize the unique optimal contract and provide conditions under which it takes an intuitive form. We extend our model to analyze costly risk-taking, and we show that the model can be reinterpreted as a dynamic setting in which the agent can manipulate the timing of output.