Task assignment and pay dispersion under moral hazard

We study a moral hazard problem where a principal assigns tasks that differ in the precision of their performance measures to agents who differ in their risk aversion. We solve for the optimal task assignment and observe that if both tasks are sufficiently easy to measure, the principal assigns the task involving the noisier performance measure to the less risk-averse agent. This assignment results in similar effort levels on both tasks and implies low pay dispersion within a firm. However, for generally noisy performance measures or if there is a significant range in the precision of the tasks' performance measures, the principal assigns the task involving the noisier performance measure to the more risk-averse agent. This assignment drives effort levels apart and results in high pay dispersion among agents. The result of varying optimal pay dispersion is preserved in settings with interdependencies among tasks such as production synergies or correlated performance measures. We further show that the optimal task assignment always assures efficient risk bearing among agents, which stipulates that the agent who is least averse to facing risks bears a greater compensation risk.