Multitask principal-agent problems: Optimal contracts, fragility, and effort misallocation

We analyze a tractable class of multitask principal-agent problems, such as the one faced by a firm with a manager overseeing several projects. We allow for tasks to be complements or substitutes. We avoid the problems associated with the first-order approach by directly characterizing the shape of the agent's indirect utility function, which exhibits a convex then concave shape in effort. We identify a new source of allocational inefficiency across tasks: excessive concentration, and its consequence, insufficient risk taking. Optimal incentive schemes in our environment are generally "fragile": small changes in fundamentals can cause the agent's effort to collapse.