Moral Hazard, Risk Sharing, and the Optimal Pool Size

We examine the optimal size of risk pools with moral hazard. In risk pools, the effective share of the own loss borne is the sum of the direct share (the retention rate) and the indirect share borne as residual claimant. In a model with identical individuals with mixed risk-averse utility functions, we show that the effective share required to implement a specific effort increases in the pool size. This is a downside of larger pools as it, ceteris paribus, reduces risk sharing. However, we find that the benefit from diversifying the risk in larger pools always outweighs the downside of a higher effective share. We conclude that, absent transaction costs, the optimal pool size converges to infinity. In our basic model, we restrict attention to binary effort levels, but we show that our results extend to a model with continuous effort choice.