INDIVIDUAL RISK AND MUTUAL INSURANCE

This paper examines how, in the presence of individual risk, economic efficiency can be achieved without an unrealistically large number of contingent claims. Market uncertainty is specified in such a way that general types of individual risk and collective risk are properly acco unted for and so that, specifically, market clearing is always satisfi ed ex post as well as ex ante. We show that consistency of beliefs and optimality of allocation can be guaranteed with an appropriate array of pure Arrow securities to spread collective risk and mutual insuranc e policies to pool individual risk. When there is individual risk comm on to like groups of individuals, pooling risk by means of mutual insu rance permits substantial economizing on market transactions, as compa red to those required if dealing instead with the full complement of p ure Arrow securities. We show that if there are N households (consisti ng of H types), each facing the possibility of being in S individual s tates together with T collective states, then ensuring Pareto optimali ty requires only H(S - 1)T independent mutual insurance policies plus T pure Arrow securities. Our results also help to clarify the question of which missing markets may affect allocational efficiency.