The Pareto-Efficient Relativity of Relative Risk Aversion

In a pure-exchange economy involving one perishable consumption good and risk-averse consumers, the elasticity of a consumer’s Pareto-efficient consumption with respect to aggregate output equals the reciprocal of the ratio of the consumer’s coefficient of relative risk aversion to average relative risk aversion. Therefore, this elasticity is unity for someone with average relative risk aversion, whereas consumers with above average relative risk aversion transfer some of their aggregate- output risk to consumers with below average relative risk aversion. This result has important implications on the financial securities needed to complete markets, inflation indexing, and central bank goals and targeting objectives.