Two Equations on the Pareto-Efficient Sharing of Real GDP Risk

For a pure-exchange, closed economy without storage, Eagle and Domian (2005) and Koenig (2011) derive similar but different equations of Pareto-efficient risk sharing. We confirm that both equations are correct. We also generalize and reinterpret Koenig’s equation. We find that Koenig’s equation as the superior one when we use the harmonic mean to compute average relative risk aversion. Our reinterpretation of Koenig’s generalized equation is that Pareto efficiency requires that the consumption of an individual with average relative risk should be proportional to the real GDP.