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Individual and Collective Welfare in Risk Sharing with Many States

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  • Federico Echenique
  • Farzad Pourbabaee

Abstract

We provide a quantitative assessment of welfare in the classical model of risk-sharing and exchange under uncertainty. We prove three kinds of results. First, that in an equilibrium allocation, the scope for improving individual welfare by a given margin (an $\varepsilon$-improvement) vanishes as the number of states increases. Second, that the scope for a change in aggregate resources that may be distributed to enhance individual welfare by a given margin also vanishes. Equivalently: in an inefficient allocation, for a given level of resource sub-optimality (as measured by the coefficient of resource under-utilization), the possibilities for enhancing welfare by perturbing aggregate resources decrease exponentially to zero with the number of states. Finally, we consider efficient risk-sharing in standard models of uncertainty aversion with multiple priors, and show that, in an inefficient allocation, certain sets of priors shrink with the size of the state space.

Suggested Citation

  • Federico Echenique & Farzad Pourbabaee, 2024. "Individual and Collective Welfare in Risk Sharing with Many States," Papers 2401.07337, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2401.07337
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