Individual and Collective Welfare in Risk Sharing with Many States
CoRR(2024)
摘要
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 -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.
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