Efficient Risk Sharing under Limited Commitment and Search Frictions

This paper examines efficient risk sharing under limited commitment and search frictions. The model features a social planner and a continuum of risk-averse workers, where the planner is able to provide consumption only to workers matched with the planner and faces an aggregate resource constraint, while workers can walk away from the match in any period and search for a new match. The formation of new matches and the exogenous destruction of existing ones substantially expand the set of feasible stationary allocations, providing a role for the social welfare function. In the benchmark case of the Benthamite social welfare function, we find that the efficient stationary allocation exhibits novel consumption dynamics: Consumption begins at a relatively low level, converges toward a certain level when the participation constraint is slack, and jumps up when it binds. We then explore the role of limited commitment in generating such rich consumption dynamics.