Enduring Relationships in an Economy with Capital and Private Information

We study efficient risk sharing in a model where agents operate linear production technologies with private information about idiosyncratic productivity. Capital is the sole factor of production, and accumulable. We establish a time-invariant, one-to-one mapping between the capital allocated to an agent and his lifetime utility entitlement. The mapping implies properties that are distinct from those in private-information endowment models. In contrast to the endowment model, the value of the risk-sharing arrangement in our model always remains above autarky value, so there is no need for long-term commitment. In our model, there are no net transfers each period across individuals, on average. This allows us to decentralize the efficient allocation into one-period insurance contracts that exhibit two-sided lack of commitment. Furthermore, while the efficient allocation implies increasing dispersion of lifetime utility entitlements and consumption, this need not lead to declines in individual consumption. When the technology is sufficiently productive, all individuals experience consumption growth.