We study informal insurance within communities, explicitly recognizing the possibility that subgroups of individuals may destabilize insurance arrangements among the larger group. We therefore consider self-enforcing risk-sharing agreements that are robust not only to single-person deviations but also to potential deviations by subgroups. However, such deviations must be credible, in the sense that the subgroup must pass exactly the same test that we apply to the entire group; it must itself employ some self-enforcing risk-sharing agreement. We observe that the stability of subgroups is inimical to the stability of the group as a whole. Two surprising consequences of this analysis are that stable groups have (uniformly) bounded size, a result in sharp contrast to the individual-deviation problem, and that the degree of risk-sharing in a community is generally non-monotonic in the level of uncertainty or need for insurance in the community.

When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state. This is true irrespective of the degree of divisibility in investments. However, divisibility (or fineness of occupational structure) has implications for both the multiplicity and Pareto-efficiency of steady states. Indivisibilities generate a continuum of inefficient and efficient steady states with varying per capita income. On the other hand, perfect divisibility typically implies the existence of a unique steady state distribution which is Pareto-efficient.