Does Wealth Inequality Help Informal Insurance?

This paper investigates the effects of inequality in the presence of voluntary risk-sharing. In any period, an agent’s resources are composed of his share of a secure endowment (wealth, land) and a random component (labor income). To be sure, the distribution of wealth does not affect the Pareto optimal payoff vectors but, by changing the autarchic utilities, affects the set of these payoff vectors that are self-enforcing. When risk-sharing is not perfect, a transfer of wealth from an agent to the other is shown to cause the frontier of the self-enforcing payoff vectors to pivot. The more power an agent has, the larger the change in his utility from an increase in his share of wealth. Surprisingly, inequality is shown to help risk-sharing in a large range of cases. Regressive transfers of wealth increase the likelihood of perfect insurance all utility functions displaying hyperbolic absolute risk aversion (HARA) at the exception of the constant absolute risk aversion for which, as it is well known, wealth effects are absent. Moreover, introducing wealth inequality between the agents can increase the sum of utilities of the agent, thereby being desirable for a social planner maximizing a symmetric and additive welfare function. These results have important welfare and policy implications for redistribution programs such as land reform. We also show that when risk aversion is decreasing individuals tend to prefer sharing risk with poorer partners. JEL Classification Numbers: D31, D8, D63, O17, Q15.