Why Praise Inequality? Public Good Provision, Income Distribution and Social Welfare

We consider a two-person Cournot game of voluntary contributions to a public good with identical individual preferences, and examine equilibrium aggregate welfare under a separable, symmetric and concave social welfare function. Assuming the public good is pure, Itaya, de Meza and Myles (Econ. Letters, 57: 289-296; 1997) have shown that maximization of social welfare precludes income equality in this setting. We show that their case breaks down when the public good is impure: there exist individual preferences under which maximization of social welfare necessitates exact income equalization. Even if the public good is pure, any given, positive level of income inequality can be shown to be socially excessive by suitably specifying individual preferences. Thus, sans knowledge of individual preferences, one cannot reject the claim that a marginal redistribution from the rich to the poor will improve social welfare, regardless of how small inequality is in the status quo.