The welfare state can be seen as an insurance device that makes lifetime careers safer, increases risk taking and suffers from moral hazard effects. Adopting this view, the paper studies the trade-off between average income and inequality, evaluating redistributive equilibria from an allocative point of view. It identifies the properties of an optimal welfare state and shows that constant returns to risk taking are likely to imply a redistribution paradox where more redistribution results in more inequality. In general, optimal taxation will either imply that the redistribution paradox is present or that the economy operates at a point of its efficiency frontier where more inequality implies a lower average income.