Summary: 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 examines the problem of optimal redistributive taxation with tax-induced risk taking and shows that constant returns to risk taking are likely to imply a paradox where more redistribution results in more post-tax inequality. In general, optimal taxation will imply either 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.