In a broader sense the welfare state ex ante can be seen as a social insurance for life-time risks, and ex post as a redistribution mechanism of incomes. Sinn (1995) has developed a normative theory of the welfare state in this view. On a constitutional plain agents determine the amount of optimal redistributive taxation behind a veil of ignorance relative to their life-time incomes. Our paper extends this theory of the welfare state by allowing for incomes which may fall below a subsistence level. If the income distribution is completely above the subsistence level, agents favour the confiscatorial tax. If some income realizations fall below the subsistence level, there are cases in which the laissez-faire-tax is socially preferred to the confiscatorial tax.