There is an irreductible conflict between, on the one hand, the desire to allocate income in society in an equitable way and, on the other, the desire to alleviate poverty. The conflict materializes itself in the problem of designing a basic income (or negative income tax) system which requires...

We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, as in the case of the absolute mean deviation, it...