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Weak differential monotonicity, flat tax, and basic income ☆


We suggest a weak version of differential monotonicity for redistribution rules: whenever the differential of two persons’ income weakly increases, then their post-redistribution rewards essentially change in the same direction. Together with efficiency, non-negativity, and the average property, weak differential monotonicity characterizes redistribution via taxation at a fixed rate and equal distribution of the total tax revenue, i.e., a flat tax and a basic income.