Differentially monotonic redistribution of income

•We suggest a differential version of monotonicity for redistribution rules.•Increasing income differentials entail increasing post-redistribution differentials.•Differential monotonicity implies a flat tax combined with a basic income.

We suggest a differential version of monotonicity for redistribution rules: whenever the differential of two persons' income weakly increases, then the differential of their post-redistribution rewards also weakly increases. Together with efficiency and non-negativity, differential monotonicity characterizes redistribution via taxation at a fixed rate and equal distribution of the total tax revenue.