Weak differential monotonicity, flat tax, and basic income

•We reconsider Casajus' (Econom Lett, 2016) foundation of flat tax and basic income.•That is, redistribution via fixed-rate taxation and equal sharing of the tax revenue.•We relax Casajus' differential monotonicity into weak differential monotonicity.•As Casajus, we also use efficiency and non-negativity, but add an average property.•These properties characterize the afore-mentioned class of redistribution rules.

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.