Monotonic redistribution of non-negative allocations: A case for proportional taxation revisited

•We reconsider Casajus' (TE, forthcoming) characterization of proportional taxation.•He characterizes taxation at a fixed rate by efficiency, symmetry, and monotonicity.•This does not work on the restricted domain of non-negative income.•On this domain, the tax rate may vary with total income.•There are upper and lower bounds on the elasticity of the tax rate function.

We reconsider Casajus' (forthcoming) characterization of uniformly proportional taxation by three properties of redistribution: efficiency, symmetry, and monotonicity. When restricted to non-negative income, these properties imply proportional taxation in a weaker sense-the tax rate may vary with total income but only in an economically reasonable way.