A note on progressive taxation and inequality equivalence

We investigate the relationship between the notion of progressive taxation and inequality reduction under a general version of the concept of inequality equivalence. We consider a two parameter formalization of the concept of inequality equivalence that both includes as special cases the intermediate inequality equivalence and the unit-consistent inequality equivalence. Both criteria could range from relative to absolute inequality views as the parameters in the formulation change. For the unit-consistent inequality equivalence the condition of non-decreasing average tax rate is necessary and sufficient to guarantee the post-tax inequality reduction for all the inequality views in between the relative and the absolute.