The name is absent

In this paper we define a bi-dimensional progression measure which is needed to establish
the Lorenz dominance criterion among post-tax income distribution. To do this, the dual tax
cuts must be simultaneously labor and capital yield-equivalent. Moreover, the relative order
of both labor and capital income distribution must coincide. We set up a lattice whereby
Pfahler-type linear tax refoms are compared.

Finally, by means of a microsimulation model and a large dataset of income tax payers we
empirically illustrate the effect of linear tax cuts on dual taxes. Our analysis is carried out to
focus on redistribution and progressivity effects as well as the elasticity of the tax functions.

7 Appendix

7.1 Theoretical part

Remark 1

Consider a unidimensional tax schedule defined by

m+1

T (x) =     Ti(x)

i=0

where 0 < t1 < ... < tm < tm+1 < 1 are the marginal types, 0 = x0 < x1 < ... < xm <
x_m+1 = ∞ are the marginal incomes and

T_i(x) = max {0, min{x_i — x_i-1, x — x_i-1}} ∙ t_i

for all i, 1 ≤ i ≤ m + 1. We say that T(x) is a stepwise tax schedule.

It can be easily checked that T(x) is progressive and convex. Further, given a linear tax
reform t'(x) = d ∙ t(x) + h defined on the average type t(x) = T(x)/x we next prove that the
new tax schedule is stepwise where 0 < d ∙ t₁ + h < ... < d ∙ t_m + h<d ∙ tm+1 + h < 1 are the
marginal types and 0 = x0 < x1 < ... < xm < xm+1 = ∞ are the marginal incomes.

30

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