can be carried out for tax hikes.
Taking into account the hypothesis of neutral revenue, Pfahler proved that his three unidi-
mensional tax cuts can be compared using the LD criterion on post-tax income distributions.
According to his results, T2 is the most redistributive reform whereas T1 is the least. On the
other hand, Jakobbson (1976) showed that it is the same to compare the residual progression
between two different tax schedules and compared, under the Lorenz Dominance, the post-
tax income distributions obtained applying the two different tax schedules to an arbitrary
distribution7.
Next we prove that the two above results can be extended to include dual taxes if the two
following conditions hold,
• (Condition 1) The aggregate labor tax liability and the aggregate capital tax liability
are equal across reforms.
• (Condition 2) The relative order of incomes of both labor and capital income distri-
butions coincides.
Observe that Condition 1 applies to the dual tax cuts and tells us that they must be simul-
taneously labor yield-equivalent and capital yield-equivalent. On the other hand, Condition
2 is applied to income distributions. This last condition does not hold if we consider real sets
of tax-payers. However, it enables us to obtain benchmark results. Moreover, this condition
makes more sense if we consider groups of tax-payers instead of single tax-payers. In Section
5 we show that assuming Condition 2 is feasible in light of real income distributions.
Given a dual tax T(x,y) and labor and capital income distributions x and y we denote
by V2(≡,y) = {xi + yi — T(xi,yi)}n=ι the post-tax income distribution and by T2(x,y) =
Then, given two income distributions x = (x1 ≤ ... ≤ xn) and y = (y1 ≤ ... ≤ yn), we say that x is Lorenz
dominated (LD) by y if and only if Lx(p) ≤ Ly(p), for p = 1, ...,n.
7In the Appendix the results needed from both Jakobbson (1976) and Pfahler (1984) are rewritten in the
adequate way to be used in this paper.
10
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