The name is absent

Figure 1: Lattice structure of the 9 linear dual tax reforms.

Finally, it is important to point out that the lattice structure referred to holds for any set
of nine linear tax cuts satisfying Condition 1, given any labor and capital income distributions
satisfying Condition 2. Moreover, if either Condition 1 or Condition 2 do not hold, we can find
quasi-progressive tax schedules and income distributions where the lattice structure does not
apply (see Example 1 in the Appendix). Hence, Condition 1 and Condition 2 are necessary
and sufficient conditions.

3.2 Local effects

We have so far focussed on the effect that linear dual tax reforms have on income distribution.
Let us now focus on the effect any of these reforms on a single tax-payer, according to Pfahler
(1984).

Let ∆Vi,j (x, y) = ∆V_i^L(x) + ∆V_j^K (y) be the total post-tax income of a tax-payer with
respect to the Ti,j reform, where ∆V_i^L(x) and ∆V_j^K (y) are, respectively, the post-tax labor
and capital incomes. A sufficient condition for Vi,j (x, y) ≥ V_k,l(x, y) is that V_i^L(x) ≥ V_k^L(x)
and VjK(y) ≥ VlK(y). By Pfhaler (1984) and Theorem 1 we obtain the following result.

14

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