The name is absent



also be partially ordered by the responsiveness of the aggregate tax liability with respect
to income. Indeed, let
Z = in=1 (xi + yi) be the pre-tax aggregate total income and
R = in=1 (L(xi) + K(yi)) the aggregate total tax liability. If Z changes only due to equipro-
portionate changes in
x and y 10, R can be viewed as function of Z.11 Suppose that, at some
initial point,
Z = Z0. Then, R = R(kZ) with R(Z) = R0 = R(Z0).

The average-rate responsiveness and the elasticity of the aggregate total tax liability with
respect to the aggregate total income are defined respectively as

(14)


R(Z)Z - R(Z)


(Φ)'


(15)


E(Z) =


R'(Z )Z

RZ.


Next, we obtain the following result, that is proved in the appendix12.

Lemma 1 Let x = (x1,...,xn) and y = (y1,...,yn) be the labor and capital income distri-
butions respectively of a (finite) set of tax-payers and T
(x, y) = L(x) + K(y) is the current
quasi-progressive dual tax schedule. Then,

A(Z) =


n=1 (βL( x2 + βK(yi) У2}
Z 2

E(Z) = 1 +


n=1 (βL(χi) x2 + βK(yi) Vi}
n=ι T (χi,yi)

Hence, we are in a position to extend Pfahler’s result (1984).

Proposition 3 Let x = (x1,...,xn) and y = (y1,...,yn) be the labor and capital income
distributions respectively of a (finite) set of tax-payers. Let also T
(, ) be a quasi-progressive
dual tax schedule and
(γ,^) R+. Then, Γ(γ, φ,T, x, y) is a lattice endowed with a partial
order
^ defined by the elasticity E(Z) of the aggregate total tax liability and the supremum
and infimum operators
, are defined in (11).

10 r = (r1,...,rn) is obtained from a equiproportionate change of s' = (s1,..., sn) if ri = ksi for all i = 1,..., n.
11 Hutton and Lambert (1979) make the same assumption.

12The proof, although similar to Hutton and Lambert (1979), is made for discrete distributions.

16



More intriguing information

1. Expectations, money, and the forecasting of inflation
2. Pupils’ attitudes towards art teaching in primary school: an evaluation tool
3. Lumpy Investment, Sectoral Propagation, and Business Cycles
4. Moi individuel et moi cosmique Dans la pensee de Romain Rolland
5. The name is absent
6. The name is absent
7. Artificial neural networks as models of stimulus control*
8. Design and investigation of scalable multicast recursive protocols for wired and wireless ad hoc networks
9. Graphical Data Representation in Bankruptcy Analysis
10. The name is absent