IMPACT OF TAXES AND TRANSFERS

Enami, Lustig, Aranda, No. 25, November 2016
If and only if П RS T1 < ( −g 1
) ( ∑
1−g 1
K = − ( ∑ g iП Ti
П T1
n K m K
i=2 +∑j=1
b j ρ Bj
1−∑n
i=2 g i +∑m
j=1 b j
n (1−g i )П RS m
RS
i=2 T +∑ (1+b i j=1 j )ρ Bj
1−∑n
i=2 g i +∑m
j=1 b j
)), then adding T 1 increases the inequality.
) (or
Condition 43:
If and only if П RS T1 = ( −g 1
) ( ∑
1−g 1
K < − ( ∑ g iП Ti
П T1
n K m K
i=2 +∑j=1
b j ρ Bj
1−∑n
i=2 g i +∑m
j=1 b j
n (1−g i )П RS m
RS
i=2 T +∑ (1+b i j=1 j )ρ Bj
1−∑n
i=2 g i +∑m
j=1 b j
)), then adding T 1 does not change the inequality.
) (or
Is the Marginal Contribution of a Transfer Equalizing?
Assuming no-reranking, the following inequality should hold:
(44) П RS RS
N > П N\Bk .
Assuming k = 1 and substituting for both sides of the inequality, we have
n
RS
m
RS
∑ i=1 (1 − g i )П Ti + ∑ j=1(1 + b j )ρ Bj
1 − ∑n
i=1 g i + ∑m
> ∑ i=1 (1 − g i)П Ti + ∑ j=2(1 + b j )ρ Bj
j=1 b j
1 − ∑n
i=1 g i + ∑m
.
j=2 b j
n
RS
m
RS
After some rearranging, we have
(45) ρ RS B1 > ( b 1
) ( ∑
1+b 1
or equivalently,
n (1−g i )П RS m
RS
i=1 T +∑ (1+b i j=2 j )ρ Bj
1−∑n
i=1 g i +∑m
j=2 b j
)
(45b)
K > ( ∑ g iП Ti
ρ B1
n K m K
i=1 +∑j=2
b j ρ Bj
1−∑n
i=1 g i +∑m
j=2 b j
).
Therefore for B 1 to be equalizing when n taxes and (m − 1) benefits are already in place, the
following conditions apply.
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