Environmental Engineering Reference
In-Depth Information
Next substitute (
5.9
) into (
5.7
) and we get
r ¼
X
p
i
d
d
q
i
ð
5
:
10
Þ
nitions in (
5.6
) (i.e. put q
i
¼ q
i
þ d
Now using the de
q
i
) into (
5.5
) and subtract
(
5.4
). Then for any set of values of
q
n
, we have:
X
p
i
d
q
i
¼ 0
d
q
1
… d
ð
5
:
11
Þ
Then it follows that:
dU
¼
U
ð
q
1
þ d
q
1
; ...;
q
n
þ d
q
n
Þ U
ð
q
1
; ...;
q
n
Þ
\
0
ð
5
:
12
Þ
Suppose that the excise tax paid is exactly offset by the reduction of this income
tax. Then
d
r ¼ 0. From (
5.10
), it follows that (
5.11
) is satis
ed.
Except in the highly improbable case of all the
d
q
'
s coming out exactly zero, it
would follow from (
5.12
) that the consumer is on a
indifference surface
than before. The change from income to excise taxes has resulted in a net loss of
satisfactions. QED.
Hotelling concludes at the end of his theorem (retaining his italics):
“
lower
”
If government revenue is produced by any system of excise taxes, there exists a possible
distribution of personal levies among the individuals of the community such that the
abolition of the excise taxes and their replacement by these levies will yield the same
revenue while leaving each person in a state more satisfactory to himself than before.
He then proceeds to measure the welfare loss as being approximately equal to:
2
X
D
w ¼ 1
=
d
p
i
q
i
Hotelling also presciently predicts that two groups of people are likely to object
to this social policy: (
5.1
) the very rich, who normally would pay more taxes than
the poor, and (b)
“
”
land speculators
(Hotelling
1938
, p. 259). For the rich, it could
be the case that the personal bene
t to them of the marginal cost principle may be
lower than when there is a toll or excise tax. Land speculators, whose land is
adjacent to the bridge, would prefer to collect the toll rather than have the bridge
paid for out of general taxes. When the political climate moves away from con-
siderations of
”
then it is clear what the dominant voices are in shaping public policy: it is the rich
and the sectional interests who stand to gain by a policy of tolls and service charges
for the outputs of public utilities.
This principle of marginal cost pricing has been the bedrock of public utility
pricing in most textbooks that cover the public sector. However, in most developed
economies, led by the example of the United States, there is pressure to reduce all
taxes, especially income taxes, capital gains taxes, and corporate taxes, and replace
“
general human welfare
”
and wellbeing to a climate of
“
low taxes,
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