American Economic Association
Optimal Corrective Taxes or Subsidies When Revenue Raising Imposes an Excess Burden
Author(s): Yew-Kwang Ng
Source: The American Economic Review, Vol. 70, No. 4 (Sep., 1980), pp. 744-751
Published by: American Economic Association
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Optimal Corrective Taxes or Subsidies when
Revenue Raising Imposes an Excess Burden
By YEW-KWANGNG*
This paper addresses the following problem. Suppose that for some reason, a tax or
subsidy on a certain good may be desirable,
for example, as it produces an external diseconomy or economy. However, a subsidy
has to be financed by other taxes and a tax
contributes to government revenue. If the
revenue can be raised by nondistortive taxes,
then this may not be a relevant issue. However, revenue has to be raised by distortive
taxes in practice (usually income or valueadded taxes). Is it then still desirable to tax
or subsidize external diseconomies or economies?' One is inclined to reply that it all
depends on the relevent interrelationships
and nothing can be said a priori due to the
second best considerations. In this paper, it
is argued that, given a reasonable assumption likely to prevail in most cases, a normal
tax or subsidy is still desirable provided the
government revenue requirement is not too
high. The "counternormal" policy of taxing/subsidizing external economies/diseconomies cannot however be ruled out
completely, even if the amount of revenue
required is zero.
This problem has been largely ignored in
the literature. The optimal taxation literature (for an introduction, see Agnar Sandmo,
1976, or Anthony Atkinson, 1977; for an
authoritative synthesis, see James Mirrlees,
1976) concentrates on taxation for revenue
and income distribution purposes without
incorporating corrective taxes or subsidies.
On the other hand, the literature on the
Pareto optimality of a competitive equilibrium (with taxes or subsidies) in the presence of externalities usually ignores the
government revenue requirement and the
impracticability of nondistortive taxes. (See,
for example, Hiroaki Osana where lump sum
taxes and subsidies are used.)2
In the following analysis, I assume that
the government revenue requirement is given
and has to be raised by a proportional income taxation. Income taxation is selected
partly for its practical importance and partly
for the fact that, if we abstract from differential rates (which may be explained by
such considerations as merit/demerit goods,
externalities, etc. themselves), general commodity taxation (for example, a value-added
tax) is equivalent to a proportional income
tax. My disregard for possible progressivity
is due mainly to the need for analytical
simplicity, but may be justified by a predominant concern with efficiency issues.3
While I keep referring to externalities, my
analysis may also be applied to other factors
justifying corrective taxes and subsidies. For
*Monash University. I am grateful to the managing
editor and a referee for helpful suggestions.
'It is true that, for a given situation, we do not have
to subsidize an external economy, we could tax it
negatively; i.e., the less the activity, the higher the total
tax bill. This is equivalent to a subsidy plus a lump sum
tax. The government does not then have to finance the
subsidy. However, while this may be good enough for
this particular externality, it will adversely affect efficiency in the long run as people will then refrain from
producing external economies. Moreover, the point of
reference to determine the negative tax or the amount
of the lump sum tax is difficult to determine in an
acceptable way. The negative tax solution to the problem may be safely dismissed as both inefficient and
impractical.
2See, however, Efraim Sadka who derives optimality
conditions for taxes with consumption externalities.
Consistent with the theory of second best, the direction
of taxes and subsidies can go either way. Sandmo
(1975) also analyzes a similar problem in a different
(commodity taxation) framework than mine. My income taxation framework recognizes the practical difficulties of a system of complicated rates of commodity
taxes and leads to the concentration on factors such as
the degress of substitutability with leisure. I am indebted to Richard Zeckhauser for drawing my attention to the last reference.
'Linearity in taxes but no strict proportionality also
receives support from the optimal income taxation
literature (see Mirrlees, 1971, and Atkinson, 1973). My
analysis can be revised to cover the linear case.
744
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VOL. 70 NO.4
NG: CORRECTIVE TAXES AND SUBSIDIES
example, the analysis below can be interpreted, without any substantive changes, to refer to merit/demerit goods.
For the benefit of nonspecialist readers,
the main results of this paper are presented
in Section I. The analysis leading to these
results is contained in Section II. The last
section remarks on the policy relevance of
my analysis and the relaxation of some of
the simplifying assumptions used.
I. Results
Using the usual simple model of the optimal commodity taxation literature and reasonably assuming that the social marginal
utility of income is positive, the following
proposition may be derived.
PROPOSITION 1: In the simple economic
model where the government revenue must be
raised by distortive income and/or uniform
value-added taxes, the presence of an external
diseconomy/economy still calls for a corrective tax/subsidy provided that (a) an increase
in the (consumer) price of the externalityproducing good is more effective in reducing
its consumptionproportionately than is an increase in the (consumer) price of labor in
increasing it, proportionately to labor; (b) a
compensated increase in the price of labor is
more effective in increasing labor supplyproportionately than is a compensated increase in
the price of the externality-producinggood in
reducing labor supply, proportionately to the
amountof thegood;4 (C) thegovernmentrevenue requirementis not too high. If the revenue
requirement is not negligible, the case for a
subsidy is weakened and may be reversed but
the case for a tax is strengthened.
After the theory of second best, it is not
surprising that a corrective tax/subsidy
4Observant readers may have noticed that condition
(a) is stated in the uncompensated form while condition (b) is in the compensated form. Due to the precise
proportionalities involved, the income effects cancel
out exactly. Hence if either condition holds in the
compensated form, it also holds in the uncompensated
form and vice versa (see Section II). I intentionally
state (b) in the compensated form, as the uncompensated form may appear less plausible than it really
is.
745
based on the partial-equilibrium analysis
may no longer be desirable in the presence
of the need to raise distortive taxes. For
example, consider a subsidy for an external
economy which must be financed by an
increase in income tax. If condition (a) in
Proposition 1 is reversed, a reduction in the
price of the good due to the subsidy is less
effective in increasing its consumption than
a reduction in the price of labor (due to an
increase in income tax) in reducing its consumption, proportionately. The subsidy (and
the required income tax to finance it) may
then be counterefficient. However, as argued
in Section II, both conditions (a) and (b) are
likely to hold for most goods. Moreover, if
either condition is violated, it is likely that
the other one does not hold either. Normal
corrective taxes/subsidies still apply due to
the following proposition.
PROPOSITION 2: Proposition 1 remains
true if both conditions(a) and (b) are reversed.
Even for cases where only one of the two
conditions are violated, it may still be
desirable to adopt normal corrective taxes/
subsidies. But the counternormal policy of
taxing/subsidizing goods producing external economies/diseconomies cannot be
ruled out completely. Due to the fact that
conditions (a) and (b) can be expressed in
uncompensated forms, the empirical task of
establishing their fulfillment is made less
difficult.
II. Analysis
Let us first analyze a deliberately simplified model so that the central argument
can be appreciated easily. Suppose that there
are n + 1 commodities in the economy, the
last one being labor. As in the optimal commodity taxation literature, assume that the
consumer side of the economy can be represented by one consumer or a community
utility function,
(1)
U(X I, x2,...
xnI
L, E)
where xi is the amount of the ith good
consumed, L is labor, and E is the amount
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of the only external effect produced either
by the consumption or production of the
first good. Abstracting from the problem of
increasing or reducing E for any given xl,
we may define the units such that E=x .
Each consumer is taken as atomistic and
takes prices, tax rates, wage rate, and E as
given (not affected by his own decision). He
maximizes (1) with respect to L and xl subject to
I
(2) (I + t)pix +
n
E: p'x'=(I
-
i= 1
Uix+ ULLT+UE4
=-(wL+WTLT+
tpXT1)
where 0 is the Lagrangeanmultiplierassociated with (4).
Differentiate(2) with respectto t and T to
obtain, respectively,
(7)
(I1 + t )P
2
Xt +
1
(I 1-T) )WL= -plx
px'i=2
(3a)
U1= X(1 + t)pI
(3b)
Ui = pi
(8)
n
(1 +t)P
=2..
n
where X, being the Lagrangean multiplier
associated with (2), is the marginal utility of
income. A subscript denotes partial differentiation, for example, Ui_ aU/ax'. The
term U1 takes into account only the internal
effect of xl upon U and does not include the
external effect through E.
Again as in the basic optimal tax model,
producers' prices and the wage rate are taken
to be fixed. Such might occur in a small
trading nation producing nontraded goods
with constant returns. The society is imagined to maximize (1) with respect to t and T,
subject to a fixed-revenue requirement
E p'x
i=2
XT+
-wL
-(1-T)wLT=
Substitute Ui and UL from (3) into (5) and
(6), and then substitute(7) and (8), respectively, into the resultingequations,yielding
(9)
- UL=X( 1-T )w
(3c)
n
(6)
n
T)WL
where t is the tax rate (subsidy if negative)
on the first good, T is the tax rate on income, pi are prices, and w is the wage rate.
Thus, only a proportional income tax (or a
uniform value-added tax) and a possible
tax/subsidy on good 1 are being considered.
The first-order conditions for a maximum
are
UEXtl=(pIxI+WTLt+tpIXtl)
-XpIXI+
(10) -XwL+ UEx
=0(wL+WTLT+tPIXT1)
Now in the consumer budget constraint
(2), (1 + t)p1_ q1 is the consumer price of x1
and (1 - T)w_ qL iS the consumer price of
labor/leisure. Thus we may write
()
(12)
=
ax'
ax
aq-l
a
aq1 at
L
T4aq ax1
where SIl-ax
1/
*__
aqL
=
w(Sw
IL
al
LaiJ
a q l 1u is the substitution
ef-
fect on xl of an increase in ql, SIL=
and I=income. Similarly, we
axl/aqLl-u,
have
TwL+tplx1=R
(4)
The following first-order conditions may be
derived:
n
(5)
SEPTEMBER 1980
THE AMERICAN ECONOMIC REVIEW
746
Uix+ ULLt+ UExl
-9(plxl + WTL,+ tplxl)
(13)
Lt,
(14)
LT=
aqt =PI
aq1 at
a
aqL aT
=
SL1-XI
(SLL+L-
a
a
Substitute (1 1)-(14) into (9) and (10), and
write in proportional form to eliminate the
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VOL. 70 NO.4
NG: CORRECTIVE TAXES AND SUBSIDIES
Lagrangean multiplier 9, giving
(15)
px'A -p1SI IUE/A
wLA +WSILUE/
p'x'B
+p'(wTSLl
+ tplSll)
wLB- w( WTSLL+ tP SLL)
where A =_ + (UE/X) (axl/aI) and B_ 1- tpl(axl/aI).
Assuming that
the second-order condition is satisfied, (15)
and (4) determine the optimal values of t
and T.
It can be shown that both A and B can be
taken as positive. Being the private (i.e., not
accounting for externality) marginal utility
of purchasing power, X can be taken as
positive. The term UEis positive/negative if
the externality is an economy/diseconomy.
Thus, if x1 is not an inferior good, A is
necessarily positive for the case of an external economy. Similarly, if xl is an inferior
good, A is necessarily positive for the case
of an external diseconomy. Ambiguities arise
only for a noninferior good with external
diseconomy and for an inferior good with
external economy. However, A is positive
(though less than one) in both cases unless
the externality is so strong that an increase
in income actually makes the community
worse off. It is reasonable to assume that
In other words, while an
-UE(ax1/aI)<X.
increase in income may reduce utility
through the externality effect, the reduction
does not overbalance the internal effect X. If
this is not true, an increase in income actually makes the community worse off. It is
then not difficult to see that these conclusions may then have to stand on their heads,
since an improvement in economic efficiency may then make things worse. It is
thus clear that A > 0 is a reasonable assumption.
Turning to examine B(= 1 -wT(aL/aI)
wT(aL/aI)
747
-aL/aI>0.
For B to be negative, tpl(ax1/
HI) would have to be larger than one which
is quite impossible, unless t is very large (or,
if ax1I/aI <0, t is negative and large in absolute value). Since I am going to argue just
for a positive/negative t (for the case of
external diseconomy/economy), the case
where t is already very large (absolutely) to
begin with is not relevant to the argument.
It is thus perfectly legitimate to take B >O.
To abstract from the complication of a
positive revenue requirement, let us for the
moment take R=O. This does not assume
the problem away completely since for a
change in t (negative t in particular), T has
to be changed to meet the requirement R = 0.
It is thus not obvious that tR 0 is optimal if
UE5 0. In fact, it can be seen that there are
cases (though unlikely to prevail) where the
sign of optimal t is reversed (i.e., becomes
the same as UE) and there are borderline
cases where t = T= 0 is optimal even if UE#
0. For this last one to be true, it can be
observed from (15) that -P1S11/WSIL=
p x /wL must hold,5 or
(16)
-Sll/x
I = SlL/L
Assuming that the usual postulates of
consumer theory are satisfied, S1l is necessarily negative. Thus (16) can be satisfied
only if S1L>O. But from the general theory
of consumption, SIL can be of any sign.
Thus, at a general level, it is possible for
(16) to hold and for t= T=0 to be optimal
even if UE#74
O. In fact, if -S I /x 1 < SI L/L,
it may be optimal to pursue the counternormal policy of subsidizing an external diseconomy and taxing an economy. The reason for this is not difficult to see. For efficiency purposes, it is the substitution effect
that counts. Take the case of an external
economy. A subsidy on xl (which reduces
ql) must be financed by an increase in income tax T (which reduces qL). But if, as
-tp1(ax1/aI)), it is clearly positive when
T= t = 0. Even if the tax/subsidy rates are
nonzero, a positive B just means that a
dollar increase in income does not induce
(through income effects) an increase in tax
revenue by a dollar or more. In fact, as
leisure can be taken not as an inferior good,
5When t = T= 0, the right-hand side of (15) reduces
top'x'/wL. On the left-hand side, since A is associated
with p
on the numerator and with wL on the denominator, we may take out the terms associated with
A without affecting the proportionality. Specifically,
(15) simplifies into (16) after putting t = T= 0 and using
cross multiplication.
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748
THE AMERICAN ECONOMIC REVIEW
far as substitution effects are concerned, the
reduction in q' is more effective in reducing
xl than is the reduction in q' in increasing
xi proportionately, the subsidy may be positively harmful. Hence, a tax on xl enabling
a lowering in T may be desirable instead.
However, it is reasonable to assume that, in
normal cases,
(17)
-SIl/xl>SlL/L
which says that a compensated increase in
is more effective in reducing xl proportionately than a compensated increase
in qL in increasing (if at all) xl, proportionately to L. This is likely to hold as a
change in the consumer price of the first
good itself can be more effective proportionately, in affecting the consumption
of xl, than a change in the price of something else. One might think that this may
not be so since the something else which
happens to be labor may be much more
important than xl. But xl and L appear in
the denominators of (7), hence the effect
due to the relative importance of the two
goods has already been taken into account.
Inequality (17) may be expressed in a
different way. Due to the symmetry of substitution effects, SI L= - SLI (the negative
sign accounts for the fact that an increase in
leisure is a reduction in labor), (17) may be
rewritten as
ql
q1 ax1I
(1) -i~jiu
(17')
a >l
q1 aL
L aqlIUI
which says that, as far as substitution effects
are concerned, xl is more elastic than L
with respect to a change in ql (the consumer
price of xl) itself. (Taking aL/aqllu to
be negative; if it is positive, the inequality
is necessarily satisfied.) A compensated
increase in ql reduces xl and increases
the consumption of the composite good
(x1,..., x +leisure). Hence, aL/aq1ju tends
to be negative. But in proportionate terms,
this secondary effect is unlikely to be more
important than the primary effect on xA
itself. The reduction in xl concentrates on
xl itself while the increase in the composite
SEPTEMBER 1980
good is spread across (not necessarily evenly
and positively) all other goods and leisure.
Hence, leisure is likely to increase by only a
small amount in absolute terms and even
less in proportionate terms if x' is less important than leisure in consumption.
It may be thought that (17') may well be
reversed since the left-hand side, though
nonnegative, may be very small. In the
limiting case, it approaches zero. In this
case, is not the right-hand side quite likely
to exceed the left-hand side? The answer is
negative. As the reduction in xl approaches
zero, the increase in the composite good
approaches zero. The right-hand side is still
likely to be smaller than the left-hand side
due to the argument of the preceding paragraph. If we allow both the left-hand side
and the right-hand side of (17') to become
exactly zero, then of course (17') becomes
an equality (i.e., equation (16)) and the optimality condition (15) is satisfied at t = T= 0.
This result is not surprising; with no possibility for substitution, a tax/subsidy serves
no efficiency-improving function.
While (17') can be shown to be true in
most cases, its reversal cannot be ruled out
completely. This may happen if the consumption of xl is not time intensive and the
close substitutes of xl are very time intensive. Then a reduction in xl does not release
much time, but the increase in the consumption of its substitutes takes up more time,
leaving less time for working. Then aL/
aqll, may be very negative, leading to a
possible (but unlikely) reversal of (17'). The
counternormal policy of taxing/subsidizing
external economy/diseconomy may then be
desirable. The requirement that xl be nontime intensive may appear counterintuitive.
Take the case of an external economy. A
subsidy increases xi which, if time intensive,
may lead to a reduction in L and may thus
be undesirable as revenue is dependent on
L. This apparent paradox can be explained.
A subsidy on x' has to be financed by an
increase in the income tax rate which reduces the consumer price of time
(labor/leisure). This tends to encourage the
consumption of more time-intensive goods
and less non-time-intensive goods. If xl is
non-time intensive and its substitutes are
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VOL. 70 NO.4
NG: CORRECTIVE TAXES AND SUBSIDIES
time intensive, the consumption of xl may
be reduced, destroying the purpose of the
subsidy. However, unless there is some
specific reason to believe that the time intensities and other possible relevant factors
are very biased, it is reasonable to take (17)
as satisfied. With this reasonable assumption (and a similar one to be mentioned
below), I can show that some tax/subsidy
on external diseconomy/economy is desirable.
If (17) holds, (16) cannot hold and t = T=
0 does not satisfy the optimality condition
(15). The left-hand side of (15) will be larger
or smaller than p'xl/wL, according to
whether UE is positive or negative. Let us
consider the case UE>. (The opposite case
can be similarly handled.) In this case of
external economy, (15) can be satisfied by
t<0 (subsidy on x') and T>0 (to meet the
revenue constraint). To see this, observe the
right-hand side of (15). The term associated
with t is pl(p'Sll) in the numerator and
in the denominator. Thus if (17)
-PI(WSIL)
holds, a negative t makes the right-hand side
larger than plxl/wL and hence tends to
make it equal to the left-hand side. The
terms associatedwith T are w(p'SLl)
in the
numerator and- w(wSLL)
in the denominator. SLL=aL/aqL
is necessarily posilq
tive. Similar to (17), it is reasonable to assume
(18)
SL1/X
> -SLL/L
which says that a compensated increase in
qL is more effective in increasing L proportionally than is a compensated increase in ql
in reducing L in proportion to xl. Or, due to
the symmetry of substitution effects, - 1L/
which says that a comxl
-SLL/L,
pensated increase in qL is more effective in
increasing L than it is in increasing xl proportionately. Then an increase in T also
makes the right-hand side of (15) larger than
p'x1/wL. Thus starting from a position of
T=t=0, making t negative and T positive
tends to satisfy (15), since, in the present
case of external economy, the left-hand side
of (15) is larger than plxl/wL. Similarly, in
the case of diseconomy, the left-hand side
of (15) is smaller than plxl/wL. Then mak-
749
ing t positive and T negative tends to
achieve (15).
If the government revenue requirement is
not negligible, T may be positive to begin
with. Then the right-hand side of (15) is
already larger than plxl/wL even at t=0.
The case for a subsidy on external economy
cannot be established without a detailed
comparison of the values of the relevant
substitution effects, external effects, etc. The
case for a tax on external diseconomy is
made even stronger, as may be expected
intuitively.
The discussion above may be summarized
into the following proposition:
PROPOSITION 1': In the simple economic
model where the government revenue must be
raised by distortive income and/or uniform
value-added taxes, the presence of an external
diseconomy/economy still calls for a corrective tax/subsidy provided that (a) a compensated reduction in the consumer price of
the externality-producinggood is more effective in increasing the consumptionof this good
than it is in increasing the labor supply, proportionately; (b) a compensated increase in
the consumerprice of labor is more effective in
increasing the labor supply than it is in increasing the consumption of the externalityproducing good, proportionately; (c) the government revenue requirement is not too high.
If the revenue requirement is not negligible,
the case for a subsidy is weakened and may be
reversed but the case for a tax is strengthened.
In fact, Proposition 1' has not gone far
enough. (It is nevertheless preserved for its
simplicity; it is sufficient for normal cases.)
Suppose that condition (a) in Proposition 1'
(i.e., inequality (17) or (17')) is reversed,
does this mean that the counternormal
policy of taxing/subsidizing external economy/diseconomy is then desirable? Not
necessarily. (Observant readers may have
noticed that I say the counternormal policy
may be desirable.) Now the left-hand side of
(15) is made smaller than plxl/wL for the
case of external economy. But a negative t
(i.e., subsidy) also makes the right-hand side
smaller. If condition (b) (i.e., inequality (18))
is also reversed, the required increase in T to
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750
THE AMERICAN ECONOMIC REVIEW
finance the subsidy also makes the righthand side smaller. It is then clear that the
normal policy of taxing/subsidizing external diseconomy/economy is still desirable. The reversal of both the two normality
conditions results in normality. This can be
explained intuitively. A subsidy on x 1 (which
reduces ql and increases xl) must be financed by an increase in T which reduces
qL.
If (17) is reversed, a reduction in
qL
greatly reduces xl and may destroy the purpose of the subsidy. However, if (18) is also
reversed, the reduction in q" increases L
even more greatly, making only a small increase in T sufficient to raise enough revenue to finance the subsidy. Though an increase in T greatly reduces (through q L) Xl,
this effect may not be sufficient to negate
the case for a subsidy as the required increase in T (if at all) is small.
The above discussion may be summarized
into the following proposition:
PROPOSITION 2': Proposition 1' remains
true if both conditions (a) and (b) are reversed.
For cases where only one of (a) and (b) is
reversed, it is not necessarily true that the
counternormal policy follows. For example,
if (a) is strongly satisfied and (b) is just
marginally reversed, normal policy may still
be desirable. In these complicated (but unlikely) cases, we have to look into the relevant values in more detail. We cannot however completely rule out the counternormal
cases even by resort to second-order conditions as when either q' or q L changes, all
goods including x2,..., xn may change,
making the values of SIL, SLL, etc. quite
flexible. Nevertheless, since SL( = -SLI)
appears in both (17) and (18), it can be seen
that when (17) is satisfied, SIL is relatively
small, making the strong reversal of (18)
unlikely. The counternormal cases, cannot
be ruled out completely, but they are extremely unlikely to prevail.
By adding the income effect term ax'/aI
to each side of (17), we may transform it
into the following uncompensated form,
(17")
-
/x >
3q
qL
/L
SEPTEMBER 1980
Similarly, (18) may also be so transformed (by adding aL/aI to each side).
From the equivalence of (17), (17'), and
(17"), and similarly with respect to (18), it is
not difficult to see that Propositions 1 and 2
in Section I are equivalent to Propositions 1'
and 2', respectively, expressed in different
ways. The uncompensated form (17") has
the advantage of being more directly verifiable empirically.
III ConcludingRemarks
The propositions established above provide insights into the problem of optimal
corrective taxes/subsidies when they have
to be financed by distortive taxes. However,
to achieve direct policy application, much
more work would have to be done. For one
thing, the propositions shed light only with
respect to the direction, but not the magnitude, of the taxes/subsidies. A useful extension of this analysis is to examine whether the optimal corrective taxes/subsidies
should be larger or smaller than those indicated by partial-equilibrium Pigouvian analysis. Secondly, it may be thought that the
relaxation of the simplifying assumptions
might change the results significantly. Let
me examine this briefly.
If the consumer side of the economy cannot be represented by a single utility function, we could either maximize a Paretian
social welfare function or maximize one individual's utility subject to the constancy of
others. Instead of plxl in (15), we would
then have a weighted sum of various individual consumption of xl (for example,
where k is used to indicate an
EklWkplXlk
individual among the s individuals, Wkis his
weight, i.e., Wk aW/aUk). Similarly, UE
and wL would also be replaced by some
appropriate weighted sums. The revised (15')
would then be fairly difficult to handle since
both equity and efficiency considerations
are blended together. If, for example, a
good-producing external diseconomy is predominantly consumed by individuals (the
poor?) with high weights, a tax on it may no
longer be desirable. However, since we have
other instruments (for example, progressive income taxation, transfer payment) to
achieve the objective of equity, the separa-
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VOL. 70 NO.4
NG: CORRECTIVE TAXES AND SUBSIDIES
tion of equity and efficiency considerations
may be justified. (For a further development
of this argument, see Appendix 9A of my
book.) Moreover, even if the separation of
equity and efficiency considerations is not
accepted, the case for a tax/subsidy is still
valid unless it is overbalanced by the equity
consideration caused by, say, a very biased
consumption pattern.
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