Recent Developments in the
Theory of Externality and the
Pigovian Solution*
Where there are external effects,l the Pigovian solution is to impose a system of taxes and/or subsidies t o equate private and social
costs/benefits. This traditional approach has been vigorously attacked
by some recent contributors to the problem of externality.2 While a
number of valid criticisms and useful proposals have been made, they
are not without shortcomings and excesses. The purpose of the present
paper is to examine some of these shortcomings and hence to reassess
the usefulness of the traditional approach. It is not intended as an
exhaustive survey of the literature, although most of the important
contributions, except those on public goods, have been covered.
I
Some of the major contributions t o recent developments in the
concepts of externality may be summarized as follows :
1. The problem of externality is a two-way one. To avoid harm
to B would inflict harm on A : ‘in general it does not matter
who has to compensate whom in the determination of the
optimum output’.8
2. The classical tax-subsidy policy is not the only way of solving
the problem of externality : central directives, mergers, or
bargaining may also be f e a s i b l w r even better than the
classical treatment. Moreover, full Pareto equilibrium can
* I am grateful to Arthur Partridge for his help in improving the presentation
of this paper.
1Throughout this paper, external effects refer to technical rather than pecuniary external economies and diseconomies.
ZSee, in particular, Buchanan [S], Buchanan and Stubblebine 171, Coase [91,
Davis and Whinston [lo], [ l l ] , [12], and Plott [ U ] . (Figures in square brackets
relate to references listed at the end of the article.)
8See Coase [9, pp. 2 ff.], Buchanan and Stubblebine [7, pp. 381-21, Mishan
[17, pp. 29 ff.], and Burrows [8, pp. 41 ff.]. The quotation is from Mishan [17,
p. 291. Burrows points out that, where there are institutional obstacles to bargaining or where bargaining costs are asymmetrical, the question of who is to compensate whom may affect allocational efficiency. In the discussion in the text, I
assume away institutional obstacles and bargaining cost ; hence this problem does
not arise.
169
A
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never be attained by means of the imposition of taxes (subsidies) on one party until all marginal externalities are
eliminated. Bilateral taxes (subsidies) are thus required.‘
3. A distinction must be made between ‘separable’ externalities
where the level of activity affects only the total cost (utility)
of another party, and ‘non-separable ’ externalities where the
marginal cost (utility) is also affected. The tax-subsidy solution is difficult to achieve in the separable case and impossible
in the non-separable [ 101.
4. If the external effect created by the production of X is due
to some input used (such as burning), the appropriate tax or
subsidy should be placed on that input rather than on the
production of X [ 23 3.
5. The presence of external benefits may call for reduced output
level on the part of those who produce these economies and
the reverse may be true in the case of external diseconomies
[31, ~ 1 .
6. The Pigovian solution is applicable only to cases of perfect
competition [ 51.
Let us examine these points in turn.
1. If we are considering only the solution of a particular existing
externality and are not interested in the effect of the solution on the
rest of the economy in the future, it is true that the problem of who
is to compensate whom is of little significance as far as Pareto
efficiency is ~ o n c e r n e d .However,
~
if the damaging party is not required by law to pay the compensation, but is able to receive compensation to reduce his activity from the damaged party either in a
private bargain or enforced by law, it will open up ‘magnificent
business prospects: any activity can be turned to profit as long as i t
is sufficiently annoying to someone else. As long as the activity absorbs
no resources, i.e., as long as the blackmailers maintain amateur standing, the economist who refrains from social judgment can find no fault
with the situation’ [26, p. 3531.
According to Davis and Whinston [ll,p. 3041, the above objection can be met by a proper definition of property rights. This concession means, however, that the problem of who has to compensate
whom is important. Moreover, the activity of blackmailing is likely
to absorb some resources and to divert them into less productive uses.6
Economists therefore are entitled to say something about the problem
of who compensates whom. But this does not mean that the ‘damaging’
party (i.e. the party whose activity is an external diseconomy to another) should always pay the compensation : the blackmailing argu4 See Buchanan [4, pp. 25 ff.], Buchanan and Stubblebine [7, pp. 382-31, C a s e
[9],Davis and Whinston [lo], [ I l l , [IZ].
5 The problem affects mainly the distribution of income. Note, however, that
the existence of welfare effects may influence the outcome. See Mishan [MI,
Dolbear [13], and Burrows [8].
K f . Andel [l].
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THEORY OF EXTERNALITY
171
ment cuts both ways. I shall endeavour to show that, to achieve
efficiency and avoid blackmailing, it is generally the second party
rather than the 'damaging' party who has to pay the compensation.
Imagine that a factory is already in existence in a certain location
and that the working of this factory necessarily emits smoke. Suppose
further that the law rules that the smoke-emitting party must compensate the damaged party for the amount of damage inflicted (assuming no difficulty in estimating the damage). Thus, if the smoke
nuisance to the owner of a house nearby is valued a t $5, the factory
owner has to pay him $5 in compensation. Suppose also that the social
and private net benefits of the factory in that location are $100, so
that the factory will remain i n production as long as B , the owner,
does not have to pay compensation in excess of $100. Now consider A
who is going to build a house by the side of the factory. Suppose the
cost of the house is $10, the benefit without the smoke is $12, and the
smoke nuisance reduces the benefit to $7. A will decide to build the
house as he can recover $5 ($12 - $7) from compensation paid by B.
But the social net benefit of the house is clearly negative. The cost of
the house is $10, while the benefit of the house is only $7. Hence the
net benefit is -$3. Thus the law that requires compensation from the
damaging party may not achieve optimum output. Moreover, there is
also the prospect of blackmailing : even if A does not have the intention
of building a house, he can still threaten B that he is going to do so
unless B agrees to pay him, say, $4.
As the factory is already there, the smoke nuisance must be taken
as given in the decision to build houses nearby, unless the smoke
nuisance is valued at greater than the benefit of the factory, in which
case the factory has to cease production o r move elsewhere. In contrast, if the houses are already there and the decision is whether or
not to build the factory, then the smoke nuisance must be regarded
as a cost of the factory. I n this case, a law that requires the payment
of compensation by the factory will help to achieve optimum output.
Therefore, in deciding who is to compensate whom, it may be said
that the first party (generally according to the calendar time of
activity) has prior claim to receive compensation. Of course, other
factors such as justice and provision of the common law also have to
be taken into consideration, but economists have little to say about
such matters.
2( a ) . Buchanan and Stubblebine argue that 'full Pareto equilibrium can never be attained via the imposition of unilaterally
imposed taxes and subsidies until all marginal externalities' are
7 Marginal externality is defined to exist when aUn/aXkr # 0, where U
' stands
for the utility (cost) if individhal (firm) g and '
.X stands for the level of the
activity k by individual r.
Infra-marginal externality exists when auu/axe' = 0 for given Xk', but
JJU'/aX,'dX,'
# 0. Nath [19, pp. 81-21 also speaks of the possibility of a
'purely infra-marginal externality' where aun/8xk' = 0 for d l values of Xk'.
This is clearly an illusion. When aU'/aXhr = 0 for all values of Xk', then
$.'aU'/aX,'dX~'
must equal zero for any values of (I and b. That is to say, there
is no externality at all.
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THE ECONOMIC RECORD
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eliminated. If a tax-subsidy method, rather than “trade”, is to be
introduced, it should involve bilateral taxes (subsidies) ’ “7, p. 3831.
Consider the traditional argument which can be illustrated by a
simplified diagram. In Figure 1, the horizontal axis measures the
activity level of B, which exerts external diseconomy on A ; the vertical axis measures the marginal valuation of A and B for the activity.
Marginal
valuation
of B
Marginal
t
I
A”
of A
FIGURE
I
As the valuation of A is measured southerly from the origin, values
in the northern quadrant mean disutilities to A. Curves A and B are
the net marginal evaluation curves for A and B respectively. The
social optimum level of the activity is at 8.But B, in maximizing his
own utility, will carry the activity u p to P . If a tax rate which, at
the margin, is equal to the negative marginal evaluation of the activity
t o A is imposed on B , the new net marginal evaluation curve of B
will be B’.8 In this case, B will end up a t 8,the social optimum. From
this Buchanan and Stubblebine argue that, a t S, equilibrium has not
It may also be noted that Nath’s revision of Buchanan and Stubblebine’s definition of marginal externality [19, pp. 65-81 is also unnecessary. In Nath‘s example,
if g pays r for Xh*,it may be said that Xh’ is not actually consumed by r who
merely re-sells it to g. Hence Xr’ should be denoted as XI’ instead. Even if we
stick to the notation of Xr- and hence must admit the existence of externality, it is
still possible to say that the externality has been ‘solved’ by the ‘trading’ between
r and g.
8 Disregarding the secondary effect of taxation on the marginal evaluation
cume.
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THEORY OF EXTERNALITY
173
been reached. For a t this point, the marginal disutility of the activity
of A is greater than the marginal utility (net of tax) to B. Hence,
there is an incentive for them to bargain a new level of the activity
S‘ which, however, is not the social optimum point. To prevent this,
Ruchanan and Stubblebine propose that A should also be taxed ‘to
insure that he will take the costs “internally” imposed on B into
account’ [7, p. 3831. It should be noted that, if the tax is positively
correlated with B’s activity level, it will shift the A curve upward to
A’, as the valuation of A is measured southerly from the rigi in.^ The
intersection of A’ with B’ a t E” (6”’) is further from the optimum
point S than is S’. It is therefore my contention that the tax should
be negatively correlated with B’s activity level from P , thus shifting
A curve down to A”.lo
The proposed bilateral taxation is usually superfluous. If it is
assumed that bargaining between the parties affected is possible, Pareto
optimum will be achieved without any taxation. If bargaining is impossible (owing, for example, to the high cost of bargaining or to the
large number of parties involved),ll a single tax on B will be sufficient to achieve the optimum.12 This latter situation was in fact
assumed by Pigou when he said that ‘the essence of the matter is that
one person A, in the course of rendering some service, for which payment is made, to a second person B , incidentally also renders services
or disservices to other persons (not producers of like services), of such
a sort that payment cannot be exacted from the benefited parties or
compensation enforced on behalf of the injured parties’ [22, p. 183,
italics added]. To be more precise, he should have added that, nor is
compensation paid by the injured party, to induce the other party to
reduce his injuring activity, fea~ib1e.l~
Bilateral taxation, however, may serve two other purposes. I n our
example above, if A can avoid the external diseconomy (for example,
by moving to another place) a t a cost of X that is less than the cost
borne by B to reduce the nuisance (i.e. ESP in Figure l), then it
would be desirable for A to do this rather than have B reduce the
9 This may need some explanation. A tax on B positively correlated with B’s
activity level (the horizontal axis) will shift B curve downward. As A’s valuation
is measured in the opposite direction from B’s valuation, a similar tax (i.e., one
which correlates positively with B’s activity) on A will therefore shift A curve
upward. For the tax to shift A curve downward, it has to be negatively correlated
with B’s activity.
10 It may be said that a subsidy to A that is negatively correlated with the
reduction in B’s activity level will have the same effect of shifting A curve to A”.
But this subsidy is equivalent to a lump-sum subsidy plus our proposed tax, i.e., a
tax that is positively correlated with the reduction in B’s activity level. Moreover,
the subsidy will fail to achieve two other purposes of bilateral taxation to be
mentioned presently in the text.
11That mutually beneficial agreement may not be reached in cases involving a
large number of parties is one of the main justifications for State action. See
Baumol [3].
12 Bilateral taxation-subsidization may be relevant where bargaining is possible
but is deemed uniust o r is more costlv than the tax-subsidv scheme and the government decides to use the tax-subsidy sdution.
18 Cf. Wellisz “26,p. 3611.
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THE ECONOMIC RECORD
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externality. But A is not motivated to do this unless he is required to
pay an amount equal t o the additional cost (or the decreased utility)
incurred by B to reduce the e~terna1ity.l~
Furthermore, the amount
of diseconomy borne by A is difficult to discover in practice. A is
motivated to exaggerate his damage so as to raise the rate of tax on
B and hence to reduce the activity of B further. However, if A is
required to pay a tax equal to the cost borne by B to reduce the
externality, he ( A ) will not benefit from the reduction of B’s activity
beyond 8.If the amount of damage is known and if it is also known
that the cost for A t o avoid the externality is certainly higher than
the cost borne by B to reduce it, bilateral taxation is unnecessary.
It is tempting to infer that, as bilateral taxation is appropriate
in the case of external diseconomies, bilateral subsidization is called
for in the case of external economies. However, it can be shown that
this is not true. This may be seen in Figure 2, which is similar to
Marginal
valuation1
ot B
C
Marginal
valuation
atA
B
‘
1
FIGURE
2
Figure 1 except that it deals with the case of external ec~nomies.’~
As B, the party producing the external economy, is subsidized to shift
his evaluation curve from B to B’, A has to be taxed (positively correlated with the increase in B’s activity) to shift his evaluation curve
to A’ to make it intersect with B’ at 5, the optimum point. Thus, in
14Cf. Coase [9,p. 411. It is also interesting to note that if the evaluation of
the activity is presented in marginal terms as in our Figure 1, rather than the
all-or-nothing example of Coase, the problem of bilateral taxation is relevant even
if we know the ‘detailed knowledge of individual preferences’ [9, p. 411. The
essential thing is that the prevention of the external economy is an all-or-nothing
matter.
15 It must be noted again that, as the valuations of A is measured southerly
from the origin, values in the negative quadrant mean positive utilities to A.
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THEORY OF EXTERNALITY
175
the case of external economies, the appropriate solution is a subsidy
to the benefiting party and a tax on the benefited party, rather than
bilateral subsidization. The apparent asymmetry can easily be explained. In both cases (external economies and diseconomies), the
affected party has to be taxed so as to make him take account of the
cost of loss (without counting the tax o r subsidy) of the affecting
party in changing his activity level, while the affecting party is usually
taxed in the diseconomy case and subsidized in the economy case.
2 ( b ) . Davis and Whinston [12] argue that, when the bargaining
methods cannot achieve a Pareto point because of the existence of a
‘Giffen paradox’ type of situation, the tax-subsidy schemes are also
incapable of reaching Pareto solutions. The Giffen situation may be
illustrated in Figure 3, where CD represents the budget line and Z
the relevant indifference curve of individual B who consumes only
two goods X and Y , represented by the respective axes. E is the point
Y
T’
T
C
Y
0
FIGURE
3
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of B's 'private' equilibrium where XI and PI are consumed. Consumption of X,however, imposes external diseconomy upon individual
A. Suppose A offers B an amount T per unit for each unit reduction
of B's consumption of X. The new budget constraint for B is represented by TED, and he reduces his consumption of X toXZ.If A offers
him higher per unit payments as represented by T', his consumption
of X may increase to X3,as the income effect swamps the substitution
effect. Suppose that Xz is the minimum level of consumption that can
be induced by this method. If the marginal disutility of X to A a t XB
is still higher than the marginal utility to B, the Pareto optimal point
cannot be reached by this type of bargaining.lB
The conclusions of David and Whinston appear to be based upon
a false equivalence between the tax-subsidy scheme and the bargaining
scheme. But there are two significant differences between the two
schemes. For one thing, bargaining would reach Pareto efficient point
only if it is beneficial to both parties, whilst the government can impose the required amount of tax or subsidy even if it makes one or
both parties worse off. Thus in Figure 3, A will not offer B a per unit
compensation in excess of T . But the government can offer B a per
unit subsidy in excess of T . Thus, if T' is the amount necessary to
attain Pareto efficiency, the government can subsidize B to that extent
even if it is worse than the smaller subsidy T from the viewpoint of
Marginal
vab"p;on
FIGURE
4
16 For more vigorous analysis, see Davis and Whinston [ 121. It must also be
noted that if successively higher rates of compensation or an all-or-nothing compensation is feasible, Pareto optimal solution can be achieved even in a Giffen
situation.
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THEORY OF EXTERNALITY
177
A. This can be seen more clearly in terms of the marginal evaluation
curves.
In Figure 4, which is similar to Figure I, B’s original net marginal evaluation for the activity in question is denoted by the curve
B and that for A by the curve AA’ (assumed constant for simplicity).
Now B will carry the activity to P whilst the social optimum is at 8.
If there is no income effect, A can pay B a per unit compensation OA
and the optimum point S can be reached. If there is positive income
effect, B’s marginal evaluation curve will shift to the right as his
income is increased (from compensation or subsidy). Suppose that
curve B shifts to B’ as OC amount of per unit compensation is paid.
The point reached will therefore be P 2 instead of PI. If the income
effect is strong enough, increased amount of compensation may actually
increase the equilibrium point of the activity. For example, if the
evaluation curve shifts to B” as compensation is increased to OA, the
new equilibrium point P3 is higher than Pa.If PP2 is the maximum
amount of the reduction in B’s activity A can get by a per unit compensation, A will not pay compensation in excess of OC. Yet apparently Pareto optimum has not been reached (FP2 # G P 2 ) .
The government can, however, achieve Pareto optimum by paying
OA amount of subsidy per unit reduction in B’s activity. The new
equilibrium point is P3 which is a Pareto optimum, as the marginal
gain to B and the marginal diseconomy to A are equal (E’P,). This
is true despite the fact that A prefers Pz to P3. The discrepancy between S and PS is caused by income redistribution (the subsidy to
B ) . Though the Pareto optimum point reached is a different optimum
point to S, it is still a Pareto optimum.
A second difference between the bargaining and the tax-subsidy
scheme should be mentioned. Although A can only compensate B to
induce him to reduce the consumption of X,the government can either
subsidize B for the reduction in consumption of X or tax B for his
consumption of X.While both subsidy and compensation have positive
income effects, taxes have a negative income effect. As the income
effect and the substitution effect are in the same direction, there can
be no ‘Giffen paradox’ in the case of taxing B. In Figure 3, a tax on
B’s consumption of X will shift the budget constraint from C D to
CF. Assuming divisibility and convexity, the rate of the tax can be
varied to achieve any desired level of B’s consumption of X. Disregarding practical difficulties, a Pareto optimal solution can therefore be achieved by the tax-subsidy scheme, even if the bargaining
method fails owing to the existence of a ‘Giffen paradox’ type of
situation.17
3(a). Davis and Whinston [lo] also argue that in the case of
reciprocal, non-separable externalities, the classical tax-subsidy solu17It may be noted that, if we wish not only to achieve Pareto efficiency but
also to compensate A fully at the same time, then a per unit tax may be insufficient
for the purpose: a combination of a per unit tax and a lump-sum subsidy may be
necessary. This is analysed by Dolbear [13] ; see also [16], [21], [141.
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tion is ‘impossible’. I n this case, the output decision of each firm
depends on that of the other, and a known, unique equilibrium solution in pure strategies for this type of game does not exist. As the
decisions of the firms cannot be predicted, the appropriate tax-subsidy
cannot be devised.
It should be pointed out that the above argument applies only to
cases where externalities are both reciprocal and non-separable.18
Moreover, the interdependence must be a significant element influencing the decisions of each unit. This usually requires the number of
firms o r individuals involved t o be small. Even if these conditions are
all met, it is not true that the tax-subsidy solution is altogether impossible. I t is true that the difficulty of devising an appropriate tax
(subsidy) is greater. It may also be true that it is quite impossible
to strike precisely at the optimal point. But most solutions of the real
world are not precisely optimal. If merger, bargaining, and central
direction are unfeasible or too costly, a tax-subsidy scheme may still
be desirable even in the case of reciprocal, non-separable externalities.
I t is true that the theoretical optimal rate of tax may not be known,
but the ‘optimal feasible’ may still be achieved by choosing a tax rate
according to the most probable output decisions of each firm. The
problem of choosing a n appropriate tax (subsidy) by the government
in the case of reciprocal, non-separable externalities is similar to that
faced by the firms in deciding their output in the case of oligopolistic
or ‘external’ (i.e. the case at present being discussed) interdependencies. That the precise decision of the rivals cannot be known does
not mean that an ‘optimal feasible’ decision based on the most probable decisions of the rivals cannot be taken.
3(b). Wellisz argues that ‘the problem of devising a Pigovian
solution for the “separable” case does not arise for, as can be readily
demonstrated, the “ separable externalities” do not affect the pattern
of resource allocation’ [26, p. 3551. This contention is clearly
erroneous. Davis and Whinston [ll, p. 3041 have already shown
mathematically that separable externalities do have an influence upon
the short-run allocation of resources. I wish t o discuss here in nonmathematical terms the errors of Wellisz’s argument. I shall also show
that separable externalities affect resource allocation even in the long
run. The argument of Wellisz is as follows :
‘The output level of a firm in a competitive industry is determined by the marginal cost and by the product price which is
parametrically given to the firm. As long as the price remains
constant and the marginal costs do not change, the optimum output level of the firm will not change. Since “separable” externalities have no effect on marginal cost, they do not alter the firm’s
optimal output level. As a consequence “separable” externalities
have no influence on the allocation of productive resources though
they do affect product distribution’ [26, p. 3551.
18 Cf.
Davis and Whinston [lo, p. 257, n. 311, and Mishan [17, pp. 28-91.
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THEORY OF EXTERNALITY
179
If the production of firm A has a separable external diseconomy
on firm B, it is true that the short-run output level of B is not affected
as its marginal cost is not changed. But the output level of firm A
itself would not be socially optimal. As its output level affects the
total cost of B, the social marginal cost of A’s production is higher
than the private marginal cost. The private output decision of A will
therefore not be socially optimal. Thus, while separable externalities
have no effect on the marginal cost of the affected firms, they have a n
effect on the social marginal cost of the affecting firms. The conclusion
of Wellisz therefore does not hold.
In addition to their effect on short-run resource allocation,
‘separable’ externalities also affect resource allocation in the long
run.1eBut Wellisz argues for the non-existence of a long-run effect :
‘It may seem that “separable” externalities affect resource allocation in the long run, through their effect on the total (produce or
shutdown) decisions of the affected firms. A firm’s optimal output
level may not change as long as the firm remains in production,
but as a consequence of the imposition of external costs, the firm
may find it most profitable to go out of production altogether.
This argument is spurious, however. I n considering the total
(produce or shutdown) decision, the firm treats all costs a s if they
were variable, even those costs which are fixed in the short run.
T h e decision t o produced or t o discontinue production i s based
on considerations of long-run marginal costs. If a n externality
modifies the long-run marginal costs of a firm, it must be classified
as “non-separable” in the long ru n ’ [26, pp. 355-6, latter italics
added].
My point can be established simply by pointing out that the
decision to produce or shutdown is not based on considerations of
long-run marginal costs but rather on long-run profitability, i.e. total
revenue minus total costs. Long-run marginal costs affect decisions
about long-run levels of output but do not determine the total (produce or shutdown) decision. Thus, the argument that ‘separable’
externalities affect resource allocation in the long run, which is termed
spurious by Wellisz, is actually perfectly correct.
4. Plott [23] argues that, if the external effect created by the
production of X is due to some input used (such as burning), the
appropriate tax o r subsidy should be placed on that input, rather
than on the production of X as generally assumed. His argument is
essentially correct. But his analysis does not take the long-run adjustment into account. If the long-run adjustment is considered, his contention that ‘a tax on X,the traditional candidate for taxation, may
make the situation worse rather than better’ [23, p. 841 will hold only
‘under more restrictive conditions than Plott ’s analysis would suggest’
10 The mathematical treatment of Davis and Whinston [ I l l referred to in the
text does not take account of the long-run effect.
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[ 15, p. 4731 ?O 21 This means that a tax on X will generally yield the
right direction of correction, though not precisely the optimal influence. Thus, if a tax on the right input is technically unfeasible
or administratively costly, a tax on X may be a reasonably good
substitute.
5. Baumol holds that ‘contrary to standard doctrine, the presence
of external benefits may very conceivably call for reduced output and
activity levels on the part of those who produce these economies and
that the reverse may be true in the case of diseconomies’ [3, p. 321.
His contention is based on the analysis of Buchanan and Kafoglis
[ 61. The latter authors argue that ‘independent or market organization of an activity that is acknowledged to embody relevant external
economies need not result in an undersupply of aggregate resource
inputs, relative to that amount required to satisfy the necessary marginal conditions for Pareto-optimality’ [6, p. 4031. Indeed, the reverse may be true. Thus, a public health programme may decrease
medical expenditures as compared with an uncoordinated private
health programme,22 where many individuals, fearing that they are
unprotected against communicable diseases likely to be spread by
some of their fellow citizens, are apt to take very strong measures of
self-protection.2s
The arguments of Buchanan and Kafoglis, and Baumol seem misleading on a significant point. I am not challenging the conclusion
that aggregate resources could be reduced after the correction of the
external economy. However, the reduction of aggregate resources is
not caused by the reduced output and activity levels on the part of
those who produce the external economies, but rather by a reduction
in resources committed by those who are benefited by the external
economies. Take the case where individual B causes external economy
upon A. Traditional analysis says that the resources committed by B
to the activity in question are less than optimal ; it does not say anything about the total resources committed by A and B together. After
B has increased his activity up to the socially optimal level, A may
conceivable reduce the resources he has committed to this same activity. Whether aggregate resources increase, decrease, or remain the
rnSimilarly, if long-run adjustments are taken into account, the case ‘where
the proper correction of the externality by means of a tax [on the input] involves
an increase in the production of X rather than a decrease’ [23, p. 861 will only exist
under very restrictive conditions, keeping in mind that perfect competition is
assumed.
21 See also [Z] in which it is argued that the long-run effect will necessarily
be in the right direction.
22 Assuming that public and private health expenditures are equally efficient.
2s See Vincent [25] for arguments that the existence of economies of scale in
the production.of benefits (outputs) from immunization is a necessary condition
for a lower total number of immunizations (inputs) to be purchased at the Pareto
optimum, and that a reduced output level for both parties at the Pareto optimum
requires that one party’s receipts of immunizations must be a more-than-perfect
substitute for the other’s receipt of immunizations. See also Olson and Zeckhauser
[a]for the argument that independent adjustment leads to less efficient production
method rather than to excessive resources.
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THEORY OF EXTERNALITY
181
same depends on the particular cases, as analysed by Buchanan and
Kafoglis [6], and Vincent [25]. In the reciprocal case where A and
B both produce external economies upon each other, it is possible that,
after socially optimum adjustment, resources committed by A or B
may decrease and so may aggregate resources commitment. But this
is not due to the fact that the benefiting person should reduce his
resource commitment, but rather to the fact that the benefited person
may be able to reduce his own resource commitment. Though in the
reciprocal case both parties are benefiting and benefited a t the same
time, the analytical reason why aggregate resources could be reduced
must be made clear.
Since traditional analysis does not say anything about aggregate
resources, it seems that, whilst Buchanan and Kafoglis’s analysis is
useful, their claim that traditional analysis is erroneous is questionable. It is also quite clear that Baumol’s contention that the presence
of external benefits may call for reduced output and activity levels
on the part of those who produce these economies is invalid.
6. Buchanan argues that ‘it is necessary to limit the Pigovian
correctives on the tax side to situation of competition’, as ‘the imposition of a corrective tax (under external diseconomy) will often
reduce rather than increase welfare in the Pareto-efficiency sense. Only
when the industry generating the external diseconomy is competitively
organized can the corrective tax be unambiguously hailed as welfareimproving, even in the presence of all of the other required conditions’
[5, p. 1751. His reasoning is very simple.** If the output is already
smaller than the socially optimum (i.e. after taking account of the
external diseconomies) owing to monopolistic restriction, a ‘corrective’
tax to reduce the output further will clearly reduce welfare. From
this argument, Buchanan also deduces that ‘there is an important
asymmetry between external diseconomies and external economies with
respect to the possible offsetting welfare effects of market structure.
With external economies, the provision of corrective subsidies reinforces the directional change in output that reforms in market structure would indicate to be desirable’ [5, p. 1771.
However, the argument of imperfect market structure can in fact
be shown to cut both ways. Owing to the existence of market imperfection (not restricted to the industry in question, but including
other industries), the output of a n industry may fall short of the
social optimum, as Buchanan recognizes, but it may also exceed the
social optimum, as the theory of second-best teaches us and Buchanan
seems to forget. In particular, even a monopolized industry may produce an output greater than the social optimum, e.g., if the degree of
monopoly in other industries is even greater. Thus, whilst it is possible
that market imperfection may render the corrective tax in the ca8e
of external diseconomy less welfare-improving (or even welfare24
Though more elaborate in illustration, his reasoning is essentially embodied
in a footnote by Wellisz [26, p. 349, n. 31.
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THE ECONOMIC RECORD
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reducing), it is equally possible that it may make the corrective tax
even more welfare-improving than is true without market imperfection. It is also clear that external economies and external diseconomies
are perfectly symmetrical ; market imperfection may either reinforce
or reduce the welfare-improving power of the corrective subsidy in the
case of external economy.
Owing to the two-way nature of the effect of market imperfection,
it is rather unconvincing that the argument of market imperfection
may be ‘presented as a contribution to the continuing dismantling of
the Pigovian tradition in applied economies, defined . . . as the
emphasis on internalizing externalities through the imposition of corrective taxes and subsidies’ [ 5 , p. 1741. For one thing, it is clearly
not true that the Pigovian corrective taxes must be limited to situations of perfect competition, as Buchanan maintains. It is only when
the monopolistic restrictive tendency in an industry (or firm) is so
strong that it outweighs the combined effect of its external diseconomy
and the monopoly power of other industries that a corrective tax is
welfare-reducing. In practice, the Pigovian corrective will only be
adopted, if at all, in cases where the deviant (non-Pareto) behaviour
is clear and important. When external diseconomies are clear and
important, corrective taxes will be welfare-reducing only if the degree
of monopoly in the industry in question is very high, in which case
another opposite corrective is called for. While the Pigovian analysis
suggests the levy of a corrective tax on external diseconomy-producing
firms, it also suggests a corrective subsidy (plus a lump-sum tax to
remove the profit, if desired) on the monopolistic firm. That the
correctives must depend on the net outcome is not in any sense contrary to the Pigovian analysis. Externality is one problem, market
imperfection another. I n economic analysis-in fact in any scientific
analysis-one must concentrate on one or at the most ti few issues
and make use of the ceteris paribus assumption.25 It is therefore inappropriate to criticize the Pigovian treatment of externality because
of market imperfection; it is as though Boyle’s law is criticized on
the ground that changes in temperature will falsify the equation
PV = constant, where P and V stand respectively for the pressure
and volume of a
II
The main conclusions from the above discussion are briefly as
follows :
(i) Though externality is a two-way problem, the question of
who has to compensate whom is important for resource
25 The only real criticism of the Pigovian treatment in this respect is its piecemeal nature (i.e., the disregarding of situations in other parts of the economy)
which has been adequately pointed out in the theory of second best.
2eMy defence of the Pigovian solution in this section is also valid against
Nath’s argument [19, pp. 88-91 that the Pigovian prescription of a subsidy to an
external economy good is not suitable if the good happens to be a ‘demerit’ good,
such as an addictive drug.
1971
THEORY OF EXTERNALITY
183
allocation because of the effect on future decisions. It is
also suggested th at the ‘first’ party should have the
priority of receiving compensation.
(ii) Bilateral taxation is not always necessary for the Pigovian
solution to external diseconomies. In the case of external
economies, the appropriate solution is not bilateral subsidization but a subsidy on the benefiting party and a tax
on the benefited party.
(iii) Contrary to the contention of Davis and Whinston, a
Pareto optimal solution can be achieved by the tax-subsidy
scheme even if the bargaining method fails owing to the
existence of a ‘Giffen paradox’ type of situation.
(iv) Even ‘separable ’ externalities affect resource allocation
both in the short run and in the long run.
(v) The solution of ‘non-separable’ externalities by a taxsubsidy scheme, while very difficult, is not altogether
impossible.
(vi) If a tax on the diseconomy-producing input used in the
production of X is unfeasible or costly, a tax on the production of X itself is usually an appropriate substitute.
(vii) Contrary t o the contention of Baumol, the presence of
external economies calls for increased level of activity and
resource commitment on the part of those producing these
economies, though the resource commitment of the benefited
party may decrease after the increased activity of the
benefiting party.
(viii) The Pigovian solution to the problem of externality is not
restricted to the case of perfect competition.
From the above, it is apparent that the classical Pigovian taxsubsidy solution to the problem of externalities is not as fruitless a n d
faulty as suggested by the recent developments in the concept of
external effects. This is not to suggest, however, that the tax-subsidy
scheme is not without its practical difficulties. I n this respect, two
points merit special mention. First, in the real world of multiexternalities and market imperfection, a correction of one externality
according to the partial analysis may actually lead away from the
optimal, unless the externality is a clear and very substantial
Secondly, ‘the tax-subsidy solution does not possess one of the most important characteristics of a perfectly functioning market mechanism.
Each time there is a technological change which affects the firms under
consideration, there would have to be a recomputation and adjustment
of the taxes and subsidies’ [ 10, p. 2521. The same applies to changes
in consumers’ preferences. Tisdell [24] has also shown that, where
different techniques of production have different external effects,
27
See the literature on the problem of second best for detailed discussion.
184
THE ECONOMIC RECORD
JUNE
neither the mere absence of externalities nor the mere presence of
Pareto irrelevant externalities (in the existing technique) is evidence
that production is conducted in a socially optimal way. In this case,
policy decisions can become immensely complicated as the absolute
social and private effects of different techniques may have to be
compared.
The first difficulty applies to all solutions, especially merger and
bargaining. While the problem of second best is diBcult to solve in
practice, it is solvable in principle by the tax-subsidy scheme or central
direction of production. But private bargaining and merger cannot
and will not take the rest of the economy into account. The second
difficulty applies particularly to central direction and, to a lesser
degree, also to bargaining. After a change, the existing agreement may
no longer be optimal and re-bargaining may be costly and timeconsuming. Merger, on the other hand, whilst free from the second
di&ulty, may lead t o monopolistic power and create problems of its
OWIl.28
Y. K. NQ
University of New England
REFERENCES
[I] Andel, N., ‘Some Notes on Equating Private and Social Cost: Comment’,
Southern Economic Joumol,Vol. XXXIII, July 1%: p. 112.
[2] Bassett, L. R., and Borcherding, T. E., Externalities and Output Taxes’,
Southern Economic Journal, Vol. XXXVI, April 1970, pp. 462-4.
[3] Baumol, W. J., Welfare Economics and the Theory of the State. Second
edition (Bell, Londy, 1%5).
[4] Buchanan, J. M., Politics, Policy and the Pigovian Margins’, Economica,
Vol. XXIT, February l%2, pp. 17-28.
[51 , External Diseconomies, Corrective Taxes, and Market Structure’,
American Econom’c Review, Vol. LIX, March 1%9, pp. 174-7.
[61
, and Kafoglis, M. Z., ‘A Note on Public Supply’, American Economic
Review, Vol. LIII, June 1%3, pp. 403-f4.
[71 - and Stubblebine, W. C., Externality’, Economica, Vol. XXIX,
NovemGr 1962, pp. 371-84.
[8] Burrows, P., ‘OnExternal Costs and the Visible Arm of the Law’, Oxford
Economic Papers. Vol. 22, March 1970, pp. 39-56.
[9] Coase, R. H., ‘The Problem of Social Cost’, Journal of Law and Economics,
Vol. 111, October 1960, pp. 1-44.
[lo] Davis, 0. A., and Whinston, A. B., ‘Externalities, Welfare, and the Theory
of Games’, Journal of Political Economy, Vol. LXX, June 1962, pp. 241-62.
r111 - ‘On Externalities, Information and the Government-Assisted Invisible H’ayl’, Economica, Vol. XXXIII, August 1966, pp. 303-18.
[121 - Some Notes on Equating Private and Social Cost’, Southern
Econom& Journal, Vol. XXXII, October 1965, pp. 113-26.
[ 13] Dolbear, T., ‘On the Theory of Optimum Externality’, American Economic
Review, Vol. LVII, March 1967, pp. 90-103.
1141 -‘Onthe Theory of Optimum Externality: Reply’, American Econamic R’micw, Vol. LVIII, June 1968, pp. 529-31.
[15] Fraser, R. D., ‘Externalities and Corrective Taxes: A Comment’, Canadian
Journal of Economics, Vol. I, May 1968, pp. 473-5.
[16] Mishan, E. J., ‘Onthe Theory of Optimum Externality: Comment’, American
Economic review, Vol. LVIII, June 1968, pp. 523-7.
Reflections on Recent Developments in the Concept of External
~ 7 1
Effects’, ’Canudian Journal of Economics and Political Science, Vol. XXXI,
February 1%5, pp. 3-34.
28 Cf. Davis and Whinston [lo, pp. 261-21.
~
1971
THEORY OF EXTERNALITY
-, ‘Welfare Criteria
185
for External Effects’, American Economic ReVim,Vol. LI, September 1961, pp. 594-613.
[I91 Nath, S. K., A Reapprtrisol of Welfare Econom’cs (Routledge & Kegan
Paul. London. 1969).
[20] Olson, M. Jr., and Zeckhauser. R., ‘The Efficient Production of External
Economies’, American Economic Review, Vol. LX, June 1970,pp. 512-17.
[21] Pauly, M. V., ‘On the Theory of Optimum Externality: Comment’, American
Economic Review, Vol. LVIII, June 1968, pp. 528-9.
[Z]
Pigou, A. C., The Economics of Welfare. Fourth edition (Maanillan, London,
1932).
[23] Plott, C. R., ‘Externalities and Corrective Taxes’, Economica, Vol. XXXIII,
February 1966, pp. 84-7.
[24] Tisdell, C., ‘On the Theory of Externalities’, Economic Record, Vol. 46,
March 1970, pp. If-25.
[25] Vincent, P. E., Reciprocal Externalities and Optimal Input and Output
Levels’, AmPricon Economic Revim, Vol. LIX, December 1%9, pp. 976-84.
[26] Wellisz, S.,‘On External Diseconomies and the Government-Assisted Invisible
Hand‘,
Economa’ca,Vol. XXXI, November 1964, pp. 345-62.
[I81