Recent Developments in the Theory of Externality and the Pigovian Solution*

Where there are external effects,l the Pigovian solution is to im- pose 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 to recent developments in the

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.

1 Throughout this paper, external effects refer to technical rather than pecuni- ary 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 bargain- ing or where bargaining costs are asymmetrical, the question of who is to com- pensate 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

concepts of externality may be summarized as follows :

A

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never be attained by means of the imposition of taxes (sub- sidies) 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 solu- tion 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 ~once rned .~ However, if the damaging party is not re- quired by law to pay the compensation, but is able to receive com- pensation 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 stand- ing, 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 objec- tion can be met by a proper definition of property rights. This con- cession 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 an- other) should always pay the compensation : the blackmailing argu-

4 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].

1971 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 com- pensate the damaged party for the amount of damage inflicted (assum- ing 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 in 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 con- trast, 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 equi- librium 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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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 ver- tical axis measures the marginal valuation of A and B for the activity.

Marginal t valuation

of B I

Marginal 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 up to P . If a tax rate which, a t 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 defini- tion 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.

1971 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 im- possible (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 suffi- cient 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 pay- ment 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 I t 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.

11 That 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 govern- ment decides to use the tax-subsidy sdution.

- 18 Cf. Wellisz “26, p. 3611.

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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 1 ‘B

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 corre- lated 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.

1971 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 ex- plained. 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. Con- sumption 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 repre- sented 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 im- pose 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 com- pensation is feasible, Pareto optimal solution can be achieved even in a Giffen situation.

1971 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 mar- ginal 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 com- pensation, A will not pay compensation in excess of OC. Yet appar- ently Pareto optimum has not been reached (FP2 # GP2) .

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 be- tween 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 CD 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. Dis- regarding practical difficulties, a Pareto optimal solution can there- fore 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 solu-

17It 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 solu- tion 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 influenc- ing 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 im- possible. 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 an 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) interdepen- dencies. That the precise decision of the rivals cannot be known does not mean that an ‘optimal feasible’ decision based on the most prob- able 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 non- mathematical 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 deter- mined 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 out- put level of the firm will not change. Since “separable” externali- ties 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.

1971 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 an 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.1e But Wellisz argues for the non-existence of a long-run effect :

‘It may seem that “separable” externalities affect resource alloca- tion 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 as 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 product ion i s based on considerations of long-run marginal costs. If an externality modifies the long-run marginal costs of a firm, it must be classified as “non-separable” in the long run’ [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 (pro- duce 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 adjust- ment into account. If the long-run adjustment is considered, his con- tention 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 in- fluence. 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 organiza- tion 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 mar- ginal conditions for Pareto-optimality’ [6, p. 4031. Indeed, the re- verse 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 mis- leading 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 any- thing 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 ac- tivity. 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.

1971 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 question- able. 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 im- position 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 welfare- improving, 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 re- inforces the directional change in output that reforms in market struc- ture 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 im- perfection (not restricted to the industry in question, but including other industries), the output of an 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 pro- duce 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 welfare-

24 Though more elaborate in illustration, his reasoning is essentially embodied in a footnote by Wellisz [26, p. 349, n. 31.

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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 imperfec- tion. 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 cor- rective taxes and subsidies’ [5 , p. 1741. For one thing, it is clearly not true that the Pigovian corrective taxes must be limited to situa- tions 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 con- trary 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 in- appropriate 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

I I The main conclusions from the above discussion are briefly as

(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 piece- meal 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.

follows :

1971 THEORY OF EXTERNALITY 183 allocation because of the effect on future decisions. It is also suggested that 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 sub- sidization 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 tax- subsidy 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 pro- duction 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, i t is apparent that the classical Pigovian tax- subsidy solution to the problem of externalities is not as fruitless and 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 multi- externalities 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 im- portant 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 time- consuming. Merger, on the other hand, whilst free from the second di&ulty, may lead to monopolistic power and create problems of its OWIl.28

University of New England Y. K. NQ

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