¹ For discussion about the significance and limitations of Second Best theory, see my paper, “Second Thoughts on Second Best,” Oxford Economic Papers, Oct. 1962.

² Even mathematical formulations are subject to ambiguity. Expressing a firm or industry's cost, revenue or profit, as a function not only of its own outputs and inputs but also of those of other firms or industries (see sections A and F) hardly reveals the essential character of external effects. For there is nothing to prevent one from reading into such a function a statement of general interdependence as in the Walrasian system.

³ Scitovsky, T., “Two Concepts of External Economies,” Journal of Political Economy, 04 1954 CrossRefGoogle Scholar; Duesenberry, J., Income, Saving and Theory of Consumer Behavior (Cambridge, Mass., 1949)Google Scholar; Ellis, H. and Fellner, W., “External Economies and Diseconomies,” American Economic Review, vol. 33, 1943 Google Scholar, reprinted in Readings in Price Theory (Chicago, 1952); Meade, J., “External Economies ana Diseconomies in a Competitive Situation,” Economic Journal, 03 1962 Google Scholar; Davis, O. A. and Whinston, A., “Externalities, Welfare, and the Theory of Games,” Journal of Political Economy, 06 1962 CrossRefGoogle Scholar; Coase, R. H., “The Problem of Social Cost,” Journal of Law and Economics, Oct. 1960 CrossRefGoogle Scholar; Buchanan, J. M. and Stubblebine, W. Craig, “Externality,” Economica, 11 1962.Google Scholar

⁴ Which means that an industry's output can be affected by means other than through the movements of existing priced factors. It also means that though an individual's “real income” remains unchanged (the prices of the existing goods he buys and the factors he sells remaining unaltered) his welfare may be changed by the activities of neighbouring industries and individuals.

⁵ How useful this procedure is as a basis on which to make recommendations depends upon an empirical question. If, for example, it transpired that for all acceptable income distributions the corresponding optimal outputs were much the same, then a movement toward an optimal set of outputs may properly be thought of as a provisional movement in the righ direction. Redistribution could then be undertaken as a separate rearrangement.

⁶ Viner, J., “Cost Curves and Supply Curves,” Zeitschrift fur Nationalbkonomie, III (reprinted in Readings in Price Theory (London, 1953)), 217 Google Scholar, suggests the term external pecuniary economies to cover reductions in the cost to industry A as it expands its purchases of materials and services from a falling cost industry B. (In our terminology, they are external economies internal to the competitive industry A.)

⁷ Viner also suggests the use of external pecuniary diseconomies to cover the case of rising supply price as a result of rising factor price when output expands. Ibid., 220. But rising supply price is inevitable in any economy where factor supplies are less than perfectly elastic and production functions are homogeneous of degree one. And if the industry is competitively organized, the equilibrium output—the point where each firm equates its average cost, including rent, to price—is the optimal output.

⁸ See Scitovsky.

⁹ It would seem that the production-on-consumption, and consumption-on-consumption, categories fit conceptually at least into this dual approach, and that private ownership of the unpriced good or factor would provide an automatic corrective. For instance, if people separately owned the fresh air they breathed, they could be induced to sell some of it to the smoky factory for pollution. If each person owned his own quiet, so that nobody could legally invade any part of it without paying him his minimum price for a portion of it, optimal output would be assured. But though this extension of the Knightian approach is suggestive, there might be difficulties even though it were possible to organize a market for fresh air or quiet. For any person who was not honest would not reveal his response to the market price, but hold out for as much as he could get, which tactic would pay since the buyer could not proceed while any single individual held out; substitution between the units of quiet is not possible, the quiet of each person in the area being strictly complementary from the standpoint of the buyer. To the buyer, it is a case of all-or-nothing; in fact an example of indivisibilities.

Nevertheless, if such a market could be made to work, say by giving each person a legal property right to his quiet, or fresh air, etc., it would ensure optimal output; whenever the aggregate value placed on the collective good exceeded its worth to the party (or parties) who would otherwise reduce or destroy it, he (or they) would be unable to proceed.

¹⁰ Though even in such cases, people who are more occupied in collecting taxes without any increase in pay may be regarded as worse off. In real terms, costs of the new economic arrangements may be unavoidable.

¹¹ A more general treatment of the sort of situation envisaged by Buchanan and Stubblebine, one in which welfare effects are not ignored, is given in Mishan, E. J., “Criteria for External Effects,” American Economic Review, 09 1961.Google Scholar

¹² The damaged parties will generally have some incentive to approach the producers of x (if they can organize themselves without too much cost) since there is scope for bargaining when the maximum they would pay to be rid of a certain number of units of x exceeds the profits made on these units by the x-producers.

¹³ One might, therefore, be tempted to argue that one of the economic advantages of putting the burden of compensation on firms rather than allowing it to fall on other people (even though these people can effectively organize in order to compensate the damaging firms, so inducing them to curtail their outputs to optimum) is that it would provide a strong incentive for these firms to undertake research into ways of eliminating the sources of the social diseconomy, thus providing an incentive to reducing social loss in the economy.

¹⁴ In private correspondence Professor Scitovsky indicated to me that he was not at all anxious to introduce into the subject a new concept of external economies; that in fact he was engaged merely in drawing attention to the many different meanings given to external economies especially in the literature on underdeveloped countries. The qualifying adjective “pecuniary” was proposed by him only in order to separate the various new meanings from the traditional concept used in equilibrium analysis, which concept is preserved by the term “technological” external economies. He agrees with my conclusion that there is no need in economic analysis for this concept of “pecuniary” external economies, and that his illustrations of them all fall into already familiar economic categories.

¹⁵ Since the orthodox position has it that in a perfectly competitive equilibrium all firms make zero profit, it may be that Scitovsky had in mind the area above the upward-sloping industry supply curve, something which, possibly, he identifies with producers' surplus.

¹⁶ Given divisibility, the hypothetical maximum profitability is also reached at the output where price equals marginal cost, if this hypothetical magnitude comprises both consumers' and producers surpluses. The marginal-cost-pricing rule should not be under attack, but the profitability criterion when the term is confined to the profits of the firm or industry.

¹⁷ Review of Economic Studies, 1949–50.

¹⁸ Of course, there can be many other ways of extending the traditional meaning of external effects to comprehend other features of industrial development that seem to call for the intervention of some agency other than those commonly associated with the market. For example Rosenstein Rodan, in considering some particular circumstances of economic development tells us that: “The planned creation of such a complementary system [of industries producing goods that are, broadly speaking, complementary in consumption] reduces the risk of not being able to sell and, since risk can be considered as a cost, it reduces cost. It is in this sense a special case of ‘external economies.’” “Problems of Industrialisation of East and South-East Europe,” Economic Journal, June 1943. If “this sense” has reference to cost reduction, it would seem that technical innovation, migration, risk pooling, three-shift systems, managerial training, increased competition, cheap foreign credits (more centralized planning for some, more market and decentralized planning for others) and any number of economic phenomena must all be gathered under the umbrella term, external economies. Such indiscriminate coinage must have the inevitable result of reducing to zero the analytic power of the original concept.

¹⁹ The case referred to by Graaff, in his Theoretical Welfare Economics (Cambridge, 1957)Google Scholar as “Excessive external effects in Consumption.”

²⁰ See Appendix.

²¹ It is evident that if, instead, the others were cheered at A's enrichment we should add to A's VMP the maximum sums they would pay for the pleasure of knowing that he had availed himself of the offer. If this sort of interdependence predominated (which is much to be doubted) then, unless the standard rule were corrected for these responses, the supply of factors and aggregate output would be below those required for a Pareto optimum.

²² It would be more accurate to say that the downward-sloping supply curve may reflect only increasing returns. For it is clearly possible also that as output is expanded factors important to this product rise in price. The rents accruing to the intra-margmal factors are included in the average cost which, however, continues to fall because of the predominance of scale effects. None the less, if we excluded these intra-marginal transfer payments the true average social cost would fall yet more rapidly, and so also, therefore, would the true marginal social cost.

²³ Knight, F. H., “Some Fallacies in the Interpretation of Social Cost,” Quarterly Journal of Economics, 08 1924.CrossRefGoogle Scholar

²⁴ We should here assume that uniformly efficient labour is readily available at a fixed wage; otherwise, as indicated earlier, we should have to make further allowance for net rents received by labour as output expands.

²⁵ It may be observed in passing that, if diminishing returns to scale prevailed, all co-operating factors would be paid their corresponding average products, and all marginal products would be lower than factor prices, which would indicate overproduction of the product in question. But then competition is not consistent with production in the diminishing-returns-to-scale range.

²⁶ The revenue yielded by an optimal excise tax is, of course, exactly equal to the maximum rents that could be charged, both being equal to the difference between average variable cost and marginal cost times the equilibrium output (or, alternatively, equal to the difference between average product of labour and its marginal product times the equilibrium employment then determined).

²⁷ Whereas Meade's expression for 1(a) is

that for 1(b) is

where x ₁ is honey output, x ₂ is apple output, and L ₁(L ₂, and C ₁; C ₂, are the amounts of labour used in honey producing and in apple growing, and the amounts of capital used in honey producing and in apple growing, in that order.

²⁸ Reasons for the view that proportionality is sufficient, even in the absence of fixed factor supplies, are given in Mishan, “Second Thoughts on Second Best,” esp. 208–12.

²⁹ Although this is the more familiar condition when couched in terms of product units, it is no less valid, as in Pigou's treatment in his Economics of Welfare, to deduce the condition that the social marginal value of the product be equal to its (market) marginal cost, in which the word social requires that we add to, or subtract from, the market value of the product the marginal effects on all other products. What is incorrect, however, is to equate marginal social product with marginal social cost, since it would involve counting the same external effects twice.

³⁰ There are, to be sure, allocative problems associated with the raising of taxes; for instance, it can be argued that a poll tax is, on allocative grounds, superior to an income tax which is superior to an unequal system of excise taxes. If there are such problems then, clearly, a Pareto optimum is not realized until the conditions are met in the raising of revenues also, but this contingency is quite consistent with the distinction between distributional and allocative effects. Concern with the problem of product-exhaustion is unambiguously distributional.

³¹ To elaborate this last point in connection with Meade's examples: although the character of the production functions may well be of interest for various reasons, it is not per se central to this question of external effects. What is central is the existing organization of the market. To be specific: we do not discover the existence of an external economy in apple production from the information that the output of honey is homogeneous of degree one in capital, labour, and apple blossoms, and homogeneous of less than degree one in capital and labour alone. For if all honey producers became aware of the need for apple blossom as a complementary input in honey production, any increase in the demand for honey without a corresponding increase in the demand for apples would be met at a lower cost by those firms which produced both honey and apples (assuming the price of apples to remain unchanged as output increased somewhat).

Industry A, in effect, is producing a joint product, apples and apple blossom. If the blossom could be sold separately, we should indeed have a demand schedule for each of the joint products and the sum of their prices in equilibrium would give the true social valuation of one apple plus the accompanying blossom. At this equilibrium, therefore, the optimal output is realized, since if we substract the demand price for blossom from the marginal cost of apples-plus-blossom, we are left with the social marginal cost of an apple alone exactly equal to its demand price. External effects have been “internalized” into the price mechanism. Similar remarks apply no less to production functions homogeneous of degree greater than one. If such increasing return industries were competitively organized their equilibrium outputs would be below optimum. The government might then have to rectify matters by granting an ad valorem subsidy to such industries. If, on the other hand, these industries were controlled by perfectly discriminating monopolists, no external economies would be evident, and intervention could not be justified on purely allocative grounds.

³² Some of the evidence for this statement may be found in Oort, C. J., Decreasing Cost as a Problem of Welfare Economics (Amsterdam, 1958), esp. chap. III.Google Scholar

³³ Whereas in the 2(a) example the equations take the form:

(x₁ being wheat output and x ₂ being timber),

in the 2(b) example they are written:

There does not seem to be any good reason for not writing them in the form x = H(L,C,x) as in the “unpaid factor” case.

³⁴ It should be noticed in passing that industries A and B are now to be recognized as increasing-returns-to-scale industries; thus the sum of the factor payments when optimal outputs are produced—when factor prices equal SVMP in each industry—will necessarily exceed the total value of the outputs in A and B, unless they are engaged in price discrimination which is, however, precluded by the assumption of competition. While they remain separate industries, they can be induced to produce optimal outputs only if they are subsidized.

³⁵ Meade's equations for this case are:

³⁶ Although the cost of the noise damage is an overhead it should not be charged to industry C as an overhead since it would have the long-run effect of reducing C's output to the point at which price was equal to average cost including this overhead. This adjustment would be incorrect since, from this reduced output, any initial re-expansion of C's output would not be accompanied by additional noise damage and indeed would initially create market value in excess of marginal factor cost.

³⁷ No losses are suffered by D industry in its new equilibrium since in the long run all factors are mobile, and those no longer employed there continue to receive the ruling rate of return in other lines of production. Even if C were legally compelled to compensate the owners of D, the sum paid over would not induce any exapnsion in D's output. It would appear as a transfer payment from the owners of C to those of D. The only welfare justification of any such a transfer in those circumstances would be on distributional grounds; for instance, a transfer to the consumers who suffer a loss of “surplus” in virtue of the higher price and output-reduction of the D good.

³⁸ An example of 1 would be a project for a single giant airliner the vibration from which made it impossible to operate a pottery industry. Only if the net profit that could be realized by a perfectly discriminating monopolist operating the airliner was large enough to cover the cost of compensation of all net pottery value foregone (equal also to the net revenue extractable by a perfectly discriminating monopolist) should it be built.

An example of 2 would be the pollution of a river in a degree that is invariant to the output of a large works, and has the effect of increasing the cost of fish proportionally to the catch. If the gains from maintaining the works (as measured above) exceed the fishing losses and if this were the only river providing fish to the economy, the new market equilibrium would reveal a reduction in the output and a rise in the price of fish which would not require correction.

An example of 3 would be Pigou's factory whose smoke damage varied with its output, but which falls as an overhead on the neighbouring population.

An example of 4 could be Meade's apple-blossom and bee-honey case, producing at levels that made external economies allocatively significant for both industries. Alternatively, we could turn to his example of rain-inducing timber production which increases wheat output. Although timber should be expanded to the point at which price is equal to social marginal cost, no correction to the consequent equilibrium output of wheat need be contemplated if the effect imparted to wheat is proportional to its total production; or, in other words, if the average cost curve is shifted proportionally downward.

³⁹ The reasons given for this decision may not convince everyone: (1) the firm is an entity that fits more easily into the analysis, (2) firms are the decision units, (3) external effects may involve aspects of duopoly which remain even when the number of firms expands, (4) using the firm as an entity gives greater generality than the traditional approach, (5) we do not run into the aggregation problem.

⁴⁰ But if the two firms are in competitive long-run equilibrium, average inclusive cost is equal to price, and, therefore, maximum profits are zero. On this interpretation welfare would be zero—which makes more sense if two competitive firms produce a negligible part of the total output than if a duopoly situation is envisaged. Nevertheless, since the necessary condition for a welfare maximum, whatever the market organization, is that price equal social marginal cost, we need have no hesitation in going along with their analysis.

⁴¹ The pay-off matrix with which they illustrate the opportunities facing two such firms, though interesting in itself seems to me to have only a superficial and formal connection with the substance of their preceding analysis. In game theory firms no longer maximize with known demand and cost functions; they are minimaxing given discrete alternatives, under conditions of uncertainty regarding the stratagem to be adopted by the other firm.

⁴² Indeed, each time there is a change in the demand conditions or in the existing technology, recomputation would be necessary. Provided the market structure remains competitive—so that each firm treats the price as a parameter—a profit-maximizing merger would be mutually beneficial and would also ensure optimal outputs.

⁴³ If such effects were uni-directional, say from B to A only, and also separable, then indeed I no correction of A's profit-maximizing output would be necessary, though correction of the output of B, which is generating the external effect, would be required.

⁴⁴ Later on, Coase tells us that the courts are usually aware of the mutuality of inconvenience, and the general doctrine has been that, since economic activity tends to promote welfare, people in the vicinity must put up with some “not unreasonable” degree of discomfort. This is doubtless an interesting fact about the courts' response to the problem. But what is the answer of the economist to this question? Coase does not provide the solution, and, indeed, it cannot be provided in a purely allocative context. However, by invoking distributional effects, criteria for such problems may be provided, as shown in my “Criteria for External Effects.”

⁴⁵ In the production-on-production case in which firms are profit-maximizers, this is valid if one is concerned only with allocative issues (and is not interested in the distribution of welfare). But it should be apparent that where the individual or group is involved, different welfare effects as between conflicting groups can make a difference in the optimal output according as a question of who compensates whom is answered.

⁴⁶ In so far as market arrangements arise “spontaneously,” those who suffer injury must, in effect, bribe those who inflict it.

⁴⁷ If an additional steer caused crop damage of $12 a year estimated at existing market prices, and $10 of the costs of that crop is labour, the remaining $2 being a rent to the farmer-owner, it should be a matter of indifference to the farmer-owner whether (i) damages awarded him were $12 provided he continued to cultivate the patch of land in question exactly as before, or whether (ii) damages awarded to him were only $2, but with no conditions attached—in which case he would abandon its cultivation. However, it is not a matter of indifference so far as allocation is concerned. If option (i) were adopted, the final contribution of $10 worth of labour to growing crops on this patch of land is nothing, since anything produced is doomed to destruction by the additional steer, whereas if that much labour were transferred elsewhere it would contribute $10 to the social product. If, on the other hand (ii) were adopted, only when the profit on the additional steer exceeded $2 would the land be taken over for cattle-raising rather than crop-raising.

⁴⁸ If the railway were not legally liable for damage, all agreements reached would involve some transfer from landowners to the railway companies in consideration of the companies' taking action to reduce potential damage to the land.

⁴⁹ I say “appears” to reach, because the lengthy, indefinite, and somewhat repetitious arguments on pp. 31–4 of his paper are difficult to assimilate. On p. 31 Coase writes that “it also seems likely that he [Pigou] was mistaken in his economic analysis.” On pp. 32–3, he asserts that “A change from a regime in which the railway is not liable for damage to one in which it is liable is likely, therefore, to lead to an increase in the amount of cultivation on lands adjoining the railway. It will also, of course, lead to an increase in the amount of crop destruction due to railway-caused fires.” Finally, on p. 34 he asks, “How is it that the Pigovian analysis seems to give the wrong answer?” And he goes on to assert that Pigou did not notice diat his analysis was dealing with “an entirely different question”; that the analysis as such is correct, but the conclusions illegitimate; that a “comparison of private and social products is neither here nor there”; and that “the proper procedure is to compare the total social product yielded by these different arrangements.” The exact interpretation of these seemingly elusive arguments is, however, less important for our purpose than the establishing of the essential correctness of Pigou's analysis in those circumstances where the costs of implementing arrangements may be ignored.

⁵⁰ Of course, if the market-value compensation to be paid to the landowner were always conditional upon his actually cultivating the land that is expected to be damaged by engine sparks, then Coase's conclusion would follow. But I find no evidence for interpreting Pigou's proposals in this fashion.

⁵¹ In the absence of any legal liability by the railways, if one acre of wheat land (with no alternative use) is damaged by engine sparks to the extent of $8, and if $5 is the “profit” or rent of that acre, it would be taken out of cultivation in order to limit the loss to $5. If the railways could reduce this damage to zero by taking off one coach, and if the profit of that coach were estimated at less than $5, then it would pay the landowner to compen-sate the railways fully for the removal of that coach. If the profit on that coach exceeded $5, however, the landowners would find it cheaper to take that acre of land out of cultivation and suffer a loss of $5. Since this hypothetical behaviour minimizes social loss, it is the correct allocative solution.

The same result, however, would occur if the railways were legally compelled to compensate the landowners for running the “marginal” coach. If the additional profit yielded by the extra coach exceeded $5, it would pay to compensate the landowner to the extent of $5 and run the coach. If, on the other hand, the profit on that coach were less than $5 it would pay them to remove the last coach.

To put it in a nutshell, the question to be asked is simply whether more value is created by allowing the marginal coach to run and inflict this damage or by removing the coach and growing the crops. And, at market prices, the answer is the same irrespective of which side has to compensate the other.

⁵² In a minor key are some lengthy criticisms of Pigou's analysis. My impression is that such criticisms arise from focusing on one or two passages to the neglect of the relevant chapters as a whole. Although it would be out of proportion to deal with such textual criticisms in a short survey of recent developments, I should like to give one example:

Coase draws attention to Pigou's remark that factory-owners installing anti-smoke devices render to the community uncompensated services—implying, according to Coase, that such factories should be subsidized. (Even if this were so, any concern over it must be on distributional grounds, since such subsidy would be quite consistent with an optimal output.) However, if the reader consults p. 184 of The Economics of Welfare, I think he will agree with me in affirming that Pigou's sentence construction there was perhaps chiefly to blame for this misinterpretation. None the less, not only does Pigou point out at the bottom of the page that this smoke inflicts a heavy uncharged loss on the community, but the footnotes on the same and on the following page make it unmistakable that the factory-owners who do not install anti-smoke devices are deemed responsible for inflicting damage on the local population. The analysis, therefore, calls for the installation of such devices from their net revenues, or for the curtailing of output to the point where price equals social marginal cost.

⁵³ This sum can be represented diagrammatically by the area between the market marginal cost curve and the social marginal cost curve above it over a range from the price axis to the socially optimal output.

⁵⁴ This marginal case they illustrate with a nice example of B's choosing the height of a fence, H _B , to build between his garden and A's garden. This is much higher than the height H _A that would have been chosen by A. The optimal height is H ₀ , somewhere between H _A and H _B , and is that height at which the marginal valuation of A's loss is just equal to the marginal valuation of B's loss. No movement from this point can make both better off.