Front Page Titles (by Subject) VI. Increasing and Decreasing Costs - Studies in the Theory of International Trade
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VI. Increasing and Decreasing Costs - Jacob Viner, Studies in the Theory of International Trade 
Studies in the Theory of International Trade (New York: Harper and Brothers, 1965).
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VI. Increasing and Decreasing Costs
Ricardo, in his statement of the doctrine of comparative costs, assumed that costs of production were constant as output was varied, and this assumption has been followed, explicitly or implicitly, in much of the later literature, and in this chapter so far. Where costs are constant no issue arises as between average and marginal costs, since these are identical. If costs to the individual producer increase as output is increased, the doctrine of comparative costs still holds, but must be stated in terms of comparative marginal costs.
If there are no external economies or diseconomies of large production, pecuniary or technological, i.e., if a producer who keeps his own output constant experiences no change in costs as the result of a change in the output of his industry as a whole, then either in an isolated country or under free trade labor will tend to be distributed among the respective industries until, at equilibrium, its marginal value return to the industry as a whole per unit of labor is equal in all industries. Assuming only two commodities and two countries and labor as the only factor of production, abstracting as usual from transportation costs, and assuming that before trade country A has a comparative advantage in marginal cost in the production of commodity M, it will be to the advantage of country A under trade to transfer its labor from the production of N to the production of M until the point is reached where its comparative marginal cost advantage ceases.1 Under constant cost, there is an apparent2 gain from trade, measured in saving in cost on the imported commodity, even on the marginal unit of trade, unless the terms of trade correspond to the relative costs of production of the country in question, when there is no gain for that country from any part of the trade. But under increasing costs, the saving in costs is confined to the infra-marginal units of trade.3
Under constant costs, a country will not both import and produce for itself any commodity unless the price relations between that and other commodities produced in that country correspond to their relative costs of production in that country, i.e., unless that country is deriving no benefit from the import of that particular commodity. This does not hold true, however, for commodities produced under conditions of increasing costs, when simultaneous importation and domestic production of a commodity indicate that all (except the marginal unit) of the imports are obtained at lower real costs than those at which they could be produced at home. Under increasing costs, both (all) commodities can conceivably be produced simultaneously under equilibrium conditions in both (all) countries. When trade is carried to the equilibrium point under increasing costs, i.e., to the point where each country is fully exploiting the possible gains from trade, the ratios of marginal real costs as between the two (all) countries will be the same for all commodities being simultaneously produced in both (all) of these countries, and it will be the comparative differences in the marginal costs which would result if the existing trade were altered in volume or direction, rather than any prevailing difference in actual marginal costs, which would explain the existing trade.
It should be apparent that charts such as charts VIII and IX above, which were constructed on the assumption of constant costs, would not be applicable to illustrate the problem of international specialization where increasing costs are operative. Since the marginal costs in each industry and country would vary with the output, there would not be a single and fixed scale of costs for the different commodities in each country. If, as was likely, the rate of increase of marginal costs as output increased differed from commodity to commodity, and differed for the same commodity from country to country, there would be no fixed order of rank of the commodities in terms of comparative marginal costs for each country, as their ranks would tend to change with substantial changes in the outputs of the respective commodities. As has already been pointed out, under equilibrium conditions specialization would be carried to the stage where the relative scales of marginal costs would be uniform for all the countries producing the respective commodities.
Schüller has made an elaborate critique of free trade which rests in large part on considerations which must be regarded as essentially short run in character or as inconsistent with free competition, and therefore as outside the scope of the present discussion.4 Such, for instance, is his argument that factors of production which are displaced from their original employment by foreign competition ordinarily fail in substantial degree to find alternative employment. His argument also that commercial policy may either attract productive resources from abroad or induce them to emigrate, and that the former is desirable and the latter undesirable, whatever its validity—and his argument is exceedingly one-sided, since if the injury to one industry from free trade in its product tends to drive its factors out of the country, the benefit to other industries and to consumers should in like manner tend to induce immigration and check emigration of the factors not engaged in this industry—is also outside the scope of this article. But an essential portion of his case is made to rest on the existence of a wide range between the money costs at which different producers within an industry can produce their output. In the long run, and even in the short run under free competition, there must necessarily be a tendency for equality of marginal money costs for all producers in a given industry, and it is these marginal costs, and not the average costs which Schüller alone considers, which are the regulator of value. None of his inferences unfavorable to free trade as a long-run policy which depend for their validity on the simultaneous existence of different costs for different producers therefore has any force.5
It has frequently been claimed by economists that if a country has a comparative advantage in costs in an industry or industries subject to increasing costs as output is increased and has a comparative disadvantage in an industry or industries subject to decreasing costs, it may not be to the interest of this country to specialize in accordance with comparative costs. All of the attempts which have been made to demonstrate this proposition follow the same general line of argument. It will be conceded beforehand that there is a trace of validity in this proposition, but a very faint one, long-run considerations alone being understood to be relevant.
In the long run, specialization in accordance with marginal cost to the industry or country must be to the advantage of a country, in so far as costs are made the criterion of advantage. If a country is at a comparative advantage in marginal costs in an industry subject to increasing costs, the transfer of a marginal unit of the productive factors from the decreasing-cost to the increasing-cost industry must necessarily yield to that country a greater increment of whichever commodity it prefers to have than this marginal unit of the productive factors would yield if left in the decreasing-cost industry. Let the country with the comparative advantage in the increasing-cost industry be designated by M, the increasing-cost product by a, and the decreasing cost product by b. At the given stage of specialization in this country, let be the marginal cost per unit of a in terms of units of the productive factors, and let be the marginal cost of b. Then XaXb will be, respectively, the number of units of a and of b produced at the margin by one unit of the productive factors. Suppose further that at the given stage of specialization in M, Xa units of a can be exchanged in foreign trade for Y units of b. Since by hypothesis M still has a comparative marginal advantage in the production of a, then Y > Xb, and by using the marginal unit of the factors of production to produce a rather than b, M gains either Y – Xb units of b, if what it wants is more units of b, or units of a, if what it wants is more units of a. In either case, M gains by further specialization in the production of a. The only basis on which specialization under these conditions of marginal cost might be unprofitable to M would be if specialization and trade were not governed by industry marginal costs.
All of the many attempts to demonstrate the possibility that specialization in accordance with comparative costs by a country with a comparative cost advantage in increasing-cost industries and a comparative cost disadvantage in decreasing-cost industries may be unprofitable for it have much in common, and only three of the more elaborate ones will be examined here, and only one in detail.6 Nicholson makes such an attempt,7 which is open to other criticism, but which can be disposed of on the ground that his analysis is not completely in marginal-cost and marginal-return terms. He posits the case of a country with a comparative advantage in the production of wheat subject to increasing costs and a comparative disadvantage in manufacturing subject to decreasing costs. As the result of the opening of trade, manufacturing becomes unprofitable, and the factors are shifted to wheat-growing, manufactures being imported in exchange for wheat. There results for the country, in an extreme case, no increase in the amount of wheat available for consumption and a decrease in manufactures. Nicholson bases his conclusions on marginal-cost analysis as far as wheat is concerned, but on average-cost analysis for manufacturing. Had he applied marginal-cost analysis to both, he could not have obtained results of this kind.
Francis Walker obtains similar results by means of arithmetical computations in terms of money income from charts showing monetary-demand and average-cost curves before and after trade.8 His procedure is defective in almost every conceivable particular. He at no point carries his analysis to a stage consistent with long-run equilibrium. He fails to provide for full employment of all the factors both before and after trade. He keeps all of his analysis on a superficial monetary level, and makes no attempt to allow for changes in the significance of the monetary unit as the result of trade, even though he includes “consumers surpluses” measured in money in his computations. His results are totally devoid of significance.
Graham9 also obtains similar results by a method of analysis not differing in any essential from that used by Nicholson, although he makes no reference to him. Graham, however, sets forth his argument in much greater detail, with less ambiguity in use of terms, and with at least passing reference to the objections which might be raised against his reasoning on value-theory grounds. He supports his argument with arithmetical illustrations, which will be reproduced here with modifications which do no violence to the original but facilitate their appraisal.
The comparative advantage of country A is in watches and of country B in wheat, and in so far as comparative costs alone are concerned trade may take place between the two countries on any terms within the limits of 4 wheat = 3 watches and 4 wheat = 4 watches. The actual ratio is assumed to be 4 wheat = 3½ watches and when trade is initiated a small amount of trade takes place at that ratio, country A exporting watches and importing wheat. Both countries appear to gain from the trade, country A getting 4 wheat at a cost in labor with which she could produce only 3½ wheat at home, and country B getting 3½ watches at a cost in labor with which she could produce only 3 watches at home.
Trade is carried further, on the same terms of exchange of wheat for watches, country B increasing her specialization in the production of wheat and country A in the production of watches. But in both countries the production of wheat is subject to increasing costs and the production of watches to decreasing costs. Each unit of trade still seems to yield gain to both the participants, since country A gets each 4 units of wheat at a labor cost at which she could only produce 3½ wheat at home, and country B gets 3½ watches at a labor cost at which she could produce only 2 2/7 watches at home. But country B is really losing from the trade, since as she increases her total output of wheat and decreases her total output of watches, the productivity of labor falls in both industries. If in case I the total trade consisted of an exchange of 4 wheat for 3.5 watches and in case II the total trade consisted of an exchange of 320 wheat for 280 watches, then in case I country B would have as its total income 796 wheat + 603.5 watches, and in case II only 730 wheat + 480 watches.
This is as far as Graham goes with his illustrations, but if the argument is sound, and if it is assumed—and there is no reason why it should not be—that the indicated trends of cost as output is varied continue to operate, they can be, and must be, carried still further, with rather spectacular results.
Except for 1 unit of labor, each country is now completely specialized in the employment in which it is at a comparative advantage. But it is profitable to the participants in trade to carry specialization to the fullest extent possible, for if the day's labor still engaged in producing watches in country B were to be diverted to growing wheat, it could with the ½ unit wheat so obtained secure in exchange of a watch, instead of only the ¼ watch which it can produce directly. Country B has nevertheless lost severely as the result of specialization in accordance with comparative advantage. If in case III it exchanges a total of 120 wheat for 105 watches, its income will consist of 79.5 wheat + 105¼ watches, as compared to 730 wheat + 480 watches under partial specialization (case II), 796 wheat + 603.5 watches under only incipient specialization (case I), and 800 wheat + 600 watches in the total absence of trade! Trade, which economists have regarded as a beneficent activity, appears under these conditions to be for one of the countries rather a form of economic suicide, and the protectionist a wise benefactor.
These extraordinary results are the consequence, and wholly the consequence, of value-theory reasoning, implicit or explicit in Graham's argument, which is either unambiguously erroneous or is of very limited practical significance. As his argument has so far been reproduced it rests on analysis in terms of average money costs for both the increasing-cost and the decreasing-cost industries. Graham concedes that in the increasing-cost industry marginal and not average costs will guide the producer, and that if the figures for output which he gives for wheat are marginal, then the increase of rent to landlords will be an offsetting item not accounted for in his analysis, which may more than compensate for the loss to B shown by his illustrations. He claims, however, that his conclusion that country B under the conditions assumed must lose by free trade is “inevitable” if his figures for wheat costs are interpreted as figures of average cost,11 provided the marginal costs are not such as to make trade unprofitable to the individuals participating therein at the terms of trade assumed by him. Graham here both concedes too much and claims too much. His interpretation of marginal cost as the cost of the most expensive unit to produce is faulty, and the excess of the marginal cost of wheat over its average cost would necessarily be much higher than he indicates, and therefore the range of trade profitable to individual traders in B, granting his other assumptions, much less than he indicates. On the other hand, he concedes too much when he says that the increase in rent to landlords when the output of wheat is increased will be an offsetting item which may more than compensate for the loss to B shown by his illustrations. The loss to B shown there exceeds the increase in the cost of producing wheat and includes this plus the increase in the cost of producing watches. But rent in terms of wheat cannot increase with an increase in the production of wheat unless the average cost exclusive of rent rises, and the increase in average cost of wheat, inclusive of rent, must therefore be greater than the increase in average rent per unit of wheat.
Regardless of whatever defects there may be in Graham's handling of the costs of wheatgrowing, his general conclusions would still be acceptable if his treatment of the costs of watch-making could be accepted as satisfactory. It is in his treatment of decreasing costs that the fatal flaw in his argument is to be found. A decrease in unit costs as output is increased may be due either to “internal” economies, i.e., economies accruing to an individual producer because he expands his output, or to “external” economies, i.e., economies accruing to an individual producer because the industry as a whole is expanding its output. Graham says that “the reasoning in the text simply assumes that a decreasing unit cost is obtained by an expansion of the production of watches; whether the cause of it be external or internal economies is immaterial to the theory....” 12 It is, on the contrary, very material to the theory, as Knight has shown in a reply to Graham's argument to which the present analysis is greatly indebted.13
Suppose, first, that the economies in the watch industry are internal. Then, since the larger the scale of plant the lower the unit costs, competition will be inconsistent with long-run equilibrium, and there will be a tendency toward the monopolization of the industry by a single concern. The principle governing the relation of cost to price is, of course, different for a monopoly than for a competitive industry, but marginal rather than average cost remains the determining factor of price and no resources will be transferred from watchmaking to wheatgrowing if a loss in value of product results therefrom. But even if, by exception, we depart from long-run assumptions and take the situation prevailing while competition still continues to be effective in the watchmaking industry, it still remains true that no resources will be transferred from watchmaking to wheatgrowing if the transfer would involve a loss in value of product. Any producer of watches in country B who reduces his output of watches to produce wheat instead loses thereby the marginal output in watches and gains only the marginal increment of wheat. If, as indicated in cases I and II above, 100 units of labor are diverted in country B from producing watches to producing wheat, the transfer of the units of labor would involve a loss of 400 watches to get 250 wheat at a time when 400 watches are worth 457 wheat. Assuming internal economies in the watch industry, there simply would be no such transfer of labor. Had Graham dealt with his problem in terms of marginal costs and marginal returns for both industries, he could not have obtained results unfavorable to free trade.
If, however, the economies are external, then the individual producer will not take them into account in regulating his contribution to the output of the watch industry as a whole. The decrease in unit costs to the other producers if he should enter the industry, and the increase in unit costs to the other producers if he should withdraw from the industry, will not affect his decisions. In such a case those changes in marginal cost to the industry as output of the industry changes which are due to the accrual or loss of external economies will play no part in the regulation of the industry's output, and a conceivable case can be made out for Graham's conclusion, but with a very limited field for its practical application.
In the first place, if the external economies are a function of the size of the world industry, and not of the national portion of it, as may well be the case, they will still be retained by a national industry which shrinks in size if this shrinkage is offset by a corresponding expansion of the foreign industry. Suppose that as the watch industry as a whole expands and increases its purchases of watchmaking machinery, such machinery can consequently be obtained at lower unit prices. If there is free trade in machinery, this economy in machinery costs will not be lost to the watch industry in a particular country merely because it is shrinking in size, if there is no shrinkage in the size of the watch industry as a whole.
Second, if the external economies resulting from size of the industry are purely pecuniary, and if what they reflect is merely bargaining advantage for a large industry in hiring domestic factors or buying domestic materials, then they are not real national economies and nothing is lost to the country when they disappear.
A conceivable case for protection on the basis of the existence of external economies in an industry which from the individual producer's point of view is at a comparative disadvantage in costs can be made out, therefore, only where these external economies are (a) dependent on the size of the national and not the world industry and (b) are technological rather than pecuniary, or, if pecuniary, are not at the expense of domestic sellers of services or materials to the industry. The scope for the application of the argument is extremely limited, especially as it seems difficult even to suggest plausible hypothetical cases of the existence of genuine technological external economies. Instead of providing a substantial “scientific” basis for the popularity of protection among the vulgar, as Graham seems to think, his thesis reduces to little more than a theoretical curiosity.
A similar theoretical case can be made for an export tax on the product of an industry subject to external technological diseconomies, on the ground that the marginal cost to the individual producer which regulates prices and the course of trade will be less than the marginal cost to the industry as a whole and to the country in the case of such an industry, and that its scale of operations should therefore be contracted. Conceivably important instances of external technological diseconomies are to be found in the grazing, hunting, and fishing industries, where no rent is charged for the use of valuable natural opportunities and they tend therefore to be overexploited with resultant waste, in competitive digging of wells over a common pool of oil, and in general when competition tends to raise costs rather than to lower them. But for both external economies and external diseconomies, what case there is for interference with competition applies to trade as a whole, and to export trade only as a part of such trade. Since external technological diseconomies tend to result in prices disproportionately low as compared to real costs, the only ground on which it can be argued that there is a basis for discrimination between domestic and foreign trade is that non-interference with the domestic trade results in unduly low prices to domestic consumers, whereas non-interference with the foreign trade results in unduly low prices to foreign consumers.
Knight goes still further in his rejection of Graham's argument. He claims that there cannot be external economies for a concern (“business unit”) A which are not internal economies for another concern B within the same industry; that under these circumstances the industry will tend to be a monopoly and that the principles which will then regulate value will not be those appropriate to competitive conditions.14 I see no logical necessity that external economies to one concern must be internal economies to any other concern, whether in the same or in another industry. But suppose it be granted that external economies to industry C are internal economies to industry D, and suppose it be granted further that industry D is under monopoly control. It will still be possible that as C's demand for D's produce increases, D's prices will decrease, if production by D is subject to decreasing costs. External economies can therefore still accrue to industry C even though these economies, external to C, are internal for another, monopolized, industry D.
Knight claims further that even if decreasing costs existed in the watch industry, country B specializing in wheat would get the same benefit from these economies by importing the watches from A as by producing them at home.15 This would be true only if as B proceeded with its specialization in wheat the terms of exchange between watches and wheat moved against watches sufficiently to offset the opposite movement of their relative marginal costs to the industries as a whole in B. Now the whole point of the argument from external economies is that where they exist, relative prices need conform only to relative marginal costs to individual producers and need not conform to relative marginal costs to the industries as a whole. The price of watches, if watch-making is subject to external economies, will be higher than their marginal money cost to the industry as a whole.
Haberler has characterized Graham's argument as but a variant of the infant-industry argument for protection.16 But the validity of Graham's thesis, if it is valid at all, is not dependent upon short-run considerations. Decreasing marginal costs are not necessarily nor typically a short-run phenomenon,17 and it is Graham's contention that if an industry is operating under decreasing costs it may pay to protect it even if it has a permanent and irremovable comparative disadvantage in costs.
Unless before that point is reached country A has already transferred all of its labor to the production of M or country B has already transferred all of its labor to the production of N and cannot supply country A with all of the units of N which A is prepared to take. The former may be the case if country A is much smaller, and the latter may be the case if country A is much larger, than country B. It will be assumed that neither is the case.
Even under constant costs, there will be no gain from the marginal unit of trade, since trade will be carried to the point at which the possibility of gain is exhausted. There will still be a gain at the margin measured in terms of cost alone, however, but the value of the export commodity will have risen relative to the value of the import commodity, so that although additional units of the foreign commodity could be obtained by import for an expenditure of labor less than that at which they could be produced at home, the market value of additional imports would be less than the value of the amount of the export commodities which would have to be given in exchange for them. Even before the marginal unit is reached, while the saving in cost as compared to domestic production will be evidence that there is gain from trade, there will be no close relationship between the amount of saving in cost and the amount of gain, and the latter will never be greater and will usually be smaller than the former.
Cf. the discussion on this point between Edgeworth, Economic journal, VII (1897), 402, note 2, and Bastable, Theory of international trade, 4th ed., 1903, pp. 196-97. Cf. also, infra, p. 547, note 24.
R. Schüller, Schutzzoll and Freihandel, 1905. Cf. the criticism of Schüller's analysis by G. Haberler, The theory of international trade, 1936, pp. 253 ff.
The analysis by Kemper Simpson, “A re-examination of the doctrine of comparative costs,” Journal of political economy, XXXV (1927), 465-79, in this case favorable to free trade, seems to me to be similarly defective through its employment of particular expenses curves, or “bulkline” cost curves, as if they were analogous to the cost and supply curves of orthodox price theory.
In addition to the three examined here, there may be cited Alfred Marshall, “Some aspects of competition” , reprinted in Memorials of Alfred Marshall, A. C. Pigou ed., 1925, pp. 261-62; T. N. Carver, “Some theoretical possibilities of a protective tariff,” Publications of the American Economic Association, 3d series, III, no. 1 (1902), 169-70.
J. S. Nicholson, Principles of political economy, II (1897), 307-09, 317-18.
F. Walker, “Increasing and diminishing costs in international trade,” Yale review, XII (1903), 32-57.
F. D. Graham, “Some aspects of protection further considered,” Quarterly journal of economics, XXXVII (1923), 199-216.
The figures in upper brackets represent the amounts of labor employed in each industry. They are not to be found in the original illustrations, but are added by the present writer to show more clearly the degree of specialization reached at each stage.
It is easy to show that the illustrations are in several respects inconsistent with equilibrium unless they are so interpreted. Graham, for example, keeps the relative values of wheat and watches constant while varying their relative costs in country B. Assuming, as he does, that average costs are significant in the determination of watch values, but marginal costs in the determination of wheat values, this assumed constancy in the relative values of watches and wheat would be impossible as the ratios of average watch costs to marginal wheat costs in B varied. His illustrations are consistent, however, with maintenance of constancy in the ratios between average watch costs and marginal wheat costs in both A and B, if generously interpreted.
Ibid., p. 204, note.
F. H. Knight, “Some fallacies in the interpretation of social cost,” Quarterly journal of economics, XXXVIII (1904), (1924),592-609.
“Some fallacies in the interpretation of social cost,” loc. cit., pp. 597-98.
“On decreasing cost and comparative cost. A rejoinder,” ibid., XXXIX (1925), 333.
Haberler, “Die Theorie der komparativen Kosten,” Weltwirtschaftliches Archiv, XXXII (1930, II), 356.
Though I would now concede that they are a possible phenomenon even in the short run, and that the argument by which this possibility is ordinarily denied is defective.