Chapter VIII
GAINS FROM TRADE: THE DOCTRINE OF COMPARATIVE COSTS

It is always to be remembered that the failure of an argument in favor of a proposition does not, generally speaking, add much, if any probability, to the contradictory proposition.

—Jevons, Principles of Science.

I. THE NATURE AND ORIGIN OF THE DOCTRINE

The classical theory of international trade was formulated primarily with a view to its providing guidance on questions of national policy, and although it included considerable descriptive analysis of economic process, the selection of phenomena to be scrutinized and problems to be examined was almost always made with reference to current issues of public interest. This was true even of the classical discussions of the mechanism of international trade, but it was more conspicuously true in the field which is sometimes called "the theory of international value," where the problems were expressly treated with reference to their bearing on "gain" or "loss" to England, or on the distribution of gain as between England and the rest of the world. Recognition of its "welfare analysis" orientation is essential to the understanding and the appraisal of the classical doctrine. Although the classical economists did not clearly separate them, and shifted freely from one to the other, they followed three different methods of dealing with the question of "gain" from trade: (1) the doctrine of comparative costs, under which economy in cost of obtaining a given income was the criterion of gain; (2) increase in income as a criterion of gain; and (3) terms of trade as an index of the international division and the trend of gain. This chapter will deal with the doctrine of comparative costs.

The doctrine of comparative costs originated as an improvement and development of the eighteenth-century criticism of mercantilist policy, and it has continued to command attention mainly because of its use as the basic "scientific" argument of free-trade economists in their attack on protective tariffs. Protectionists have an obvious motive for attacking the doctrine, but it has also been rejected by economists whose animus seems to arise from the fact that it was one of the outstanding products of the English classical school, by economists who deal with it as an exercise in pure price theory and as such find it unsatisfactory, and by economists who believe that they have at their command a superior technique than it affords for the appraisal of commercial policy. Never widely accepted on the Continent, the doctrine now is clearly on the defensive everywhere.

The doctrine of comparative costs maintains that if trade is left free each country in the long run tends to specialize in the production of and to export those commodities in whose production it enjoys a comparative advantage in terms of real costs, and to obtain by importation those commodities which could be produced at home only at a comparative disadvantage in terms of real costs, and that such specialization is to the mutual advantage of the countries participating in it. In the exposition of the doctrine the "real" costs are expressed as a rule in terms of quantities of labor-time, but with the implication, as throughout the classical theory of value, that these quantities of labor-time correspond in their relative amounts within each country to quantities of subjective cost. The legitimacy of this assumption that labor-time costs are proportional to real costs is examined at length later in this chapter, and for the present will not be questioned.

There has been some measure of confusion as to the nature of the comparisons between costs which the doctrine contemplates. According to Cairnes:

...when it is said that international trade depends on a difference in the comparative, not in the absolute, cost of producing commodities, the costs compared, it must be carefully noted, are the costs in each country of the commodities which are the subjects of exchange, not the different costs of the same commodity in the exchanging countries.^*1

But it is not costs at all which are directly to be compared, but ratios between costs, and it is unessential whether the cost ratios which are compared are the ratios between the costs of producing different commodities within the same countries or the ratios between the costs of producing the same commodities in different countries.

Commodity	Real costs per unit
	Country A	Country B
A...	m	r
B...	n	s
C...	p	t

In the illustration given above, it does not matter whether the ratios compared are , and , on the one hand, or m:r, n:s, and p:t, on the other hand. In the first set of comparisons, country A has its greatest comparative advantage in the production of that commodity whose cost in A appears as the numerator in the first term of the lowest of these ratios, and its greatest comparative disadvantage in the production of that commodity whose cost in A appears as the denominator in the first term of the lowest of these ratios. In the second set, country A has its greatest comparative advantage in the production of that commodity whose cost in A appears as the first term in the smallest of these ratios, and its greatest comparative disadvantage in the production of that commodity whose cost in A appears as the first term in the highest of these ratios. Whatever numerical values are assigned to the unit real costs, both these methods of comparison will necessarily produce identical results, though the first method will ordinarily be found much more convenient to use. If the first method is used, the units used in the measurement of cost need not be identical or even comparable in the two countries. It is then not necessary, for instance, to know whether m is greater or less than r, or whether n is greater or less than s.

In the beginnings of free-trade doctrine in the eighteenth century the usual economic arguments for free trade were based on the advantage to a country of importing, in exchange for native products, those commodities which either could not be produced at home at all or could be produced at home only at costs absolutely greater than those at which they could be produced abroad. Under free trade, it was argued or implied, all products, abstracting from transporation costs, would be produced in those countries where their real costs, were lowest. The case for free trade as presented by Adam Smith did not advance beyond this point.

In an earlier chapter, however, it has been shown that several writers prior to Adam Smith, and especially the author of Considerations on the East-India Trade, 1701, stated the case for free trade in terms of a rule which would provide the same limits for profitable trade as does the doctrine of comparative costs, the rule, namely, that it pays to import commodities from abroad whenever they can be obtained in exchange for exports at a smaller real cost than their production at home would entail. Such gain from trade is always possible when, and is only possible if, there are comparative differences in costs between the countries concerned. The doctrine of comparative costs is, indeed, but a statement of some of the implications of this rule, and adds nothing to it as a guide for policy.^*2

Many of the classical economists, both before and after the formulation of the doctrine of comparative costs, resorted to this eighteenth-century rule as a test of the existence of gain from trade. Ricardo incorporated it in his formulation of the doctrine of comparative costs:

Though she [i.e., Portugal] could make the cloth with the labor of 90 men, she would import it from a country where it required the labor of 100 men to produce it, because it would be advantageous to her rather to employ her capital in the production of wine, for which she would obtain more cloth from England, than she could produce by diverting a portion of her capital from the cultivation of vines to the manufacture of cloth.^*3

Malthus had credited as a factor contributing to the prosperity of the United States her ability to sell "raw produce, obtained with little labor, for European commodities which have cost much labor."^*4 To this, Ricardo replied:

It can be of no consequence to America, whether the commodities she obtains in return for her own, cost Europeans much, or little labor; all she is interested in, is that they shall cost her less labor by purchasing them than by manufacturing them herself.^*5

This explicit statement that imports could be profitable even though the commodity imported could be produced at less cost at home than abroad was, it seems to me, the sole addition of consequence which the doctrine of comparative costs made to the eighteenth-century rule. Its chief service was to correct the previously prevalent error that under free trade all commodities would necessarily tend to be produced in the locations where their real costs of production were lowest.

In his Principles, first published in 1817, Ricardo presented the doctrine of comparative costs by means of what was to become a famous illustration, in which the quantity of wine which required for its production in England the labor of 120 men could be produced in Portugal by 80 men, while the cloth which in England required the labor of 100 men could be produced in Portugal by 90 men. Portugal would then import cloth from England in exchange for wine, even though the imported cloth could be produced in Portugal with less labor than in England.^*6

Credit for the first publication of the principle of comparative costs is generally given to Ricardo. Leser,^*7 however, in 1881, assigned to Torrens the credit of discovery of the doctrine on the strength of the following passage in Torrens's Essay on the External Corn Trade, 1815:

If England should have acquired such a degree of skill in manufactures, that, with any given portion of her capital, she could prepare a quantity of cloth, for which the Polish cultivator would give a greater quantity of corn than she could, with the same portion of capital, raise from her own soil, then tracts of her territory, though they should be equal, nay, even though they should be superior, to the lands in Poland, will be neglected; and a part of her supply of corn will be imported from that country. For, though the capital employed in cultivating at home might bring an excess of profit over the capital employed in cultivating abroad, yet, under the supposition, the capital which should be employed in manufacturing would obtain a still greater excess of profit; and this greater excess of profit would determine the direction of our industry.^*8

Leser's comment attracted no notice, but some years later credit for priority in formulating the doctrine of comparative cost was again claimed for Torrens, this time by Professor Seligman.^*9 Professor Hollander has replied, in defense of Ricardo's claims, that much of the evidence in support of Torrens presented by Seligman was not relevant or was of questionable weight; that even after the appearance of Ricardo's Principles Torrens never realized the full significance of the comparative cost doctrine and never made explicit use of it; and that Ricardo's claims to priority could not be overcome merely by the fact that Torrens, in a single paragraph, had correctly stated the doctrine "in outline" before Ricardo had published his Principles.^*10

Torrens clearly preceded Ricardo in publishing a fairly satisfactory formulation of the doctrine. It is unquestionable, however, that Ricardo is entitled to the credit for first giving due emphasis to the doctrine, for first placing it in an appropriate setting, and for obtaining general acceptance of it by economists. Hollander, moreover, appears to be justified in his contention that the doctrine was never an integral part of Torrens's thinking. While Torrens again stated the doctrine, and stated it very well, in at least two of his publications,^*11 and incidentally first used the term "comparative cost" in connection with the doctrine,^*12 these later statements are frankly presented as improvements on Torrens's earlier views resulting from the discussion of the problem by other economists. Torrens's grasp of the doctrine, moreover, was not so firm that he could not occasionally display confusion about its meaning and implications.^*13

Much of the evidence from Torrens's writings which Seligman cites to demonstrate that he was an exponent of the doctrine of comparative costs shows only, as Hollander says, that Torrens accepted the argument that international division of labor was beneficial, or that he accepted the principle that it paid to import commodities if they could thus be obtained at lower cost than the cost of producing them at home, a principle which I have shown above to have had its origin early in the eighteenth century.

The only claim to priority over Ricardo with reference to the doctrine of comparative costs which Torrens made^*14 was based on the passage in the 1815 edition of the Essay already cited above. Hollander surmises that even this earlier passage itself may owe something to discussion of the question with Ricardo, but until it is at least made clear that Torrens and Ricardo were already acquainted in 1815, not much weight is to be attached to this possibility. On the other hand, Torrens's own claim to priority should not be given too great emphasis, since Torrens was erratic both in his claims and in his acknowledgments, and could be abundantly quoted against himself.^*15

Ricardo's illustration implies a number of important assumptions which, in conformity with his usual practice, he never expressly states. His conclusions have been criticized both on the ground that they do not follow from his assumptions, and on the ground that the assumptions necessary for the validity of his conclusions are unrealistic and that with their abandonment or correction the conclusions would cease to hold. It is more or less obvious that Ricardo based his analysis on the following assumptions: ample time for long-run adjustments; free competition; only two countries and only two commodities; constant labor costs as output is varied; and proportionality of both aggregate real costs and supply prices within each country to labor-time costs within that country. Those criticisms or corrections of Ricardo's analysis which do not involve a rejection of his assumptions will be examined first, and the more fundamental criticisms which question the validity of his assumptions will be dealt with later.

II. THE DIVISION OF THE GAIN FROM TRADE

An Alleged Error in Ricardo.

Ricardo has been charged with claiming, on the one hand, that all the gain from trade goes to one of the countries^*16 and, on the other hand, that all the gain goes to each country,^*17 instead of finding it to be divided between the two countries.

The data given in Ricardo's arithmetical illustration are as follows:

Country	Amount of labor required for producing a unit of
	Cloth	Wine
Portugal...	90	80
England...	100	120

In order that all the benefit from trade should go to England, English cloth must exchange for Portuguese wine in the ratio of I unit cloth for 9/8 unit wine. In order that all the benefit should go to Portugal, English cloth must exchange for Portuguese wine in the ratio of i unit cloth for 5/6 unit wine. But Ricardo states that English cloth will exchange for Portuguese wine in the ratio of I cloth for I wine: "Thus England would give the produce of the labor of 100 men [= 1 cloth] for the produce of the labor of 80 [= 1 wine]."^*18 At this ratio, the gain would be divided approximately evenly between the two countries. Ricardo, therefore, was guilty of neither error attributed to him.

James Mill, in the first edition of his Elements of political economy, did commit the error of attributing all the gain to each of the countries, but he corrected it in the third edition, 1826.^*19 Einaudi at one time attributed the error to Ricardo as well as to James Mill, and on the strength of a suggestion of Torrens's raised the question whether it was not James Pennington who first perceived and corrected the error.^*20 Sraffa,^*21 in reply, pointed out that Ricardo had not been guilty of the error, and that J. S. Mill, in his Autobiography,^*22 had stated that his father made the corrections in the 1826 edition of his Elements as the result of criticisms made by himself and by George Graham in 1825.

Another co-worker of J. S. Mill's, William Ellis,^*23 early in the same year, 1825, had presented an arithmetical illustration similar to those used by James Mill, and had concluded therefrom that the gain would be equally divided between the two countries. It seems, therefore, that the error was detected about the same time by several members of the group associated with James Mill.

Relation of Comparative Costs to the Terms of Trade

In Ricardo's illustration, the two commodities exchange for each other under trade in a ratio almost exactly halfway between their comparative cost ratios in the two countries.^*24 Ricardo does not indicate whether he regards this precise ratio as required by the conditions of the problem as he had stated them, or how the actual ratio would in practice be determined. Ellis in 1825 and James Mill in 1826 also stated that the gains from trade would be equally divided between the two countries. McCulloch presented the doctrine of comparative costs in terms of an arithmetical illustration under which the ratio of gain was equal for both countries.^*25 It is doubtful whether these writers attached any special significance to these arbitrary^*26 terms of trade, since in the early writings of the classical school, and especially in the works of Longfield and Torrens, recognition can be found of the fact that the location of the equilibrium terms of trade was variable and depended on the relative strength of the demand of the two countries for each other's products. Pennington, however, seems to have been the first explicitly to point out in print that the comparative costs set maximum and minimum rates for the terms of trade, and that within these limits the operation of reciprocal demand could fix the terms of trade at any point.^*27

Torrens had long been insisting vigorously that the terms of trade were determined by reciprocal demand, and his emphasis on this in connection with the tariff controversy in the 1840's^*28 had aroused considerable opposition on the part of economists who found Torrens's application of it as an argument against unilateral reduction of tariffs distasteful. The interest aroused by Torrens's discussion led J. S. Mill to publish in 1844 some essays written in 1829 and 1830, of which one dealt with the same problem. It was from his exposition in the Essays,^*29 repeated and developed later in the Principles,^*30 and not from Longfield, Torrens, or Pennington, that later economists took over the doctrine. No country would give in exchange for a unit of a foreign commodity A more units of a commodity B than it could produce at a real cost equal to that at which a unit of A could be produced at home. The comparative costs set the limits, therefore, within which the two commodities could exchange for each other, but the actual ratio is set by the reciprocal demand of the two countries for each other's products. The greater the demand for B in terms of A in the country with a comparative advantage in the production of A, the closer, other things being equal, would the rate of exchange of A for B approach to their relative costs of production in that country. The greater the demand for A in terms of B in the country with a comparative advantage in the production of B, the closer, other things being equal, would the rate of exchange of A for B approach to their relative costs of production in this other country. Under equilibrium conditions, however, the value of the exports must equal the value of the imports. Of the possible ratios of exchange between A and B, that one would be the actual ratio which made it possible to meet this condition, i.e., that ratio at which the quantity of A offered by one country would equal the quantity of A which the other country would be willing to take.

Trade at One of the Limiting Ratios.

Nicholson later pointed out, with the aid of a series of arithmetical illustrations, that if there were only two countries and two commodities, and if the relative magnitudes of the two countries were not the same, the terms of trade would probably settle at or near the comparative costs of the larger country, i.e., the smaller country would get all or nearly all the gain from trade. He suggested that the omission of consideration of the relative size of the two countries had resulted in some measure of confusion in J. S. Mill's analysis.^*31 Graham has more recently repeated this argument, although without reference to Nicholson. Graham has carried the argument further by pointing out explicitly that approximate equality in importance of the commodities as well as of the countries was necessary if under the conditions stated each country was to get a substantial share of the benefits from trade.^*32 Graham asserts, on the basis of this argument, that the situation which to J. S. Mill was only an "extreme and barely conceivable case," namely, that all the benefit should go to one of the countries, was, under the conditions of constant costs, only two countries, and only two commodities, rather the normal case. He agrees with J. S. Mill that division of the benefit is the normal case, but only because ordinarily more than two commodities enter into trade, so that when the terms of trade are moving against a country because of excessive export of one commodity, it begins to export other commodities in which its comparative advantage is less, and thus checks the adverse movement of its terms of trade. He concedes, however, that Bastable has recognized these probabilities in trade between a small and a large country, but criticizes his manner of dealing with the problem.^*33

Graham's reasoning is sound, but his criticism of J. S. Mill is only partially justified. The passages in Mill's Principles which he attacks are quotations, presented as such, from Mill's Essays written long before. In the same chapter of the Principles in which these quotations appear, in a section first added in the third edition (1852), Mill explicitly raises the same problem, and gives the same answer as does Graham. He asks why, in a particular illustration given by him, he should assume that trade would result in the benefit being divided instead of all of it going to one of the countries. He answers that in such a case the country which gets all the benefit from trade would probably find it to its advantage to import from the other country additional commodities in which that other country had a comparative advantage, although a lesser one than in its original export commodity, in exchange for additional quantities of its own export commodity, until a state was reached where the other country no longer produced any of the commodity which it imported and the terms of trade had become such as to divide the benefit between the two countries. "And so with every other case which can be supposed."^*34 Pennington had already, in 1840, pointed out that the entrance of more commodities and more countries into trade would tend to prevent the terms of trade from establishing themselves at a point at which all of the gain goes to one of the countries.^*35

The Possibility of Partial Specialization.

Graham^*36 cites as another error in Mill's analysis, the following passage:

Cost of carriage has one effect more. But for it, every commodity would (if trade be supposed free) be either regularly imported or regularly exported. A country would make nothing for itself which it did not also make for other countries.^*37

Graham shows that if trade is at one of the limiting ratios this is erroneous even on the assumption of constant costs, since a country which trades on terms corresponding to its own relative costs of production may be, and is likely to be, producing at home some portion of its consumption of the commodity which it imports. It seems clear, however, that while Mill at first held that complete specialization would necessarily follow from free trade in the absence of transportation costs, he later adhered to it only on the assumption that trade did not take place at one of the limiting ratios, when the proposition would be correct. In correcting, in the third edition of his Principles, his earlier doctrine that with trade in only two commodities the terms of trade would ordinarily be such as to divide the benefit between the two countries, he also corrected this error. In the case which he assumes of trade at one of the limiting ratios, he makes one of the countries specialize only partially in the commodity which it exports. If Germany had a comparative advantage in linen and England in cloth, and if at the ratio of exchange equal to their relative costs of production in Germany the latter was willing to take more cloth than England could supply, then if no third commodity entered into the trade "England would supply Germany with cloth up to the extent of a million" and "Germany would continue to supply herself with the remaining 200,000 by home production."^*38 Whewell had previously shown, on the basis of Mill's own illustrations, that on the assumptions of constant costs, only two commodities, and only two countries, one of the countries was likely to find itself in a position where it derived no gain from trade, and that such country might specialize only partially in the production of the commodity in which it had a comparative advantage.^*39

Graham points out that Bastable also asserted the impossibility of only partial specialization under conditions of constant costs, only two countries, and only two commodities.^*40 Here again, however, he has not read his author carefully enough. In dealing with what he calls the "special case" of trade between a small and a large country Bastable had clearly, although inconsistently with his general denial, asserted the possibility—as far as the context indicates, perhaps even the probability—that the larger country will only partially specialize in the production of the commodity in which it has a comparative advantage.^*41 In 1897, moreover, Edgeworth criticized Bastable's position, and showed that Mangoldt had long before demonstrated the possibility of partial specialization by one of the countries,^*42 and in an appendix added in the third edition Bastable conceded his error.^*43

Ricardo had supported his argument for the benefit of international specialization in accordance with comparative costs by the following analogy with trade between two persons:^*44

Two men can both make shoes and hats, and one is superior to the other in both employments; but in making hats, he can only exceed his competitor by one-fifth or 20 per cent—and in making shoes he can excel him by one-third or 33 per cent;—will it not be for the interest of both, that the superior man should employ himself exclusively in making shoes, and the inferior man in making hats?

Pareto, citing this passage from Ricardo, argued that it was erroneous in its implication that complete specialization would necessarily be advantageous, as compared to no specialization at all. He showed by means of arithmetical illustrations that complete specialization would under some circumstances result in more of one commodity but less of the other, as compared to no specialization, and that, depending on the relative demands for these commodities, the increase in one commodity might not be sufficient to offset in value the deficit in the other commodity.^*45 This has occasionally been interpreted as a partial rejection of the principle of comparative costs as an argument for free trade.^*46 If it were so intended, it could, of course, easily be refuted by showing that specialization in accordance with comparative costs, to the extent that such specialization would tend to be carried under free trade, would not, under the conditions stated, result in a loss. But it seems an injustice to Pareto to interpret him in this way. His criticism appears to be directed only against the proposition that complete specialization is necessarily profitable as compared to no specialization. Pareto himself shows that where complete specialization would not be profitable it would not take place even under free trade.^*47

Ricardo's statement that it would be to the interest of two individuals to specialize completely if each had a comparative advantage in the production of one of the commodities seems an inadequate basis, moreover, upon which to convict him of the belief that complete specialization would necessarily be profitable to each of two countries if they had comparative differences in costs of production. It so happens that the sentence cited by Pareto to show that Ricardo held this belief follows immediately in Ricardo's text an express stipulation that partial specialization by one of the countries is a possibility:

It will appear, then, that a country possessing very considerable advantages in machinery and skill, and which may therefore be enabled to manufacture commodities with much less labor than her neighbors, may, in return for such commodities, import a portion of the corn required for its consumption, even if its land were more fertile, and corn could be grown with less labor than in the country from which it was imported.^*48

Another writer, A. F. Burns, later repeated Pareto's demonstration that complete specialization may be unprofitable.^*49 This writer goes further, however, than did Pareto, for he definitely argues as if specialization along the lines of comparative advantage necessarily involves complete specialization, and then claims that whenever such specialization results in more of one commodity but less of another it is impossible to show that free trade has been profitable. He overlooks the fact that if the specialization is voluntary it will not be carried to the point where the marginal unit exported is worth less on the market than what is obtained in exchange for it, and, therefore, that while there may be no profit from trade for one of the countries under the conditions stated, there must be profit for at least one of the countries, and there can be loss to neither, if in each country the prices of its own products are proportional to their real costs.

III. TRADE IN MORE THAN TWO COMMODITIES

The problems connected with the doctrine of comparative costs have usually been examined under the simplifying assumptions that there are only two commodities and only two countries, in the belief that while the introduction of more commodities or countries into the problem would complicate the analysis it would require no serious qualitative change in the conclusions reached on the basis of the simple assumptions as to the nature and profitability of international specialization.^*50 This position seems to me substantially correct, although certain problems relating to foreign trade tend to be neglected when these assumptions are followed.

Graham has, however, put forth the claim that because of its adherence to the assumptions of only two countries and only two commodities, "the classical theory of international values seems...to be open to grave objections, objections which, while they do not subvert its foundations, nevertheless call for a substantial modification of its conclusions,"^*51 and in a later article^*52 he has expressed his criticism in still stronger terms. Some of his criticisms are well taken, and expose genuine weaknesses in the classical expositions of the theory. As Graham explains, however, his objections are mainly directed against the reciprocal-demand theorizing of J. S. Mill and Marshall, and not against the doctrine of comparative costs, which is alone the concern of this chapter. The classical economists, moreover, departed from the rigid assumption of only two commodities more often than Graham would lead one to suppose. Several instances, in which analysis in terms of more than two countries bore on the relationship between comparative costs and terms of trade, are examined below.

Longfield appears to have been the first to attempt to extend the Ricardian analysis so as to deal explicitly with more than two commodities. Where there are only two commodities, then, given the comparative costs, there is no question as to which commodity each country will respectively import and export. But when there are more than two commodities the question as to what commodities will be exported and what imported by each of the countries cannot be so readily answered. Longfield's solution, although not entirely satisfactory, approached closely to what later became the accepted one. He abstracts from transportation costs, and from all elements in real costs but labor costs, and assumes tacitly that when trade is under way all prices will be identical in the two countries. He then assumes tentatively that wages in each country are uniform in all occupations. He offers, apparently without realizing it, several different and inconsistent solutions. He first asserts that wages in the two countries will be proportional to the average productivities of labor in the two countries. If English labor, presumably before trade, is on the average three times as productive as French labor, and therefore English money wages three times as high as French wages, then in all those industries in which English labor is, say, four times as productive as French labor money costs will be comparatively low, and these commodities will be exported; while in those industries in which English labor is not more than twice as productive as French labor, money costs will be comparatively high, and these commodities will be imported. "Commerce will flow according as the proportion [of labor productivity] in particular trades is below or above the average proportion."^*53

Later he argues that if, while England was exporting the product of industries in which her labor was twice as productive as that of foreign countries, she acquired a threefold superiority in some other new industries, then her greater superiority in the new industries would make the old ones unprofitable. Labor in the old industries would have to be paid at the same rate as in the new, or at three times the rate prevailing abroad, and as its productivity in the old industries was only twice that of foreign labor, foreigners could produce the old products more cheaply in terms of money costs.^*54

Still later he provides a slightly different solution:

...if a nation enjoyed an immense superiority in the production of two or three articles of very general demand, the wages of her laborers might be, in consequence, so high that she could not compete with the rest of the world in any other manufacture, under a system of free trade. Let us suppose the productiveness of English labor to be ten times as great as that of any other nation, in the production of tin, calico, coals, cutlery, and pottery. The wages of her laborers will, in consequence, be much greater than those in any other nation; suppose them eight times as great, and suppose that English labor is only twice as productive as foreign labor, in the manufacture of other commodities. These latter, therefore, will be fabricated in the rest of the world, at the fourth part of the price which it will cost to make them in England.^*55

Longfield here presented correctly two important elements of the correct solution, namely, that for each country the commodities exported would be in the upper and the commodities imported would be in the lower range of its potential products with respect to comparative advantage in real costs, and that comparative money wage rates in the two countries would determine the precise line of division between export and import commodities. Where he failed, however, was in not providing a satisfactory explanation of the mode of determination of the ratio between wages in the two countries. His first two solutions are both obviously arbitrary and incorrect. Wages in the two countries would be proportional neither to the average productivities in all pretrade employments, nor to the productivities in the two countries in the relatively most productive employment of one of the countries. His final formula, where he makes the wage rate in England exceed the wage rate abroad by a somewhat smaller ratio than the ratio of superiority of English labor over foreign in those employments in which England is comparatively most efficient, is correct as far as it goes, but is insufficient basis for a definite solution of the problem. This was an important step forward, but Longfield's contribution unfortunately attracted no attention, and other leading writers did not deal at all with the problem of what determines the relative level of money incomes in different countries or accepted an unsatisfactory solution offered by Senior.

Senior argued that within any country the level of money wages in all occupations—proper allowance being made for differences in the attractiveness of different occupations—was determined by the wages which labor could earn in the export industries, and that the comparative levels of wages in the export industries of different countries were determined by the comparative prices which the export products of the different countries could command in the world markets.^*56 This became standard doctrine, although it left unanswered the question, given more than two commodities, as to how it was determined what would be the export industries. The prevailing level of wages would obviously be a factor in determining which industries could find export markets for their products. But to explain the determination of which industries should be export industries by reference to the general wage level, and to explain the general level of wages by reference to the level of wages prevailing in the export industries, would obviously be reasoning in a circle. Senior's argument sufficed to show that under equilibrium conditions wages in the non-export industries must be equal to wages in the export industries and that wages in different countries must be proportional to the value productivities of labor in the export industries of the respective countries. Senior failed to show, however, that wages in the non-export industries were determined by wages in the export industries instead of both sets of wages being the common product of a number of factors.

In the writings of Ricardo and the two Mills no approach to a solution of this problem is to be found. Torrens, in an elaborate discussion bearing evidence of indebtedness to Senior and Long-field, made some progress. He pointed out that the extent to which a country could confine its exports to the commodities in whose production it was at or near the upper limit of its scale of comparative advantage depended on the extent of the foreign demand for these commodities. The wider the range of commodities which it had to export in order to employ its labor to the best advantage, the lower, other things equal, would be its relative level of money wages as compared to other countries.^*57 Cairnes also attacked the problem, and reached the correct conclusion that while the general level of wages and foreign trade were intimately connected, the connection was one not of simple cause and effect operating in a single direction, but of joint dependence on the "productiveness of industry" as a whole and on the demands for different commodities.^*58 He left vague, however, the precise nature of the inter-relationships between productivities, wage levels, and international specialization.

A minor writer, P. J. Stirling, attempted to deal with the problem,^*59 but did not carry it as far as had Longfield. He claimed that the two countries would find it to their interest to exchange at each other's "par," or on terms proportional to the cost of production of the exchanged commodities. "The terms of the exchange are regulated by the relative efficiency of the labor of the two countries in the production, not of all commodities, but of those commodities in the production of which their efficiency is most nearly equal." He thus assimilated the theory of international value to the theory of domestic value, completely where there is some product whose cost is identical in the two countries, and approximately where there is no such product. He presented the following case:

1,000 days labor will produce in
England	Mexico
50 iron	50 iron
25 tin	400 silver
50 wheat	100 wheat
150 cloth	75 cloth

Tin and silver are commodities peculiar to England and Mexico, respectively, and iron has identical costs in both countries. England will export cloth and import wheat, in the ratio of 150 units cloth to 100 units wheat, or the reciprocal of the ratio of their costs of production in the countries where they can be respectively produced at a comparative advantage. Although he does not expressly say so, silver and tin will also presumably exchange in the reciprocal of the ratio of their costs of production, or 400 units silver for 25 units tin, and iron will not move in trade. He says that if the English output of iron should increase to 55 units per 1000 days labor, other things remaining the same, then the rate at which English cloth would exchange for Mexican wheat would be 150 units cloth for 110 units wheat, which, it will be noted, makes the double factoral terms of trade with respect to these two commodities conform to the reciprocal of the ratio between the costs in the two countries of the commodity, iron, in which these costs approach most closely to equality. This is of course a purely arbitrary solution. But it has at least the one point of merit that it posits that the commodities which each country will export and import, respectively, will lie in the upper and the lower range of its series in terms of comparative advantage.

The necessary further step toward a satisfactory solution was taken by Mangoldt.^*60 He shows that, cost of production being regarded as constant, each country will specialize in the production of a group of one or more commodities, that the commodities within each of these groups will exchange for each other in proportion to their real costs of production, and that the terms on which the commodities belonging to the two different groups will exchange for each other will be determined by the effect of the reciprocal demand of the two countries for each other's export commodities on the relative money rates of remuneration of the productive factors in the two countries. To find a basis for determining which country will export any particular commodity. Mangoldt posits the existence of a commodity such that, when its real costs in each of the respective countries are multiplied by the rates of remuneration prevailing there, there will result a money cost which is equal in both countries. Mangoldt presents his argument by means of laborious arithmetical illustrations, but it seems preferable to expound it with the aid of Edgeworth's ingenious logarithmic illustration, which, among other advantages, dispenses with the necessity of positing a commodity which is just on the margin of export or import.

Let the two columns of letters on either side of the vertical line in chart VIII (a) represent the logarithms of the real costs of the commodities a, b, c, d, e, in the two countries, with the left-hand column representing costs in country I and the right hand column representing costs in country II. Locate the points a, b, c, d, e by marking off from a fixed point o the logarithms of the real costs of the respective commodities in country I. Assume that the right-hand column can be made to slide freely up and down while the left-hand column is held rigid. From any fixed point o' on this sliding column mark off in the same way and on the same scale as for country I the points a', b', c', d', e', representing the logarithms of the real costs of the respective commodities in country II. Slide the right-hand column up or down to make oo' equal the logarithm of the ratio of wages in country II, (w_i), to wages in country I, (w_ii), so that

putting o' below o when wages in country II are lower than wages in country I, as in Chart VIII(a), and putting o' above o when wages in country II are higher than wages in country I, as in chart VIII(b).^*61 The relative rates of wages in the two countries, and therefore the distance of o' below or above o, will be determined by the reciprocal demand of the two countries for each other's products, which in turn will be partially determined by the comparative costs. Real costs in the two countries remaining the same, any shift in their reciprocal demand for each other's products would result in a change in relative wages in the two countries and therefore in a corresponding shift, upward or downward, in the movable right-hand column in chart VIII(a). If the demand of country I for country II's products in terms of its own products increased, other things remaining the same, the right-hand column in VIII(a) would slide upward, and vice versa. The vertical distances from o, when the right-hand column is adjusted properly, of the points a, a', b, b', etc., will then show the logarithms of the money costs of production of the different commodities in the two countries in terms of a common currency unit.

Since the reciprocal demands are not shown in this chart, it does not show how the comparative wage rates are determined. It shows, however, given the real costs in each country and the comparative wages as determined by reciprocal demand, what commodities each country will export and import, respectively, and on what terms. If the wage rates are as indicated in chart VIII (a), the money costs of production will be higher in country I for commodities a, b, and c, and lower in country I for commodities d and e, then in country II. Country I will therefore export d and e, and import a, b, and c. The commodity terms of trade as between each pair of export and import commodities will be indicated by their comparative prices: e.g., the number of units of commodity a obtained by country I in return for 1 unit of d will be the number of units of b obtained by country I in return for one unit of e will be and so forth. If there were a commodity with equal money costs of production in both countries, that commodity might be exported or imported by either country, might not move at all in foreign trade, or might be exported from one country to the other while being produced in both countries, quite consistently in each case with the conditions stated.

Whatever commodities country I will export and whatever ones she will import, the ratio of the logarithms of the real costs, and therefore also the ratio of the real costs in country I to the real costs in country II, will be lower for each of the commodities exported by country I than for any of the commodities imported by country I. Thus in (a) of the above chart, where country I exports commodities d and e and imports commodities a, b, and c, and are both smaller than or ^*62 But as Edgeworth points out:^*63

This theory brings into view an incident which is apt to be masked as long as we confine ourselves to the case of two commodities,...namely, that it is not in general possible to determine a priori, from a mere observation of the [real] costs of production in the respective countries before the opening of the trade, which commodities will be imported and which produced at home.... Thus if o' in the figure be pushed up a little, the distances o'a', o'b' etc., being preserved constant, e will become an export (from country no. I) instead of an import. But the position of o' depends not only the cost of production in each country, but also on the law of demand in each country for the different commodities.

This can perhaps be more clearly brought out by a comparison of (a) and (b). The scales of comparative costs are the same in both (a) and (b), but because of different reciprocal demands in the two cases the ratio between wages in country I and wages in country II is higher for (a) than for (b). As a result, country I exports only commodities d and e in case (a), as compared to commodities, b, c, d, and e in case (b).

IV. TRADE BETWEEN MORE THAN TWO COUNTRIES

The older writers rarely departed from the simplifying assumption that only two countries participated in foreign trade, and there are therefore only a few instances to be examined of discussion of the problems of international trade in terms of more than two countries.

William Ellis, in an attempt to meet the argument current in his time that England would suffer injury if competition with her staple export industries should develop abroad, introduced for the first time a third country into arithmetical illustrations of the type used by Ricardo and James Mill in their exposition of the doctrine of comparative costs.^*64 He began with England and France engaged in trade, with England having a comparative advantage in cottons and France in silk. He then showed that the entrance into the trade of a third country, Brazil, with a comparative advantage in sugar, did not result in a loss to England. This, of course, did not meet the issue, and to have made his point he would have had to show that England could not lose from the entrance of Brazil into trade even if Brazil's comparative advantage was in the same commodity, cotton, as England's.^*65

In his only reference to a third country, J. S. Mill first considered the effect on the terms of trade of England with Germany of the entrance into trade of a third country exporting the same commodity as Germany, namely, linen, and concluded that in consequence England would get her linen more cheaply in terms of English cloth. He then assumed that the third country produces neither linen nor any other commodity in demand in England, but has a demand for English cloth, and produces commodities which are in demand in Germany, and concluded that here also England's terms of trade with Germany would improve as the result of the entrance of the third country into trade, as Germany would have to induce England to take more of her linen in order to obtain the means of paying for her imports from the third country.^*66 This seems to me to be correct reasoning as far as it goes. But there are other possibilities, unfavorable for England, which Mill left unmentioned, as, for instance, if this third country had no demand for English cloth but was herself a potential exporter of cloth and importer of German linen.

Torrens, in The Budget, had argued that if Cuba imposed a duty on English cloth, the restoration of equilibrium in the trade balance of the two countries would require a relative fall in the price of English cloth as compared to Cuban sugar. Merivale replied that if an alternative source for sugar was available to England, although at a somewhat higher price than that at which Cuban sugar was available before the imposition of the Cuban duty on cloth, the rise in the price of Cuban sugar and the fall in the price of English cloth "would soon bring into play the competition of the next cheapest country producing the same commodities as Cuba." While the Cuban duty, therefore, would affect adversely the terms of trade of England, the injury to her would be much less than if Cuba were the only source of sugar.^*67 Torrens, in reply, criticized some of the details of Merivale's argument, but conceded that on Merivale's assumption that sugar could be obtained from other sources at a price not much higher than the Cuban price prior to the imposition of the Cuban duty on English cloth, the terms of trade would not shift seriously against England.^*68

Cairnes claimed that, while if there were only two countries with wide differences in their comparative costs of producing the staple articles of trade there would be a very considerable range within which the terms of trade could be determined under the influence of comparative costs, if there were more countries competition from one or more of these countries would prevent the terms of trade from settling at either of the limiting rates.^*69 This is valid as a probability, but Cairnes proceeded to too rigorous a conclusion:

...it is not the difference in the comparative costs of production in each pair of trading countries that fixes the limits to the possible variations of international values under the influence of reciprocal demand, but, among all countries mutually accessible for commercial intercourse, the difference of comparative costs, as it exists in the particular countries in which that difference is least. The limits of variation are thus set by the minimum, not by the maximum, difference in comparative cost among the various exchanging and competing countries.^*70

There is no such necessity. Assume the following situation:

Commodity
	Units of real cost per unit of product
	Country I	Country II	Country III
M...	1	2	3
N...	2	1	1

If at the ratio of three of N for one of M country III is willing to supply all of commodity N which all three countries want, then this will be the effective rate of exchange of the two commodities, and trade between country I and country III will take place on terms corresponding to the "maximum difference in comparative cost among the various exchanging and competing countries."

Triangular (or multiangular) trade has been examined by Graham,^*71 Taussig,^*72 von Mering,^*73 and earlier writers,^*74 by means of arithmetical examples of one type or another. Edgeworth's logarithmic illustration, modified so as to apply to more than two countries, seems to me, however, to be better suited to the purpose than arithmetical illustrations.

Chart IX is constructed on the same principles as chart VIII, except that four countries are included, instead of only two. What commodities each country will export and import and on what terms will be determined by the comparative costs in conjunction with the comparative wage rates, and the latter in turn will be determined, in part, by the reciprocal demands. For chart IX (a), the following situation will prevail under equilibrium conditions:

Country	I	II	III	IV
Exports...	A	C	B	D
Imports...	C,D	A,B,D,E	A,C,D,E	A,B,C

In addition, country I may either export or import or not trade in commodities B and E, and country IV may either import or export or not trade in commodity E, these commodities being on the margin of trade for those countries. The ratios in which the commodities will exchange for each other will, of course, be the reciprocals of their price ratios in a common currency. Their prices will be the antilogs of the logarithms of lowest money costs represented by the vertical distances from O₁ on a right line, as indicated below:

Commodity	A	B	C	D	E
Price = antilog of...	O2A1	O1B2	O2C3	O1D4	O2E4

In IX, (b) all the real costs are the same as in (a), but because the reciprocal demands are different in (b) from what they are in (a), money costs, prices, and the conditions of trade are also different, as compared to (a). Under equilibrium conditions, the following situation will prevail in (b):

Country	I	II	III	IV
Exports...	A	C	B	D,E
Imports...	B,C,D,E	B,D,E	A,C,D,E	A,B,C

In addition, country II may either import, export, or not trade in commodity A, this commodity being on the margin of trade for that country. The prices of the commodities will be as follows, measured as before by the antilogs of the indicated vertical distances:

Commodity	A	B	C	D	E
Price=antilog of...	O1A1	O1B3	O1C2	O1D4	O1E4

For country I, the change in the demand situation from (a) to (b) improves its terms of trade with the outside world, i.e., enables it to get B,C,D, and E in greater quantities per unit of its export A, or per unit of real cost, than before.

V. TRANSPORTATION COSTS

The theory of international trade is usually expounded on the assumption that there are no transportation costs, and this has occasionally been made a basis of criticism. But abstraction from transportation costs is also a common feature of the exposition of the theory of trade in a single market—"closed economy"—and such abstraction does not apear to be logically less permissible in the one case than in the other. Notwithstanding, moreover, the common assumption that transportation costs are relatively much more important in foreign than in domestic trade, it is by no means clear that such is the general situation. Cases are common where internal freight costs from producer to consumer are higher than international freight costs from producer to consumer, as can be seen from a study of the transportation item in the reports on costs of production in different countries made by the United States Tariff Commission.^*75 The role of transportation costs, both of products and of factors of production, in contributing to regional differences of prices is an important field for study. It has not, however, been historically the particular responsibility of the theory of international trade, and judging what has so far been done in this field, under the name of Standortslehre, it is not yet apparent, in spite of the claims of its exponents,^*76 that the indebtedness will be by the theory of international trade to Standortslehre rather than the other way round.

The relation of transportation costs to production costs and the terms of trade can be illustrated by chart X, a slight modification of Marshall's graphic method of dealing with foreign-trade problems. In country A a given amount of labor can produce either one unit of copper or one unit of wheat, and in country B a given amount of labor can produce either 3/2 units copper or ½ unit wheat. Country A will export wheat, and country B will export copper. In the absence of transportation costs, wheat will exchange for copper on terms within the limits of 1 wheat = 1 copper ( = OA in chart) and 1 wheat = 3 copper ( = OB = 3 × OA, in chart). AA' represents the export supply curve of wheat in terms of copper of country A. BB' represents the import demand curve of wheat in terms of copper of country B. The chart as drawn implies that in the absence of trade (or with trade on terms of 1 wheat = 1 copper) country A would consume (OA × AE) units of copper, and that in the absence of trade (or with trade on terms of 1 wheat = 3 copper) country B would consume BF wheat.

The actual transportation is assumed to be provided by the exporter. The charges for transportation are assumed to be 1 unit wheat payable in the export country for each 9 units of wheat transported and 1 unit copper payable in the export country for each 5 units of copper transported. With the transportation costs in the specified amounts, the possible limits of the terms of trade will be 1 wheat = 1.2 or Oa copper and 1 wheat = 2.7 or Ob copper. Country A's export supply curve for wheat in terms of copper will be aa', and country B's import demand curve for wheat in terms of copper will be bb'. The equilibrium terms of trade, which would have been 1 wheat = OK copper in the absence of transportation costs, will be 1 wheat = mr copper, net after payment of transportation costs, for country A, and 1 wheat = ml copper, net after payment of transportation costs, for country B. It is to be noted that with the existence of transportation costs the terms of trade net after payment of transportation costs will be different for the two countries, the difference being absorbed in meeting the costs of transportation. Given elasticities greater than unity for both the foreign-trade curves, volume of trade will be smaller and the net terms of trade will be less favorable for both countries when there are transportation costs than when these are zero. In the present case the existence of transportation costs will reduce the amount of wheat imported by country B from OH to Om units, and will reduce the amount of copper imported by country A from (OH × OK) units to (Om × Or) units.^*77 The division of the costs of transportation as between the two countries will, as J. S. Mill contended, be determined by "the play of international demand."^*78

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.^*79 Under constant cost, there is an apparent^*80 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.^*81

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.^*82 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.^*83

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 1/X_a be the marginal cost per unit of a in terms of units of the productive factors, and let 1/X_b be the marginal cost of b. Then X_a X_b 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, X_a 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 > X_b, and by using the marginal unit of the factors of production to produce a rather than b, M gains either Y - X_b 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.^*84 Nicholson makes such an attempt,^*85 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.^*86 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.

Graham^*87 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.

Case I. Incipient Specialization:*88	4 wheat = 3½ watches
Country A	Country B
(200)	(200)
1 day's labor = 4 wheat	1 day's labor = 4 wheat
(200)	(200)
1 day's labor = 4 watches	1 day's labor = 3 watches

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.

Case II. Intermediate Specialization:	4 wheat = 3½ watches
Country A	Country B
(100)	(300)
1 day's labor = 4.5 wheat	1 day's labor = 3.5 wheat
(300)	(100)
1 day's labor = 4.5 watches	1 day's labor = 2 watches

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.

Case III. Full Specialization:	4 wheat = 3.5 watches
Country A	Country B
(1)	(399)
1 day's labor = 5 wheat	1 day's labor = ½ wheat
(399)	(1)
1 day's labor = 5 watches	1 day's labor = ¼ watch

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 7/16 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,^*89 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...."^*90 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.^*91

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 mach