Studies in the Theory of International Trade

Chapter IX
GAINS FROM TRADE: THE MAXIMIZATION OF REAL INCOME

It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.

—Aristotle, Ethica Nichomachea, 1094 b, as cited by T. V. Smith, International Journal of Ethics, XLVI (1936), 385.

I. "MASS OF COMMODITIES" AND "SUM OF ENJOYMENTS": RICARDO AND MALTHUS

In the comparative-cost approach to the problem of gain from foreign trade, the stress is put on the possibility of minimizing the aggregate real costs at which a given amount of real income can be obtained if those commodities which can be produced at home only at high comparative costs are procured through import, in exchange for exports, instead of being produced at home. In the later development of the theory of international trade, several methods of dealing with the income aspects of foreign trade are introduced, and in the exposition of Marshall and Edgeworth, though the comparative costs are still a factor in the situation,*1 they appear in the analysis only implicity through their influence on the reciprocal-demand functions, which, in so far as they are welfare functions, represent "net" income or income-minus-cost quantities.

Ricardo and Malthus, in the course of a discussion of concrete problems of trade policy, offered some indication of the nature of the "welfare" presuppositions of their gain analysis. In Mill, Marshall, and Edgeworth these presuppositions are left unexpressed, as far as their international-trade analysis is concerned, and must be inferred from their other writings. As will perhaps be made evident, it is a question whether Marshall and Edgeworth, notwithstanding their more elaborate techniques of analysis, improved substantially upon what Ricardo and Malthus said, scanty though that was, with respect to the criteria of gain or loss from foreign trade.

Malthus attributed to Ricardo—whether rightly or wrongly is open to argument—the position that the saving in cost under free trade resulting from obtaining the imported commodities in exchange for exports instead of by domestic production not only demonstrated the existence of gain from trade but measured the extent of the gain. To this proposition Malthus objected that the excess in the cost of domestic production of the imported commodities over the cost of obtaining them in exchange for exports provided a grossly exaggerated measure of the gain from trade where the imported commodities could not be produced at home at all or could be produced only at extremely high costs.*2

Mr. Ricardo always views foreign trade in the light of means of obtaining cheaper commodities. But this is only looking to one half of its advantages, and I am strongly disposed to think, not the larger half. In our own commerce at least, this part of the trade is comparatively inconsiderable. The great mass of our imports consists of articles as to which there can be no kind of question about their comparative cheapness, as raised abroad or at home. If we could not import from foreign countries our silk, cotton and indigo...with many other articles peculiar to foreign climates, it is quite certain that we should not have them at all. To estimate the advantage derived from their importation by their cheapness, compared with the quantity of labor and capital which they would have cost if we had attempted to raise them at home, would be perfectly preposterous. In reality no such attempt would have been thought of. If we could by possibility have made fine claret at ten pounds a bottle, few or none would have drunk it: and the actual quantity of labor and capital employed in obtaining these foreign commodities is at present beyond comparison greater than it would have been if we had not imported them.

Malthus held that the gain from trade consisted of "the increased value which results from exchanging what is wanted less for what is wanted more"; foreign trade, "by giving us commodities much better suited to our wants and tastes than those which had been sent away, had decidedly increased the exchangeable value of our possessions, our means of enjoyment, and our wealth."*3 Malthus, here as elsewhere, meant by "value" or "exchangeable value" not value in terms of money but purchasing power over labor or "labor command." He reached the conclusion that foreign trade increases the sum of "labor command" in the following fashion: foreign trade, when it results in a new assortment of commodities available for use which is "better suited to the wants of society" than the pre-trade one, increases income in the form of profits without a proportionate decrease in other forms of income, and therefore increases the amount of money available for payment as wages, or the demand for labor; wages do not rise in proportion to the rise in total money income; therefore the new income constitutes a greater sum of "labor command" than the old one.*4 Malthus would, therefore, presumably deny that there was gain from foreign trade if money wage rates rose relatively as much as total monetary income, so that there was no increase in "labor command." To measure gain by the increase in "labor command" without reference to the terms on which labor can be commanded is a fantastic procedure if laborers are recognized as constituting part of the population.

Malthus would have done much better if he had stopped with the exchange of "what is wanted less for what is wanted more" as constituting the content of the gain from foreign trade. He got into this muddle in an attempt to rebut the proposition with which Ricardo's famous chapter on foreign trade opens: "No extension of foreign trade will immediately increase the amount of value in a country."*5 Malthus regarded this as an absurd proposition, whereas if he had ever succeeded in mastering Ricardo's peculiar use of terms he would have seen that it was a sterile truism. Ricardo's proposition rests upon his use of the quantity-of-labor cost as the measure of value and upon his tacit assumption that foreign trade influences what labor shall produce but does not affect immediately how much labor shall be engaged in production.

Ricardo, however, did not measure gain by changes in "value" as defined by him, and therefore did not deny that foreign trade resulted in gain. After laying down his proposition that foreign trade will not immediately increase the amount of value in a country, Ricardo went on to say that "it will very powerfully contribute to increase the mass of commodities, and therefore, the sum of enjoyments."*6 What was intended by Ricardo as the main proposition was, at least for our present purposes, of no importance. The incidental comment, on the other hand, was of great importance. It suggests two income tests of the existence, and perhaps also two income measures of the extent, of gain from trade, namely, an increase in the "mass of commodities" and an increase in the "sum of enjoyments." Ricardo did not expand these suggestions, but in his Notes on Malthus he repeated them: if two regions engage in trade with each other "the advantage...to both places is not [that] they have any increase of value, but with the same amount of value they are both able to consume and enjoy an increased quantity of commodities," adding, however, that "if they should have no inclination to indulge themselves in the purchase of an additional quantity, they will have an increased means of making savings from their expenditure."*7

Both types of test, needless to say, involve in their application serious logical or practical difficulties. The "mass of commodities" is significant only as it is accepted as a measure or index of the "sum of enjoyments" and the "sum of enjoyments" is not itself directly measurable. The use of "mass of commodities" as a measure of gain from trade, or even as an index of the direction of change, would involve in practice the use of an index number of national real income. As in the case of the measurement of real costs, the determination of the proper weights for the quantities of different commodities presents serious, and in strict theory insoluble, problems. There is no evidence that Ricardo gave any thought to these problems. Malthus, however, in defending his own "labor command" test, succeeded in locating the most vulnerable point in the "mass of commodities" test. Where the commodities imported were such as in the absence of foreign trade could not have been produced at home, or could be produced only at prohibitively high costs, Malthus objected, "we might be very much puzzled to say whether we had increased or decreased the quantity of our commodities,"*8 presumably because after trade the country would have more of the imported but less of the native commodities than before trade with no means available of comparing exactly the amount of increase in the one with the amount of decrease in the other.

Malthus could have gone further: even if there were more of every commodity after trade as compared to before trade, the removal of the duties would certainly have resulted in an increase in the quantity of commodities in any physical sense, but there would not necessarily have been an increase in real income or in "sum of enjoyments." The argument should scarcely call for elaboration. The removal of duties tends to alter the distribution of the national money income unfavorably for the owners of the services entering relatively more heavily into the production of the hitherto protected commodities than into the production of the export commodities. The removal of duties tends also to raise to domestic consumers the prices of the export commodities relative to the prices of the hitherto protected commodities. Suppose that labor enters relatively more heavily into the production of the protected commodities than into the production of the export commodities, and that labor is a heavy consumer of the export commodities but a light consumer of the protected commodities. The removal of the duties, therefore, operates injuriously to labor in two ways: it lowers the relative share of labor in the national money income, and it raises the prices, relative to other commodities, of the things on which labor spends its wages. It is still possible that labor may gain from the removal of the duties, for under the conditions given it is still possible for the buying power of money wages over the things laborers buy to be greater after the removal of the duties than before. Even if labor does lose, other classes will necessarily gain more than labor loses in physical income, if in measuring physical income the quantities of particular commodities are weighted for purposes of summation by their prices under free trade, or their prices under protection, or any intermediate scale of prices, and if the import duties were not merely nominal but were actually restrictive of import of the dutiable commodities.*9 But if labor is relatively a low-income class, the removal of import duties might result in a loss of physical income to labor which, weighted by its utility coefficient, might conceivably be greater than the gain in the physical income of the other classes, similarly weighted by its utility coefficient. It is possible, therefore, that even with the usual abstractions from short-run immobilities and rigidities, from monopoly conditions, and from changes in aggregate real cost on the production side, free trade may result in an impairment of psychic income. But the combination of adverse circumstances necessary to produce this result is so formidable as to justify the conclusion that there is ordinarily a strong presumption that free trade—given the usual long-run assumptions—will increase the national real income. Economic analysis can here at best yield only strong presumptions, but this limit in the power of economic analysis extends to the entire field of welfare analysis.

Haberler, on the basis of a combination of a priori and empirical considerations, claims that in the long run the functional distribution of real income is unlikely to be appreciably different under free trade than under protection, and that in so far as it would change with the adoption of free trade the change would more probably be favorable than unfavorable to labor. Free trade, he argues, will result in a rise in the real prices of those factors which are "specific to" the export industries; it will result also in a rise, though a lesser one, in the real prices of non-specific factors; and it will result in a fall in the real prices of those factors which are specific to the protected industries which must reduce their operations or disappear under free trade. Labor is in the long run the least specific of all factors. It will therefore be in the intermediate position, and will gain from the general increase in productivity.*10

While Haberler's conclusions may be sound, this reasoning seems inadequate justification for them. Haberler uses "specific" to mean occupational immobility, whether due to technical or to other causes. He compares the mobility of only labor and "material means of production," which latter is scarcely an elementary factor of production. Natural resources of the agricultural or mining type are no doubt the most specific of the factors, but in the long run it would seem to be free capital and not labor which is the least specific. In any case, it would seem to be not occupational mobility in general, but occupational mobility as between the tariff-sheltered and the unsheltered industries which would be of primary significance for this problem. If labor was used relatively heavily by the protected industries, relatively lightly by the unsheltered industries, and if its marginal productivity decreased slowly in the former and rapidly in the latter as more labor was employed while the other factors were held constant, the removal of tariff protection would lessen the relative share of labor in the national money income. I see no a priori or empirical grounds for holding this to be an improbable case. But even if labor on the average had low occupational mobility and were employed relatively heavily in the protected industries, its real income might still rise with a removal of tariff protection even though its money income and its relative share in the national money income and the national real income all fell, if it was an important consumer of the hitherto protected commodities, and if the prices of these commodities fell sufficiently as a result of free trade to offset the reduction in money wages in the new situation.

The concessions made above to the protectionist case do not qualify the conclusion that free trade—given the usual assumptions—necessarily makes available to the community as a whole a greater physical real income in the form of more of all commodities, and that the state, if it chooses, can, by appropriate supplementary legislation, make certain that the removal of duties shall result in more of every commodity for every class of the community. When the Cobden Treaty was negotiated, Proudhon complained that while it admittedly made cottons cheaper and more abundant in France, it made wine dearer and scarcer, and that the French masses lost more from the latter consequence of the treaty than they gained from the former. It cannot be said with confidence, on a priori grounds alone, that Proudhon was mistaken. But the French government could have brought it about that the Cobden Treaty should not result in a reduction in wine consumption in France—or by any stratum of the French population—by levying special income taxes on the class which consumed cotton goods relatively most heavily and using the proceeds to subsidize the class which consumed wine relatively more heavily, or by levying internal consumption taxes on cottons (at lower rates than the effective amount of the import duties which had been removed) and using the proceeds as a subsidy to domestic wine consumption, or by some other stratagem of this general character, designed to offset an undesired effect of the reduction of duties on the distribution of the national income.

Free trade, therefore, always makes more commodities available, and, unless it results in an impairment of the distribution of real income substantial enough to offset the increase in quantity of goods available, free trade always operates, therefore, to increase the national real income. That the available gain is ordinarily substantial there is abundant reason to believe, but the extent of the gain cannot in practice be measured in any concrete way. These conclusions, which are little more than a paraphrase of some words of Cairnes's,*11 are, in my opinion, very nearly as far as the argument can with advantage be carried. The remainder of the chapter is devoted to an examination—as sympathetic as I can make it—of the more elaborate methods of analysis by which J. S. Mill, Marshall, Edgeworth, and others obtained results which were, seemingly at least, more precise and conclusive, with respect to the income gains from trade.

II. RECIPROCAL DEMAND AND THE TERMS OF TRADE

From the time of Ricardo on, the commodity terms of trade have been widely accepted as an index of the trend of gain from trade. Some writers have also derived a measure of the ratio in which the gains from trade were divided between two trading areas from their commodity terms of trade taken in relation to the comparative costs of production of the two areas. In earlier chapters the terms of trade have been dealt with merely as manifestations of certain objective price relations, without reference to their gain significance. Before proceeding to an examination of the validity of the use of the terms of trade as an index of gain, it is necessary to consider further the objective relationship of the terms of trade to other international trade phenomena, and especially the connection between the "reciprocal demands" and the commodity terms of trade. Analysis of this connection begins with Torrens and John Stuart Mill. Marshall and Edgeworth later made it a field for the exercise of their geometrical skill, but admittedly without departing substantially from J. S. Mill's mode of approach or conclusions. While a number of writers have reproduced their analysis in sympathetic fashion, Graham alone has subjected it to really severe criticism. This section, therefore, will be confined to an examination of the contributions of Mill, Marshall, and Edgeworth, with reference at appropriate points to Graham's criticisms. Since the original sources are all readily available, the summaries presented here will be restricted to the minimum necessary to afford a sufficient basis for appraisal of their techniques of analysis and their most general conclusions.

John Stuart Mill.

Mill's discussion of the relationship between reciprocal demand and the commodity terms of trade was in the main a pioneer achievement, and probably constitutes his chief claim to originality in the field of economics.*12 The problem for which Mill seeks an answer is the mode of determination of the commodity terms of trade. He first simplifies the problem by assuming only two countries and only two commodities.*13 Mill held that the equilibrium terms of trade must be within the upper and lower limits set by the ratios in the respective countries of the costs at which the two commodities could be produced at home, but that the exact location of the terms of trade would be determined by the demands of the two countries for each other's products in terms of their own products, or the "reciprocal demands."*14 Equilibrium would be established at that ratio of exchange between the two comodities at which the quantities demanded by each country of the commodities which it imports from the other should be exactly sufficient to pay for one another, a rule which Mill labels the "equation of international demand" or "law of international values."*15

Shadwell later objected that Mill had not really solved the problem by his "equation" or "law," but had merely stated the truism that "the ratio of exchange is such that the exports pay for the imports,"*16 and Graham makes substantially the same criticism.*17 Except for the case of pure barter, however, there is nothing "truistic" about the equality in value of imports and exports, and in fact they would ordinarily not be equal even after allowance for "invisible" items if, as is proper for present purposes, money and the money metals were not counted as exports or imports. It would be true, however, that Mill would not have accomplished very much if he had merely established the necessity under equilibrium of equality in value between imports and exports. But as Bastable pointed out in reply to Shadwell, "Mill's theory does not consist merely in the statement of the equation of reciprocal demand, but [also] in the indication of the forces which are in operation to produce that equation."*18 The terms of trade, according to Mill, are determined by the reciprocal demands, conceived in the schedule or function sense, subject to the condition that imports shall equal exports in value. A fair reading of Mill's chapter warrants no other interpretation. There is, moreover, supporting evidence for this interpretation. Mill, as we have seen, stated that "This law of international values is but an extension of the more general law of value, which we called the equation of supply and demand." To what appears to have been a criticism similar to Shadwell's made by Cairnes against Mill's use of the analogous "equation of supply and demand" in his general value theory, Mill replied:*19

I think that the proposition as laid down [i.e., "the equation of supply and demand"] is something more than an identical proposition. It does not define—nor did it, as I stated it, affect to define—the causes of variations in value. But it declares the condition of all such variations and the necessary modus operandi of their causes, viz., that they operate by moving the supply to equality with the demand or the demand to equality with the supply.

To explain the determination of the terms of trade by reciprocal demand and the "equation of international demand" Mill used arithmetical illustrations. It is not surprising, therefore, that his results had sometimes a more restricted range of validity than he appeared to recognize. But the following summary and graphical illustration of his results in one of his hypothetical cases*20 may serve, nevertheless, to reveal the pioneer character of his analysis.

There are two countries, Germany and England, two commodities, cloth and linen, and production is tacitly assumed to be under conditions of constant real cost. In England 10 yards of cloth cost as much to produce as 15 yards of linen, while in Germany 10 yards of cloth cost as much to produce as 20 yards of linen. England will therefore be an importer of linen and an exporter of cloth, and the possible range of the terms at which cloth will be exchanged for linen is between 10 of cloth for 15 linen and 10 of cloth for 20 linen. Mill assumes that the reciprocal demands are such that equilibrium will be established at 10 of cloth for 17 linen.

Mill now assumes that an improvement is introduced in the method of production of linen in Germany, so that it now costs per unit only two-thirds as much as before. This will increase the German demand for cloth in terms of linen, and will cause 10 yards of cloth to exchange for more than 17 linen. Mill tacitly assumes here that the German demand for cloth in terms of units of German effort of production will remain unchanged, so that the German demand for cloth in terms of linen will at all points be 50 per cent higher than before. He concludes that the degree in which the amount of linen exchanging for 10 of cloth rises above 17 depends on the character of the English demand for linen in terms of cloth. When the German offering price of linen in terms of cloth is lowered: (a) if the quantity of linen England will take increases "in the same proportion with the cheapness" of the linen, i.e., if the English demand for linen in terms of cloth prices has unit elasticity, the new equilibrium terms of trade will be 10 cloth for 25½ linen; (b) if the quantity of linen England will take increases "in a greater proportion than the cheapness" of the linen, i.e., if the English demand for linen in terms of cloth prices has an elasticity greater than unity, the new equilibrium terms of trade will be 10 cloth for 25½—linen; (c) finally, if the quantity of linen England will take increases "in a less proportion than the cheapness" of the linen, i.e., if the English demand for linen in terms of cloth prices has an elasticity less than unity, the new equilibrium terms of trade will be 10 cloth for 25½ + linen.

Chart XII, a modification of the Marshallian foreign-trade diagrams so as to make the vertical axis represent the linen-cloth terms of trade instead of the total quantity of linen, shows that Mill's conclusions, given his assumptions, are correct.*21 The reduction in the cost of producing linen in Germany results in the terms of trade moving against linen. Given the effect of the reduction in the German cost of producing linen on the German demand for cloth in terms of linen, the degree of this movement of the terms of trade against linen is smaller, the greater is the elasticity of the English demand for linen in terms of cloth.*22 When the elasticity of the English demand for linen in terms of cloth (the E curve) is unity, the new terms of trade are 10 cloth for 25½ linen. When the elasticity of the English demand for linen in terms of cloth (the E" curve) is greater than unity, the new terms of trade are 10 cloth for 25½—linen. When the elasticity of the English demand for linen in terms of cloth (the E' curve) is less than unity, the new terms of trade are 10 cloth for 25½ + linen. All these results are in conformity with Mill's findings.

As the result of criticisms from W. T. Thornton, and others, Mill, in the third edition (1852) of his Principles, introduced new matter intended to meet the objection that he had failed to demonstrate that, given the reciprocal demands, there was a unique rate of exchange between cloth and linen at which the condition of equilibrium that the value of imports should equal the value of exports would be met.*23 There has been general agreement that this additional material was unsatisfactory and unnecessary. Where at least one of the reciprocal demands is inelastic there may be more than one equilibrium set of terms of trade, and the problem is then indeterminate.*24 Where both the reciprocal demands are elastic, there must be a unique equilibrium set of terms of trade, which is adequately determined by Mill's original procedure.

Marshall.

Marshall's treatment of the relation of reciprocal demand to terms of trade is in the main an exposition and elaboration in geometrical form of Mill's analysis.*25 Marshall invented for this purpose a new type of supply-and-demand diagram, in which the vertical and the horizontal axes each represent the total quantity of one of the two commodities, thus differing from his domestic-trade diagrams, where only one commodity, and money prices, are involved, and where the vertical axis represents price per unit.*26 As against the alternative procedure followed here in charts VII, X, and XII, of making the vertical axis in the international-trade diagrams represent the terms of trade, equivalent to price, Marshall claims for his own procedure: first, that it makes the curves of the two countries "symmetrical" and, second, that the alternative procedure would have some (unspecified) advantages, but "this want of symmetry would have marred, though it would not have rendered impracticable, the application of the method of diagrams to the more elementary portions of the theory; but in other portions it would have led to unmanageable complications."*27

The issue is merely one of comparative convenience, and has no other significance. I have found it much more convenient as a rule to follow the procedure which Marshall rejects, i.e., to make the vertical axis represent terms of trade rather than the total quantity of one of the commodities. Aside from whatever aesthetic value may attach to the "symmetry" which is abandoned when this alternative procedure is followed, the only disadvantage in substituting the "terms-of-trade diagrams" for Marshall's diagrams is that whereas in Marshall's diagrams it can readily be determined by inspection, for both of the curves, whether their demand elasticity is greater, less, or equal to unity, and for both of the commodities, what will be the total amounts exchanged under equilibrium, in my diagrams, to which I will henceforth refer as "terms-of-trade diagrams," this information is directly available only for one of the curves and one of the commodities. But my diagram has the advantage that on it the commodity terms of trade can be read off directly from the vertical axis, whereas on Marshall's diagram they can be found only by determining the rate of slope of the vector from the O point to the point of equilibrium.

The general nature of Marshall's analysis of the relationship between the reciprocal demands and the terms of trade can conveniently be illustrated by means of one of Marshall's propositions which Graham has criticized. That the use of terms-of-trade diagrams has some practical advantages over Marshall's procedure will become evident, I believe, if the simplicity of the diagrams presented here is compared with the complexity of those used by Marshall in the same connection. Marshall claims that if the English demand for German goods undergoes a given percentage increase the following rule holds:

The more elastic the demand of either country, the elasticity of the demand of the other being given, the larger will be the volume of her exports and of her imports; but the more also will her exports be enlarged relatively to her imports; or, in other words, the less favorable to her will be the terms of trade.*28

Graham objects that the rule holds for Germany, but not for England, where "the more elastic the demand of E, the demand of G being given, the smaller will be the volume of E's imports and exports, and the less will her exports be enlarged relatively to her imports."*29 Marshall applies his conclusions only to curves of the "normal" type, i.e., curves whose "demand elasticities" in my terminology are greater than unity,*30 while Graham makes no qualification whatsoever with respect to the nature of the curves. Since the results in some respects vary in direction according to whether the elasticities are greater or less than unity, it will be assumed that Graham also intended to restrict his conclusions to cases where the elasticities are greater than unity. Since "increase" of demand can be given a variety of meanings, and the results obtained will depend on what meaning is chosen, I will assume, as does Marshall, that when a reciprocal demand "increases" it shifts to the right by a uniform percentage at all points of the original curve.

Marshall's proposition is tested with reference to the influence of the elasticity of Germany's curve in chart XIII, where EE is the original English supply curve (equivalent to Marshall's original English curve), E'E' is the increased English supply curve, GG is the less elastic and G'G' is the more elastic German demand curve. The more elastic the German demand curve: (1) the greater is the increase in the German exports (i.e., the rectangle a'om't' > aomt); (2) the greater is the increase in German imports (i.e., om' > om); and (3) the smaller is the amount of movement favorable to Germany in the terms of trade (i.e., Aa' < Aa). These results are all in conformity with Marshall's—and Graham's—findings.

The divergent propositions of Marshall and Graham with respect to the influence of the elasticity of England's curve are tested in chart XIV, where GG is the German reciprocal-demand curve, EE and E'E' represent the less elastic English reciprocal-demand curve before and after its increase, and ee and e'e' represent the more elastic English reciprocal-demand curve before and after its increase. The more elastic the English reciprocal demand, then when the English demand increases: (1) the smaller is the increase in the English exports (i.e., om < om'); and (2), the smaller is the movement of the terms of trade against England (i.e., Aa'<Aa'). Both these results confirm Graham's rather than Marshall's findings.

There remains to be considered Marshall's finding that the greater the elasticity of the English curve the greater will be the increase in the English imports when the English reciprocal demand increases, and Graham's contrary finding that the increase in the amount of English imports will be negatively correlated with the elasticity of the English curve. Marshall says, in effect, that in chart XIV aomt > a'om't', while Graham contends that aomt < a'om't'. Their conclusions, it is to be remembered, are here being checked only for the cases where all the curves have demand elasticities greater than unity. Since the less elastic the original English supply curve, the further to the right from T along the GG curve is the intersection of the increased English supply curve with the German curve (i.e., t' is to the right of t), and since, because GG has an elasticity of demand greater than unity, the further from the zero vertical axis is the point of intersection of the increased English curve with the German curve the greater must be the size of the rectangle bounded by the perpendiculars dropped from that point to the zero axes, therefore, a'om't' > aomt. Graham, therefore, is here again right, and Marshall wrong. The unnecessary complexity of Marshall's diagram seems to have concealed from him the fact that it provided no answers to the questions which he was putting, for the diagram by which he attempts to demonstrate the nature of the dependence of the results of an increase in the English reciprocal demand on the degree of elasticity of that curve shows three original English curves, different in locus as well as elasticity, and fails to present a comparison of the effects of an increase in an original English curve according as that original curve has high or low elasticity.*31

Edgeworth.

In Edgeworth's treatment of the relation of reciprocal demand to the terms of trade the Marshallian graphical technique is still further elaborated, with conclusions similar in their general tenor, but with more detailed differentiation of the various possible types of cases.*32 Of special interest is his diagram*33 reproduced above (chart XV), intended to show the nature of the relationship between the comparative costs and the reciprocal demands.

Chart XV is constructed on the Marshallian model, where the total amount of German linen is measured on the Y axis and the total amount of English cloth on the X axis. The lines OS and OT are added, however, their slopes representing, on the assumption of constant costs of production, the (constant) ratio of the cost of production of a unit of linen to that of a unit of cloth, for England and Germany respectively. These lines therefore represent, respectively, the terms on which England could obtain linen and Germany could obtain cloth in the absence of foreign trade, and the equilibrium terms of trade must fall between these two lines. As Edgeworth draws the diagram, however, it is open to a criticism to which all the Marshallian diagrams as usually drawn are equally open, if they are supposed to represent two commodities or classes of commodities both of which are producible at home at constant costs (or at constant relative costs). In Edgeworth's diagram the OE curve begins immediately at its origin at O to rise above the OS line, and the OG curve to fall below the OT line.*34 But the OE curve will not diverge from the OS line until the point on OS is reached which corresponds by its vertical distance from the X axis to the amount of linen which England would consume and produce in the absence of foreign trade. Let us suppose that the amount of linen which would be produced and consumed in England in the absence of foreign trade is equal to ON. England would therefore be willing to export, at the limiting ratio of linen to cloth set by its home costs, any quantity of cloth not exceeding NM, or OL. The English export supply curve of cloth, in terms of linen, therefore, instead of being OE, would be identical with OS until the point M was reached, and would diverge from OS away from the OX axis only beyond M, the entire curve having somewhat the appearance of OME. Similar reasoning applies to the relationship of the OG curve to the OT line.*35

Graham.

Graham has criticized the reciprocal-demand aspects of the theory of international value as presented by J. S. Mill and Marshall as being fallacious in their essence.*36 Some of his criticisms have already been examined.*37 Still others, of greater consequence if valid, are here taken up for scrutiny.

Graham claims that where there are more than two commodities and more than two countries (all of them able to produce all or most of the commodities) fluctuations in the rate of interchange between the various commodities must be confined within a rather narrow range.

This is due to the fact that any alteration in the rate of interchange will affect the margin of comparative advantage of some country in the production of some one of the commodities concerned, will bring that country in as an exporter where formerly it was an importer, or as an importer where formerly it was an exporter, according as the terms of interchange move one way or the other, and, by the affected country's addition to the supply or demand side, will keep the terms of interchange from moving far from their original position.*38

Graham claims that Mill, Marshall, and their school grossly exaggerated the importance of reciprocal demands in determining the terms of trade and correspondingly minimized the importance of comparative-cost conditions in the determination of the terms of trade, and he attributes this error mainly to their assumptions of only two countries and of only two commodities, or of fixed physical compositions of each country's exports and imports. He claims to demonstrate that "the character (urgency, elasticity, and the like) of reciprocal national demand schedules for foreign products is...of almost no importance in determining long-run ratios of interchange of products...."*39

Graham here does point to a defect in the exposition of Mill and his followers, but he exaggerates its prevalence, misinterprets the exact nature of the defect, and errs himself in the opposite direction. In the exposition of Mill and his followers, the defect is not that they exaggerated the importance of reciprocal demand in the determination of the terms of trade, which is logically impossible, but that, whatever they may have known, they did not sufficiently emphasize the influence of cost conditions on reciprocal demand. The terms of trade can be directly influenced by the reciprocal demands and by nothing else. The reciprocal demands in turn are ultimately determined by the cost conditions together with the basic utility functions.*40

What Mill and his followers overemphasized was the importance of the basic utility functions in determining the terms of trade. This defect in the exposition of Mill and his followers was undoubtedly promoted by the practice of confining the analysis to two countries and to two commodities, or to exports and imports of a fixed composition as far as the range of commodities was concerned, and to the assumption of constant costs, for under these conditions the cost conditions exhaust their influence in setting fixed maximum and minimum limits to the range of variation of the terms of trade.

Whatever may have been true of Mill, however, Marshall, Edgeworth, and other followers of Mill were aware of the fact that the greater the number of countries and the greater the number of commodities, the greater is the influence of cost conditions on the reciprocal demands and therefore on the terms of trade, and the smaller, therefore, given the cost conditions, the range of possible variation in the terms of trade as the result of given changes in the basic utility conditions. The first quotation following shows that Marshall appreciated the importance of multiplicity of commodities and of countries in causing the reciprocal demands to be elastic and therefore in restricting the range of variation of the terms of trade, and the second quotation, from Edgeworth, shows that Bastable and Edgeworth both recognized the similar effect of multiplication of countries.

It is practically certain that the demands of each of Ricardo's two countries for the goods in general of the other would have considerable elasticity under modern industrial conditions, even if E and G were single countries whose sole trade was with one another. And if we take E to be a large and rich commercial country, while G stands for all foreign countries, this certainly becomes absolute. For E is quite sure to export a great many things which some at least of the other countries could forego without much inconvenience: and which would be promptly refused if offered by her only on terms considerably less favourable to purchasers. And, on the other hand, E is quite sure to have exports which can find increased sales in some countries, at least, if she offers them on more favorable terms to purchasers. Therefore the world's demand for E's goods...is sure to rise largely if E offers her goods generally on terms more advantageous to purchasers; and to shrink largely if E endeavors to insist on terms more favorable to herself. And E, on her part, is sure on the one hand to import many things from various parts of the world, which she can easily forego, if the terms on which they are sold are raised against her; and on the other to be capable of turning to fairly good use many things which are offered to her from various parts of the world, if they were offered on terms rather more favorable to her than at present.*41

The theory of comparative costs is not very prominent from the mathematical point of view....That the point of equilibrium [terms of trade] falls between the respective [trade] indifference-curves is the geometrical version of comparative costs. The expression which occurs in some of the best writers, that international value "depends on" comparative cost, is seen from this point of view to be a very loose expression. (No doubt, as Professor Bastable has pointed out, when there are numerous competing nations, the limits fixed by the principle of comparative cost are much narrowed and accordingly it becomes less incorrect to regard the principle as sufficient to determine international value).*42

Graham's own error lies in his failure to distinguish between the reciprocal demands and the basic internal utility functions and to see that the cost conditions can operate on the terms of trade only intermediately through their influence on the reciprocal demands. Graham fails, apparently, to see that in the elaborate arithmetical illustrations which he presents as demonstrations that the terms of trade are fixed within narrow limits by the cost conditions irrespective of the state of the reciprocal demands, there are present, explicitly or implicitly, rigorous utility and demand assumptions, and that, consequently, his illustrations really show that it is the ost conditions plus the utility conditions which determine the reciprocal demands, and that it is only indirectly, through their influence on the reciprocal demands, that the cost conditions exercise any influence at all on the terms of trade.*43

Even if the reciprocal demands were highly elastic, moreover, while substantial movements in the commodity terms of trade would thereby be rendered less probable, they would not, as Graham contends, become impossible.*44 Let the original reciprocal-demand schedules be as elastic as one pleases, short of infinite elasticity, if they undergo pronounced shifts in position in opposite directions there will result a substantial change in the commodity terms of trade, as experiment with a Marshallian diagram will readily confirm.

Graham points out that in their explanation of the determination of the terms of trade by reciprocal demands the neo-classical writers from J. S. Mill to Edgeworth assume a fixed composition, as far as the list of commodities is concerned, of the exports and imports of each country. He claims, however, that commodities may shift from the export to the import status, or may cease to be exported or imported, and that the terms of trade determine (or are a factor in the determination of) the line of comparative advantage and, therefore, the composition of the export and import lists of any country.

It is, in consequence, impossible to determine international values on the premise of a fixed composition of export and import schedules of the several countries reciprocally concerned. In taking this premise the neo-classical writers are, in fact, implicitly assuming the very ratio of interchange of products which they are trying to discover, since the premise can be valid only on the supposition of some definite ratio of interchange. This defect in logic not only completely vitiates the general theory of international values which they set up, but it also renders useless for this, though not for another, purpose, the whole geometrical and algebraic supplement to the theory which reached its apogee, perhaps, in the work of Marshall.*45

Graham rejects Marshall's suggestion of a "representative bale" and Edgeworth's suggestion of an "ideal" export or import commodity as solutions of the problem:

It must be obvious that reciprocal demand is for individual commodities and not for any such uniform aggregate of labor and capital as a unit of the consolidated commodities concerned may incorporate, and that to construct demand schedules for representative bales the physical composition of which is inevitably changing as we move along the schedules, with commodities even shifting from one demand schedule to its reciprocal, is not only to build imaginary bricks with imaginary clay but also to commit the worse fault of assuming a homogeneity in the bricks which, though a logical necessity for the construction of the demand schedules in question, is at the same time a logical impossibility.*46

I understand Graham's argument to be that the theory of international values, as presented, say, by Marshall, is completely vitiated by its use of reciprocal-demand and terms-of-trade concepts requiring for their logical validity a non-existent fixity in the physical composition of the exports and imports of each region, and that the remedy lies in carrying on the analysis in terms of reciprocal demands for and ratios of interchange between individual commodities.

In trying to express in terms of averages the changes in relative prices of groups of export and import commodities where the physical constituents of the groups change we encounter the insoluble problem of economic index numbers.*47 Marshall and Edgeworth probably gave inadequate attention to this problem, though it is impossible to conceive of their not being aware of it. Their "representative bale" concepts are obviously but euphemisms for "averages," although where constant costs are assumed weighting of export commodities by relative prices does give an unambiguous and precise index of the terms of trade as a ratio between the quantities of productive services whose products have equal value.*48 It is a far cry, however, from conceding that precise and unambiguous measurement of the changes in the aggregate terms of trade is impossible where, as is always the case, the physical constituents of the exports and the imports are undergoing relative changes to conceding that analysis resting upon averages computed in the usual or "standard" ways is thereby rendered worthless. If that were true, then economics would indeed be in a hopeless plight. Graham's objection would then serve to condemn every economic concept involving a sum or an average, including his own concept of single "commodities," as he would soon discover if he were to attempt to define a "commodity," say wheat, so that it did not involve a medley of different things constantly undergoing relative changes in quantity, quality, and price. The use of such concepts, in spite of their admitted imperfections, can be defended only because superior alternatives are unavailable, and because their imperfections are believed—or hoped—not to involve a range of probable error in the results obtained by their use sufficiently great, or uncertain, to deprive these results of significance for the purpose on hand.

What Graham offers as an alternative for the use of imperfect "average" concepts, namely analysis in terms of pairs of single commodities, is not a satisfactory one. The significance of the results obtained when expressed in terms of a pair of single commodities depends upon whether the commodities singled out are "representative" or not of broad classes of commodities, and the problem of finding proper criteria of "representativeness" is essentially but another manifestation of the "averaging" problem. Analysis of the determination of the terms of trade cannot itself be carried on in terms of pairs of single commodities, except on the assumption that these are the only commodities entering into trade, or are "representative" of trade as a whole. "Reciprocal demand" is not only an aggregative concept, but it designates an economic force which operates as an indivisible entity. "Each transaction in international trade is an individual transaction," but the terms on which it is conducted are set for it by the market complex as a whole. The prices of any particular export commodity and any particular import commodity are functionally related to each other, react upon each other, not directly (except to an insignificant degree) but through their membership in the price and utility and cost systems of the trading world, taken as a whole. In the case of foreign trade, changes in the desires for or costs of particular commodities operate to change the ratios of interchange between these commodities and other commodities only indirectly through their influence on money flows and on aggregate demands and supplies of commodities in terms of money. The reciprocal-demand analysis is an attempt, imperfect but superior to available substitutes, to describe the aggregate or average results of such changes in desires or costs when they affect appreciably a wide range of commodities.

III. TERMS OF TRADE AND THE AMOUNT OF GAIN FROM TRADE

Terms of Trade as an Index of Gain from Trade.

From the beginning of the classical period, if not earlier, the trend of the commodity terms of trade has been accepted as an index of the direction of change of the amount of gain from trade, and it is therefore an old doctrine that a rise in export prices relative to import prices represents a "favorable" movement of the terms of trade. It has been recognized at times that the proposition is valid subject only to important qualifications, but systematic discussion of the qualifications which are necessary, or of the nature of the connection between the commodity terms of trade and the amount of gain from trade, seems to be almost totally lacking in the literature.

Ricardo had little to say of the terms of trade as related to the gain from trade, perhaps because the question then came up only in connection with the unwelcome arguments that by monetary expansion, or by protective duties, the commodity terms of trade of a country could be made more favorable. While Ricardo did not deny that, of itself, an increase in the amount of foreign goods obtained in return for a unit of native goods was a favorable development, he was careful to point out that whether or not it reflected a genuine improvement in the position of the country depended on how it came, or was brought, about. He was, in general, skeptical of the possibility of bringing it about deliberately, through governmental action,*49 but conceded, reluctantly, that the levy of import duties might have such a result, accompanied, however, by offsetting disadvantages:

We shall sell our goods at a high money price, and buy foreign ones at a low money price,—but it may well be doubted whether this advantage will not be purchased at many times its value, for to obtain it we must be content with a diminished production of home commodities; with a high price of labor, and a low rate of profits.*50

Although J. S. Mill laid much greater emphasis than did Ricardo on the connection between the terms of trade and the amount of gain from trade, he also did not accept a favorable movement of the commodity terms of trade as necessarily indicating a favorable movement of the amount of gain from trade. Thus, while he conceded that the imposition of protective import duties operated to change in a favorable direction the terms on which the remaining imports were obtained, he claimed that this advantage was more than offset by the loss of the benefit which had previously accrued from the trade in the commodities now produced at home under tariff protection.*51 Similarly, when he showed that a reduction in the real cost of production of Germany's export products would operate to turn the terms of trade against Germany, he refrained from drawing the conclusion therefrom that the reduction in cost would be injurious to Germany even in the least favorable case where the commodity whose cost of production had been reduced was not consumed at all within Germany itself.*52

As we shall see later, Marshall and Edgeworth both adopted changes in "consumer's surplus," or its supposed equivalent, as a better index of change in the amount of gain from foreign trade than the movement in the commodity terms of trade. Taussig pointed out specific circumstances under which the commodity terms of trade would be a misleading index of gain from trade.*53 The general position of the major writers in this field was, it seems, therefore, that an increase in the amount of imports obtained per unit of exports was presumptive evidence of an increase in the amount of gain from trade, but that the validity of the presumption was subject to the absence of countervailing factors. As examples of such countervailing factors, Marshall took account of increases in the cost of the export commodities and Taussig referred to a decrease in the desire for the import commodities. But systematic inquiry into the relationship between the commodity terms of trade and the amount of gain from trade is not, I believe, to be found in the literature.

Jevons criticized Mill's use of the commodity terms of trade as a measure of the gain from trade on the ground that the total amount of gain from trade depended on total utility, whereas the commodity terms of trade were related to "final degree of utility": "in estimating the benefit a consumer derives from a commodity it is the total utility which must be taken as the measure, not the final degree of utility on which the terms of exchange depend."*54 In utility terms, the total amount of gain from trade can be defined as the excess of the total utility accruing from the imports over the total sacrifice of utility involved in the surrender of the exports. If it be permitted to waive the difficulty of applying utility theory to a group of persons or a "country," the commodity terms of trade will at any moment always equal the ratio of the marginal disutility of surrendering exports to the marginal utility of imports. Disturbances will change the terms of this ratio, but not the ratio itself. The marginal unit of trade, therefore, will never, under equilibrium conditions, yield any gain, and whether or not a "favorable" movement of the commodity terms of trade will represent an increase in net*55 total utility will depend on what, if any, changes occur (1) in the utility function for imports, (2) in the disutility function for exports, (3) in the volume of trade. Reasoning such as this was presumably the basis of Jevons's comment. As will appear from the subsequent analysis, however, Jevons went further than this reasoning would justify, when he suggested that Mill's argument that the gain from trade increased with the relative cheapening of imports as compared to exports was less likely to be true than its converse, on the ground that "he who pays a high price must either have a very great need of that which he buys, or very little of that which he pays for it,"*56 a proposition whose plausibility derives from the very defect of analysis which he had charged against Mill, namely, disregard of the total utility aspects of the problem.

There follows an examination of the possibility of so modifying the concept of terms of trade as to make it less open to Jevons's criticism that it rests on a confusion of final degree of utility with total utility, although this examination is for the most part only implicitly in terms of utility analysis.

Different Concepts of Terms of Trade.

We will write e to represent the export commodities, i to represent the import commodities, P for the price index number, o for the initial year, and I for the given year. An index of the commodity terms of trade can then be represented symbolically as

where the index measures the trend of the "physical" amount of foreign goods received in exchange for one "physical" unit of the export goods, with a rise in the index indicating a favorable trend, and vice versa.*57

The case cited by J. S. Mill, where a reduction in the real cost to Germany of producing her export commodities would result in a movement unfavorable to Germany of the commodity terms of trade but might nevertheless not involve a reduction in the amount of gain derived by her from her foreign trade, suffices to demonstrate that the commodity terms of trade may fail to provide a satisfactory guide even of the direction of the trend of gain from trade if, when the commodity terms of trade are changing, changes in the same direction are occurring in the costs of production of the export commodities. If it were possible to construct an index of the cost of production in terms of the average technical coefficients of production of the export commodities, and if the commodity terms of trade index was multiplied by the reciprocal of the export commodity technical coefficients index, the resultant index would provide a better guide to the trend of gain from trade than the commodity terms of trade index by itself. This modified terms of trade index, which for lack of a better name I designate as the single factoral terms of trade index, can be represented symbolically as:

where represents the reciprocal of the index of cost in terms of quantity of factors of production used per unit of export, and T_c,f represents the index of the physical amounts of foreign goods obtained per unit of cost in terms of quantity of factors of production.*58

A still closer approach to an index of real gain from trade would be achieved if the single factoral terms of trade index were multiplied by the reciprocal of an index of the "disutility coefficients" of the technical coefficients of the export commodities. The resultant index would be a real cost terms of trade index, which could be represented symbolically as:

where represents the index of amount of disutility (amount of irksomeness) per unit of the technical coefficients, and T_c,f,r represents the index of the physical amount of foreign goods obtained per unit of real cost.

The amount of gain from trade depends, however, not only on the amount of foreign goods obtained per unit of real cost involved in the production of the export commodities, but also on the relative desirability of the import commodities as compared to the commodities which could have been produced for home consumption with the productive resources now devoted to production for export. To take account of changes in the relative desirability of the import commodities whose internal consumption is precluded by the allocation of productive resources to production for export when such changes in relative desirability are due to changes in tastes, it would be necessary to incorporate in the "real cost of trade index" an index of the relative average*59 utility per unit of imported commodities and of native commodities whose internal consumption is precluded by allocation of resources to production for export. If we write U for average desirability or "utility" and a to designate the commodities whose production for domestic consumption is forgone as the result of resort to production for export, then represents the index of relative desirability of import and forgone commodities, respectively, and the new terms of trade index, in which the index of relative desirability is incorporated, can be designated as the utility terms of trade index, and represented symbolically as

*60

Still another terms-of-trade concept was used by the older writers, namely, the number of units of the productive services of the foreign country whose product exchanged for the product of one unit of the productive services of your own country. This concept might be designated as the double factoral terms of trade, and its index could be represented symbolically as

The older writers usually accepted the double factoral terms of trade as identical in their trend with the commodity terms of trade, which would be correct under their assumptions of production under conditions of constant costs and historically stable costs.*61 But with costs variable, whether with respect to output or to time, the trends of the two indices could be substantially divergent. The double factoral terms of trade index would approach more closely to an index of the international division of gain than to an index of the absolute amount of gain for either country. If the commodity terms of trade and the index of export costs of a given country, A, remained the same, so that its single factoral terms of trade index remained unaltered, its double factoral terms of trade index would rise or fall according as the cost in the other country, B, of producing its exports rose or fell. But such divergence of the double factoral from the single factoral terms of trade index would have no welfare significance for country A, and, under the conditions stated, would merely indicate an impairment or improvement of productivity in country B.

Taussig has introduced still another concept of terms of trade, the gross barter terms of trade, or the ratio of the physical quantity of imports to the physical quantity of exports, the greater this ratio the more favorable being the gross barter terms of trade.*62 His purpose in introducing this concept is to correct the commodity, or "net barter," terms of trade for unilateral transactions, or exports or imports which are surrendered without compensation or received without counterpayment, such as tributes and immigrants' remittances. He gives an illustration where the price of wheat exported from the United States to Germany is 80 cents a bushel, and the price of linen imported into the United States from Germany is 76 2/3 cents a yard, so that the commodity terms of trade are 10 wheat for 10.4 linen. But of the 10,250,000 bushels wheat exported by the United States only 9,000,000 bushels are exchanged for German linen and the remaining 1,250,000 bushels are sent to Germany as the commodity equivalent of a compulsory tribute of $1,000,000. The United States thus surrenders 10,250,000 bushels wheat and receives 9,400,000 yards linen, with the ratio therefore, approximately 10 bushels wheat for 9.2 yards linen. This last ratio is Taussig's gross barter terms of trade.

It is appropriate, perhaps, to make allowance in an index of gain from trade for unilateral transactions, or transactions without offsets on the other side, if such gains or losses can be properly attributed—which for most cases of unilateral transactions seems doubtful—to foreign trade as their source or occasion.*63 But to use the statistics of commodity exports and imports as the basis for calculating the gross barter terms of trade would in practice be liable to lead to seriously misleading results. Such procedure would lead to treatment as unilateral transactions of commodity exports or imports whose compensating import or export had taken place in the past—as in the case of exports whose cash proceeds are used to liquidate old indebtedness—or would take place in the future—as in the case of import surpluses constituting an import of borrowed capital—or took the form of an "invisible" import or export of services not recorded in the commodity trade statistics.*64 It would seem, therefore, that, as Haberler suggests, allowance should be made separately for unilateral transactions, instead of incorporating them in the terms of trade index.

A further limitation of the terms of trade as an index of the amount of gain from trade, to which all the concepts of terms of trade differentiated above are subject, is that the terms of trade indices relate of a unit of trade and therefore fail to reflect whatever relationship there may be between the total gain from trade and the total volume of trade. But if whatever concept of terms of trade is used is accepted as a satisfactory index of the trend of gain from trade per unit of trade, multiplication of the terms of trade index by a physical index of the volume of trade will give an index of the total amount of gain from trade. For example, if we accept the commodity terms of trade as an index of amount of gain per unit of trade, and write Q for volume of trade, our index of total gain from trade would be

One advantage of a total gain index over a unit gain index would be that it would clearly show that an increase in the total amount of gain from trade was consistent with an unfavorable movement in the index of unit gain from trade if the unfavorable change in the latter was associated with an increase in the volume of trade.*65

Terms of Trade and the International Division of Gain from Trade.

J. S. Mill seems to have believed that the commodity terms of trade, taken in conjunction with its comparative costs, provided a criterion of the proportions in which the total gain from the trade of a particular country with the outside world was divided between that country and the rest of the world. He did not state clearly how he would determine the proportions in any particular case, given the actual terms of trade and the two limiting sets of cost ratios, but in one illustrative case, where costs of producing cloth and linen were in the ratio of 15:10 in England and of 20:10 in Germany, and where the actual terms of trade were 10 English cloth for 18 German linen, Mill says that "England will gain an advantage of 3 yards on every 15, Germany will save 2 out of every 20."*66 Cournot interprets this passage as postulating that England has a gain of 20 per cent and Germany a gain (or economy) of 10 per cent, although no percentages appear in Mill's text. He points out, first, as ground for rejecting this mode of measuring the comparative gain from trade of two countries, that if one of the commodities could not be produced in England at any cost the English percentage of gain from trade would be infinite. He proceeds to a further criticism on mathematical grounds, which seems to me both unimportant of itself and irrelevant to Mill's position unless it can be shown that Mill thought that England and Germany would, in his illustration, divide the gains from trade in the proportions of 20 and 10. Cournot says that it would be equally legitimate to hold that England as the result of trade gets 15 yards of linen for 8 1/3 yards of cloth instead of for 10 yards of cloth, a saving of 16 2/3 per cent, while Germany obtains, as the result of trade, 11 1/9 yards of cloth instead of 10 yards of cloth, for 20 yards of linen, a gain of 11 1/9 per cent. Measured this way, the ratio of the English to the German gain is 16 2/3: 11 1/3, instead of 20:10. "Or, les questions de calcul n'admettent pas de telles ambiguités. C'est qu'à vrai dire l'une et l'autre manière de compter sont purement arbitraires."*67

The real difficulty lies, however, in the inadequacy of the commodity terms of trade as a criterion of amount or division of gain from trade. The fact that, given the amount of gain, it will be expressed in different percentages of gain according to what commodity is used as the base, seems to me to present a problem which is insoluble but of no consequence.*68 It can be questioned also whether the proportions in which the total gains from trade are divided between two areas should be regarded as of much importance to either country, especially if the only procedures by which a country could divert to itself an increased proportion of the total gain should be such as would operate to reduce the absolute amount of gain it derives from trade—a not unlikely situation. If production is under conditions of varying costs, moreover, or if more than two commodities are involved, there will not be a single pair of comparative-cost ratios from which to compute the division of gain from trade. In the case of production under conditions of increasing cost, a situation is quite conceivable in which all the commodities which the respective countries import are also produced at home and in which, therefore, there are no comparative differences in marginal costs under equilibrium, but where a substantial gain from trade nevertheless accrues from all the infra-marginal units of trade.*69 In such a case, the method of computing the division of the gain from trade by comparison of the commodity terms of trade with the comparative marginal-cost ratios would be patently absurd.

Statistical Measurement of the Trend of the Terms of Trade.

Statistical attempts to measure the trend of terms of trade for actual countries and periods have been restricted to measurements of the commodity or of the gross barter terms of trade, and chiefly to measurements of the former. The problem of statistical measurements is obviously a less formidable one for these two concepts of terms of trade than for the more complex and less objective ones examined above, but even if these simpler concepts are used the necessity of choice of index number formula to be used in computing the terms of trade index presents some difficult and in some respects insoluble problems.

The writers who have constructed statistical indices of the commodity terms of trade for particular countries and periods have made use of a wide variety of index number formulae, but have as a rule either offered no explanation of their particular choice of formula or have defended it on purely statistical grounds, such as simplicity, "reversibility," or availability of data.*70 Here, as elsewhere, it would appear that the choice of a formula should be made to depend on economic as well as on purely statistical considerations.

Let us suppose that an original static equilibrium in a particular country is disturbed by capital borrowings, that no changes occur except those resulting from the borrowings, and that the question asked is: What is the effect of the borrowings on the relative prices in the borrowing country of its export and its import commodities? Let us suppose also that the type of index number of export and of import prices which should be used in constructing the terms of trade index is a weighted aggregate index. Should the quantity weights to be used in comparing the terms of trade of a pre-borrowing with a borrowing year be those of the base, or pre-borrowing, year or those of the end, or borrowing, year?*71

The proper answer depends on whether the question is asked as a question in the theory of the mechanism of international trade or as a question in the "theory of international values" or the theory of gain (and loss) from foreign trade. If the familiar proposition of the theory of the mechanism of international trade that capital borrowings tend to raise export prices relative to import prices is to be tested statistically in terms of weighted index numbers, the weights used must be the quantities exported and imported prior to the borrowings, since it is with the effect of borrowings on the relative prices of those commodities exported and imported before the borrowings that this proposition is concerned.

If what is to be tested, however, is the proposition that capital borrowings tend to improve the terms on which the borrowing country exchanges its exports for imports, the question of what type of weighting to use cannot be so readily answered. Gains to the borrowing country from the more favorable terms on which its exports are exchanged for imports can accrue only to the extent that such exchanges actually take place.*72 In computing the export and import price indices for this purpose, should the prices therefore be weighted by the quantities exported or imported when the borrowings are under way, rather than by the pre-borrowing quantities?

In a closed economy, abstracting from sampling errors, the operation of the (ordinary Marshallian) elasticities of demand will tend to cause negative correlation between the relative changes in the p's and the relative changes in the q's, if the changes in the relative prices of particular commodities are due to changes in their relative costs of production, and to cause positive correlation if the changes in the relative prices are due to relative changes in demands for particular commodities. Similarly, in foreign trade, if the changes in the export prices of our country result from changes in the relative world demands for its various export commodities, then the relative changes in the export p's and the relative changes in the export q's will tend to be positively correlated, whereas if the changes in the export prices are due to changes in the internal cost conditions, the relative changes in the p's and q's will tend to be negatively correlated. Similarly, the relative changes in the import o's and the import q's will tend to be positively correlated if they result from changes in the import demands for the various import commodities, and will tend to be negatively correlated if they result from changes in the foreign costs of production of these commodities.

But price indices based on end-year weights tend to have an upward bias as compared to price indices based on beginning-year weights if the changes in the p's and the changes in the q's are positively correlated, and a downward bias if the changes in the p's and the changes in the q's are negatively correlated. In the choice of formulae to be used in constructing the price indices on which the terms of trade index as an index of gain is to be based, there is no obvious principle to follow in choosing between beginning-year and end-year weights, since neither procedure permits a wholly satisfactory comparison of the terms on which the actual exports and imports of the two years are exchanged. If the correlation between the changes in the p' and the changes in the q's has the same sign for both exports and imports, and if the same type of weighting is used for both price indices, the terms of trade index will tend to be unaffected by the choice made between weighting methods. But if the sign of the correlation between the changes in the p's and the changes in the q's is not the same for both exports and imports, or if different methods of weighting are used for the two price indices, the terms of trade index obtained for the end-year may differ substantially with differences in the choice of weighting-method.

There may be no rational basis for choice between beginning-year weight and end-year weights in constructing an index number of terms of trade where the problem consists of determining the effect of a particular disturbance on terms of trade in the "gain" sense. Comparison of the results obtained by the alternative methods of weighting in particular cases may be made, however, to serve as a check on the conclusions otherwise reached as to the nature of the disturbance. The type of correlation between the changes in the p's and the changes in the q's for the exports and the imports, respectively, and, therefore, the direction of the biases in the two price indices when based on end-year as compared to when based on beginning-year weights, should depend on the nature of the disturbance.

This reasoning can be illustrated by reference to the problem of the influence of capital borrowings on the terms of trade of the borrowing country. It has been argued above that capital borrowings tend to result in a rise in export prices and a fall in import prices in the borrowing country, not because of a relative shift in tastes whether in the world as a whole or within the borrowing country in favor of the export commodities of the borrowing country, but because of a relative rise in the money costs of production of the products of the borrowing country as compared to the commodities it imports. If this reasoning is correct, we should expect to find the changes in the export p's and q's of the borrowing country to be negatively correlated, and its export-price index number for the end-year should be higher, therefore, if beginning-year weights are used than if end-year weights are used. If the export prices had risen primarily because of a rise in the world demand for the export commodities, the reverse results should be expected. Similarly, in the case of the import commodities, we should expect capital borrowings to result in negative correlation between the changes in the p's and the changes in the q's, and the import price index number, to be higher, therefore, for the end-year when beginning-year weights are used than when end-year weights are used; whereas if the changes in the import prices had resulted primarily from changes in the tastes of the population of the capital-borrowing country, the reverse result should be expected.

In my study of the Canadian experience under heavy capital borrowings, 1900 to 1913, I found that an export price index based on beginning-year weights rose to 135.6 in the end-year, as compared to 120.2 for an export-price index based on end-year weights, and that almost without exception the commodities whose exports constituted an increased proportion of the total Canadian export trade at the end as compared to the beginning of the period were commodities whose prices had risen by less than the average rise in export prices as a whole. These results are hard to explain for a small country, which would naturally tend to push most vigorously its exports of those commodities which had risen most in price, except on the theory that the rise in Canadian export prices relative to world price levels was the result primarily of a rise in Canadian production costs. I found confirmation of this theory in the fact that in general the commodities which did not clearly reveal the restrictive effect on Canadian exports of the general upward trend of money costs in Canada were commodities whose costs, because of conditions special to these commodities such as production from newly-discovered or newly-developed natural resources, escaped in part at least the general upward trend. Lack of necessary information prevented similar analysis of the import price trends for Canada. Studies by other writers of the effect of capital borrowings or other disturbances on relative prices have not treated these problems*73 and as a rule have dealt with cases where the disturbance was too small to be expected to have a clearly traceable effect on the price trends. The problem deserves further investigation, especially by the experts in index-number technique.

IV. "NET BENEFIT" IN INTERNATIONAL TRADE: MARSHALL

In what is in substance an attempt to find an objective counter-part for total utility analysis, Marshall applied to the problem of gain from trade a concept analogous to his concept of consumer's surplus.*74 Marshall here uses the terms "surplus" or "net benefit" instead of "consumer's surplus," perhaps because his procedure in his international trade analysis is supposed to account for "producer's surplus" as well as for "consumer's surplus." In chart XVI,*75 OG is country G's reciprocal-demand curve, and under equilibrium OH units of G's commodity are exchanged for OB units of the commodity of the other country, E. OR is the tangent to OG at O, intersecting BA produced at R. Through P, any point on OG, draw OPp to cut BR in p; and produce MP to P¹, so that, M¹ being the point at which it cuts HA, M¹P¹ may be equal to AP. Then G is willing to pay for the OMth E-bale at the rate of PM G-bales for OM E-bales: i.e., at the rate of pB G-bales for OB E-bales. Country G therefore obtains a surplus on the OMth bale at a rate which if applied to OB bales would make an aggregate surplus of AP G-bales, or M¹P¹ G-bales. Thus her surplus on that OMth E-bale is equal to . If P, starting from O, is made to move along OG, then P¹ will start from U, the foot of the perpendicular drawn from R on OY; and it will trace out a curve UP'A ending at A. Then the aggregate surplus or net benefit which G derives from her trade will be an OBth part of the aggregate of the lines M¹P¹ as P¹ passes from U to A: that is, it will be an OBth part of the area UHA. Draw VW parallel to OX, so that the rectangle VHAW is equal to the area UHA. Then will be country G's net benefit from trade, measured in G-bales.*76

Marshall reaches these results by virtue of an interpretation of the reciprocal-demand curves which seems to me invalid. He assumes that since country G would have been willing to take an OMth E-bale at the rate of Bp G-bales for OB E-bales, but actually gets the OMth bale—as all the other bales—at the rate of AB G-bales for OB E-bales, Ap/OB G-bales represents the surplus on the OMth E-bale. But this assumes that country G would have been willing to take an OMth E-bale at the Bp/OB terms even if she had already purchased (OM-1) E-bales at terms less favorable than Bp/OB and it assumes similarly that country G would be willing to take an OBth bale at the AB/OB terms if she had already purchased (OB-1) E-bales at terms less favorable than AB/OB; i.e., it assumes that the rate at which earlier E-bales were actually obtained will not affect the rate at which country G would be willing to buy additional E-bales. The marginal utility to G of the G-bales she still retains will, however, be greater the greater the number of G-bales she has already surrendered, and, therefore, the amount country G would be willing to pay for an OBth E-bale, when all the OB bales are procured at the same price in G-bales, AB/OB, must be greater than the price she would be willing to pay for an OBthe E-bale, when all the preceding (OB-1) E-bales had been paid for at prices in G-bales higher than AB/OB. All of Marshall's M¹P¹'s, therefore, except the initial one UH, and consequently also the aggregate surplus for country G, are made by Marshall to appear greater than they would be if correctly computed. This exaggeration of the amount of surplus is inherent in Marshall's method of computing it, which is capable of producing such improbable results as a surplus, measured in G-bales, many times greater than the total amount of G-bales actually exported, and—if the OG curve is inelastic—may produce such meaningless results as a surplus, measured in G-bales, greater than the total amount of G-bales which G can produce.

Correctly to determine the consumer's surplus measured in G-bales, it is necessary to go behind G's reciprocal-demand curve to her utility functions with respect to the G- and the E-commodities. Assuming this information to be available, we can proceed as in chart XVII, where the dotted lines and curves are a reproduction of chart XVI, included for comparative purposes only. By a procedure analogous to Marshall's, we can draw the curve OG_1, such that at any point on it, P_1, P₁M/OM or p₁B/OB represents the number of G-bales which country G would be willing to give for an OMth E-bale, when it had already bought (OM-1) E-bales at the maximum prices in G-bales for each successive E-bale which it would have been willing to pay, if necessary, given the prices at which the preceding purchases had been made. Except for the common point of origin, O, the OG₁ curve would be lower at every point, with respect to the OX axis, than the reciprocal-demand curve, OG, at the corresponding points. On MP¹ mark off, from M^1, M¹P₁¹ = Ap_1, where Ap₁/OB equals the excess or deficiency in G-bales of what country G would be willing to pay for an OMth E-bale if all the preceding E-bales had already been purchased at the maximum prices country G was willing to pay, over the price actually paid, or AB/OB. If P_1, starting from O, is made to move along OG_1, then P₁¹ will start from U and trace out a curve ending at A_1, the point at which the OG₁ curve cuts BR. The aggregate surplus will then be SAA₁/OB representing what the sum of the deficits on the purchases beyond the S₁ point would have amounted to if each unit of E-bales in turn were assumed to have been paid for at the AB/<