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. 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. 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.” 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.”

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,” and Graham makes substantially the same criticism. 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.” 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:

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 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. 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. 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 equilbrium that the value of imports should equal the value of exports would be met. 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. 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. 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. 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.”

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.

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.” Marshall applies his conclusions only to curves of the “normal” type, i.e., curves whose “demand elasticities” in my terminology are greater than unity, 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.

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. Of special interest is his diagram 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. 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.

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. Some of his criticisms have already been examined. 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.

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. ...”

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.

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.

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).

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.

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. 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.

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.

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. 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. 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.