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• Preface
• Studies In the Theory of International Trade
• Chapter I: English Theories of Foreign Trade, Before Adam Smith: I
• I. Introduction
• II. “ Mercantilism” and “bullionism”
• III. the Balance-of-trade Doctrine
• IV. Reasons For Wanting More Bullion
• V. Employment and the Balance of Trade
• Chapter II: English Theories of Foreign Trade, Before Adam Smith: Ii
• I. Legislative Proposals of Mercantilists
• II. the Collapse of Mercantilist Doctrine
• III. Some Modern Interpretations of English Mercantilism
• Chapter III: The Bullionist Controversies: I. The Inflation Phase
• I. the Participants In the Controversy
• II. the Factual Background
• III. Premium On Bullion As Evidence of Excess Issue: the Bullionist Position
• IV. Qualifications Conceded By the Bullionists
• V. Possible Objections to the Bullionist Position
• VI. the Anti-bullionist Position
• VII. the Balance of Payments Argument
• VIII. the Possibility of Excess Issue By Banks
• IX. Responsibility For the Excess Issue: Bank of England Vs. Country Banks
• X. Responsibility For Excess Issue: the Credit Policy of the Bank of England
• Chapter IV: The Bullionist Controversies: II. The Deflation Phase
• I. the Resumption of Cash Payments
• II. Responsibility of Resumption For the Fall In Prices
• III. the Economic Effect of Changing Price Levels
• IV. Ricardo's Position On the Gold Standard
• V. Reform Without Departure From the Metallic Standard
• VI. Paper Standard Currencies
• Chapter V: English Currency Controversies, 1825–1865
• I. Introduction
• II. the “currency School” -“banking School” Controversy
• III. the “palmer Rule ”
• IV. the Bank Act of 1844
• V. the Possibility of Overissue of Convertible Bank Notes
• VI. the Role of Deposits, Bills of Exchange, and “credit” In the Currency System
• VII. the Technique of Credit Control
• VIII. the Relation Between Bank of England Operations and Specie Movements
• IX. Currency Reform Proposals
• Chapter VI: The International Mechanism Under a Simple Specie Currency
• I. Introductory
• II. the Mechanism According to Hume
• III. an Omitted Factor? Relative Changes In Demand As an Equilibrating Force
• IV. Prices In the Mechanism: the Concept of “price Levels ”
• V. the “terms-of-trade” Concept
• VI. the Prices of “domestic” Commodities
• VII. the Mechanism of Transfer of Unilateral Payments In Some Recent Literature
• VIII. a Graphical Examination of Pigou's Analysis 1
• IX. Some Elaborations On the Basis of Pigou's Analysis
• X. an Alternative Solution
• XI. Types of Disturbance In International Equilibrium
• XII. Specie Movements and Velocity of Money
• XIII. Commodity Flows and Relative Price Levels
• XIV. Exchange Rates
• XV. A Criticism of the Purchasing-power Parity Theory 1
• Chapter VII: The International Mechanism In Relation to Modern Banking Processes
• I. Automatic Vs. Managed Currencies
• II. Primary and Secondary Expansion of Means of Payments
• III. Short-term Loans In the International Mechanism
• IV. Primary and Secondary Expansion In Canada , 1900–13
• V. the International Mechanism and Business Cycles
• Chapter VIII: Gains From Trade: the Doctrine of Comparative Costs
• I. the Nature and Origin of the Doctrine
• II. the Division of the Gain From Trade
• III. Trade In More Than Two Commodities
• IV. Trade Between More Than Two Countries
• V. Transportation Costs
• VI. Increasing and Decreasing Costs
• VII. Prices, Money Costs, and Real Costs
• VIII. Dependence of Comparative Cost Doctrine On a Real-cost Theory of Value
• IX. Differences In Wage Rates In Different Occupations
• X. Variable Proportions of the Factors and International Specialization
• XI. Variable Proportions of the Factor and Comparative Real Costs
• XII. “ Opportunity Cost” Analysis As a Substitute For Real Cost Analysis
• Chapter IX: Gains From Trade: the Maximization of Real Income
• I. “ Mass of Commodities” and “sum of Enjoyments”: Ricardo and Malthus
• II. Reciprocal Demand and the Terms of Trade
• III. Terms of Trade and the Amount of Gain From Trade
• IV. “ Net Benefit” In International Trade: Marshall
• V. Total Net Utility Derived From International Trade: Edgeworth
• VI. the Gain From Trade Measured In Money
• Appendix: a Note On the Scope and Method of the Theory of International 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.1 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.2 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.” 3 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.” 4

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,” 5 and Graham makes substantially the same criticism.6 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.” 7 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:8

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 cases9 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.10 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.11 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.12 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.13 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.14 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.15 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.” 16

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.17

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.” 18 Marshall applies his conclusions only to curves of the “normal” type, i.e., curves whose “demand elasticities” in my terminology are greater than unity,19 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

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.20

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.21 Of special interest is his diagram22 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.23 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.24

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.25 Some of his criticisms have already been examined.26 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.27

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. ...” 28

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.29

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.30

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).31

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.32

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.33 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.34

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.35

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.36 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.37 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.

[1]Mill first presented his analysis in Essay 1 of his Essays on some unsettled questions of political economy, written in 1829–30, when he was twenty-three years of age, but not published until 1844. He reproduced it, with extensions, but also with important omissions, in the first edition (1848) of his Principles of political economy, bk. iii, chap. xviii, “Of international values.” Edgeworth could not find terms of praise too high for this chapter; it was a “great chapter” (Papers relating to political economy, 1925, II, 7), a “stupendous chapter” (ibid., II, 10, 20), and an exposition of the general theory which was “still unsurpassed” (ibid., II, 20). Graham, on the other hand, declares that it presents doctrine which is “in its essence fallacious and should be discarded.” —“The theory of international values,” Quarterly journal of economics, XLVI (1932), 581.

[2]Graham's heaviest criticisms are directed against Mill's alleged error in assuming that the conclusions derived from this simplified case had general validity. Cf. supra, pp. 453–54.

[3]Mill does not seem to have used this term, whose first use is commonly attributed to Torrens.

[4]Cf. Mill, Principles, Ashley ed., p. 592: The law ... may be appropriately named the equation of international demand. It may be concisely stated as follows. The produce of a country exchanges for the produce of other countries at such values as are required in order that the whole of her exports may exactly pay for the whole of her imports. 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.

[5]J. L. Shadwell, A system of political economy, 1877, p. 406.

[6]“Theory of international values,” Quarterly journal of economics, XLVI (1932), 606.

[7]Bastable, Theory of international trade, 4th ed., 1903, p. 180.

[8]J. S. Mill to Cairnes, June 23, 1869, The letters of John Stuart Mill, H. S. R. Elliot ed., 1910, II, 207. (Italics in the original text.) Mill's reasoning here is clear enough, and sound enough, if it is remembered that, like all the earlier English economists, Mill distinguished in his thinking, even if not in his terminology, between “demand” as a quantity actually taken at a particular price and “demand” as a schedule of quantities which would be taken at different prices.

[9]Principles, Ashley ed., pp. 585–88, 594–95.

[10]Cf. Edgeworth, “On the application of mathematics to political economy,” Journal of the Royal Statistical Society, LII (1889), 557, fig. 3, for a similar demonstration by means of a Marshallian diagram.

[11]The differences in the methods of constructing Marshall's and my curves do not call for differences in the elasticity formulae, if the same symbols are used to represent the same variables in the two diagrams. In both diagrams each curve can be regarded either as a demand curve or as a supply curve, each with a distinct elasticity coefficient. There will thus be a total of four elasticities. Write X for the total amount of E-goods, Y for the total amount of G-goods, the subscripts E and G for the countries England and Germany respectively, y = Y/X for the price of E-goods in G-goods, and 1/y = X/Y for the price of G-goods in E-goods. Then if eDE is the elasticity of English “demand” or willingness to buy German goods, eSE is the elasticity of English willingness to sell English goods, eDG is the elasticity of German willingness to buy English goods, and eSG is the elasticity of German willingness to sell German goods, then:

The demand elasticity and the supply elasticity of each country are of course closely related to each other, as they are but different aspects of the same phenomenon. The relationship between the two elasticities for England can readily be shown:

Similarly,

When the coefficient of demand elasticity of a country is unity, therefore, thecoefficient of its supply elasticity is zero. In the text, reciprocal-demand curves are referred to as “elastic” if the coefficient of their demand elasticity is numerically greater than unity and of their supply elasticity is algebraically greater than zero and as “inelastic” if the coefficient of their demand elasticity is numerically smaller than unity and of their supply elasticity is algebraically smaller than zero.

Although expressed in different terms, this usage corresponds to Marshall's use of the terms “elastic” and “inelastic” in connection with his reciprocal demand curves. (Cf. Marshall, Money credit & commerce, pp. 337–38, note.)

[12]Mill, Principles, Ashley ed., pp. 596–604.

[13]Cf. Marshall, Money credit & commerce, p. 354, note 3.

[14]Cf. letter from Marshall to Cunynghame, June 28, 1904; “As to international trade curves:—mine were set to a definite tune, that called by Mill.” (Memorials of Alfred Marshall, A. C. Pigon ed., 1925, p. 451.)

[15]Marshall's analysis is available in his The pure theory of foreign trade (printed for private circulation in 1879, reprinted in 1930), and his Money credit & commerce (published in 1923, though in the main written much earlier), bk. III, and appendices H and J.

[16]The pure theory of foreign trade, p. 2.

[17]Marshall, Money credit & commerce, p. 178.

[18]Graham, “The theory of international values,” Quarterly journal of economics, XLVI (1932), 601.

[19]Cf., supra, p. 539, note II, and Marshall, loc. cit., p. 342.

[20]Cf. Money credit & commerce, p. 343, fig. 12.

[21]F. Y. Edgeworth, “The pure theory of international trade,” in Papers relating to political economy, 1925, II, 31–40 (first published in Economic journal, 1894, in substantially the same form).

[22]Papers, II, 32.

[23]His diagram is drawn on too small a scale to make this certain, but the absence of any statement to the contrary in his text and the fact that in all his other diagrams his reciprocal demands are drawn curvilinear from their point of origin warrants this interpretation.

[24]Cf. supra, chart X, p. 468, for a terms-of-trade diagram drawn with reference to these considerations.

Edgeworth states that if production is not under conditions of constant cost, “there should be substituted for the straight line OS (and mutatis mutandis for OT) a curve of constant advantage, or indifference-curve (not shown in the figure) representing states for which the advantage to England is no greater than if there had been no trade.” (Papers, II, 33.) He must mean a curve representing states for which the importation of an additional unit of the G-good by country E would be no more advantageous than its production at home, if this curve is to be the analogue for variable costs of his OS line. In chart XV, OS is not a “no-gain from trade” curve, but is a curve of “no-gain from import as compared to domestic production of the G-good.” If country E were to export more than OL units of E-goods at the

terms—or even on terms more favorable to itself—it might be incurring a loss from undue specialization of the sort discussed in the preceding chapter. (See supra, p. 451.) The location in the chart of a “no-gain from trade” curve requires knowledge of the utility functions as well as of the cost conditions. It would never fall below the OS line (or, in the case of variable costs, the OS' curve) and would never rise as high as the OE curve. (See infra, p. 572.) I have inserted in chart XV a “no-gain from import as compared to domestic production of the G-good” curve, OS', applicable to conditions of increasing costs. At any point, b, on OS', the slope with respect to OX of a tangent to OS' at that point represents the number of units of G-goods which could be produced at home by country E at a cost equal to the cost of producing a unit of E-goods in addition to what would be its output of E-goods if it was exporting Od E-goods in exchange for db G-goods. (The slope with respect to OX of the tangent to OE at a represents the number of units of G-goods per unit of E-goods in which country E would be willing to export Od units of E-goods.) Since production is under conditions of increasing cost, the number of units of the G-good which country E could produce at the same cost as an additional unit of the E-good will be greater, the greater its output of E-goods. As OS' is drawn concave upward in chart XV, it is implicitly assumed that increased export of E-goods involves increased output of E-goods, i.e., that as more E-goods are exported, the domestic consumption of E-goods decreases, if at all, by a smaller amount than the increase in exports. The OS' curve must be drawn below the OE curve at all points, and the identity of the two curves from O to C in chart XV is an error. Since in country E, for each output of E-goods corresponding to a given export by it of E-goods, its relative marginal costs of production of E-goods and G-goods must correspond to its supply-price of E-goods in terms of G-goods, a tangent to the OS' curve at any point must be parallel to a vector drawn from O to the vertically corresponding point on the OE curve. This excludes the possibility of identity of the two curves for any part of their course.

[25]“The theory of international values re-examined,” Quarterly journal of economics, XXXVIII (1923), and “The theory of international values,” ibid., XLVI (1932).

[26]Supra, pp. 453 ff. and 536 ff.

[27]“Theory of international values re-examined,” loc. cit., p. 86.

[28]“Theory of international values,” loc. cit., pp. 583–84.

[29]The nearest approach to this proposition that I have found in the literature is the following, by Haberler: “Marshall employs ... so-called reciprocal supply-and-demand curves. This theory forms an essential supplement to the theory of comparative costs; indeed, the latter, if carried through to its logical conclusion, merges into the former.” (The theory of international trade, 1936, p. 123.)

[30]Marshall, Money credit & commerce, p. 171.

[31]Edgeworth, Papers, II, 33. The sentence placed in parentheses appears in the original as a footnote.

[32]Cf., for instance, Graham's illustration (“Theory of international values re-examined,” loc. cit., p. 76) and the accompanying text, where it is assumed “that before international trade is opened up, each country devotes one third of its resources to each of the three products, and that each increases its consumption of the three products proportionately as it secures gains from international trade” (p. 70) even though important changes in relative prices are assumed to take place. With the additional information given as to the economic size of the countries, their cost conditions, and the prices within each country before trade, Graham is justified in his claim that the data given suffice to determine within narrow limits the equilibrium terms of trade when foreign trade is opened up. But he fails to substantiate his claim that it is the cost conditions alone which determine the terms of trade. If the cost conditions are left unchanged but his utility assumptions altered, the equilibrium terms of trade can be changed, within broad limits, in whatever degree and direction is desired.

The same criticism applies to the interpretation given by C. F. Whittlesey—“Foreign investment and the terms of trade,” Quarterly journal of economics, XLVI (1932), 449, 459—of results similar to Graham's obtained from arithmetical illustrations involving similar assumptions.

Whereas Graham criticizes the writers in the classical tradition for minimizing the influence of comparative costs on the terms of trade, Angell criticizes them for their alleged belief that comparative costs “in themselves alone, provide a sufficient a prior explanation of the course and terms of trade.” (Angell, Theory of international prices, 1926, pp. 371–73.)

[33]Cf. “Theory of international values,” loc. cit., p. 604: “If both demand schedules were elastic, movements in the terms of trade must necessarily be small.”

[34]Graham, “Theory of international values,” loc. cit., pp. 582–83. (Italics are in the original.)

[35]Ibid., p. 583.

[36]Cf. A. C. Pigou, Essays in applied economics, 1930, p. 150: The value of imports in general in terms of exports in general is a notion of exactly the same sort as the value of things in general in terms of money. No precise significance can be given to this notion, and no completely satisfactory measure of changes in it can be devised.

[37]I.e., of what I call the “double factoral terms of trade.” See infra, p. 561.