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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

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.1 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,2OG 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.3

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,

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

terms even if she had already purchased (OM—1) E-bales at terms less favorable than

and it assumes similarly that country G would be willing to take an OBth bale at the

terms if she had already purchased (OB—1) E-bales at terms less favorable than

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,

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

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-com modities. 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,

or

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—I) 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

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

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

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

terms after each preceding E-bale had been paid for at the maximum price in G-bales which E would have been willing to pay, if necessary, given the prices at which the preceding purchases had been made. If V₁W₁ is drawn so as to make the rectangle V₁HAW₁ = the area UHS — SAA_1, then the aggregate surplus of country G, measured in G-bales, will be V₁H, which is necessarily less than VH.

While the amount of surplus for country G will, therefore, necessarily be smaller than VH in chart XVI, it will increase with any decrease in the price of E-bales in terms of G-bales, provided this decrease in price is not the result of a change in country G's utility curves for G-goods or for E-goods—provided, that is, that it is not the result of a change in the OG curve—and if the OG₁ curve is known it will be possible to determine the amount of change in surplus. Changes in VH will normally be in the same direction, though not in the same degree, as changes in V₁H when the changes in the commodity terms of trade are not the result of changes in OG. For such changes, therefore, the effects on the surplus of country G, measured in G-bales, would be the same in direction, but would be smaller in degree, if determined by the method here presented than if determined by Marshall's method. If Marshall's “surplus” is accepted as a measure of gain, Marshall's method will therefore produce results which for such changes are qualitatively right though quantitatively wrong.

Allyn Young,4 however, claimed that Marshall's consumer's surplus was a wholly unusable concept in international-trade theory: “consumer's surplus, as Marshall measures it, is not additive. Its sum, for any one consumer, comes precisely to zero”;5 the objections against use of the concept are even stronger in the field of international trade theory than in the field of domestic trade theory.6

It is a familiar objection against Marshall's concept of consumer's surplus as used by him in domestic-trade theory, and an objection whose validity he conceded, that it is not “additive”; i.e., that the surpluses as computed by him for separate commodities cannot simultaneously exist. But in international-trade theory, Marshall posits only one surplus, that associated with the foreign trade as a whole.7 The surplus, moreover, is in international-trade theory measured in commodities having a direct utility of their own—or representing primary disutility—so that it cannot be said of G-bales, as it can of money, that their utility is merely a reflection of the utility of what can be obtained in exchange for them, and that the two utilities must therefore be equal.8

[1]Marshall, Money credit & commerce, 1923, pp. 160–63, 338–40.

[2]Chart XVI is a slightly simplified reproduction of Marshall's fig. 9, ibid., p. 339.

[3]The above is Marshall's exposition (ibid., p. 339) reproduced verbatim except for the modifications made necessary by my modification of his chart and except for a few minor verbal changes in the interest of clarity.

[4]Allyn Young, “Marshall on consumer's surplus in international trade,” Quarterly journal of economics, XXXIX (1924), 144–50. The main theme of this article, however, was not the validity of the consumer's-surplus notion, which was discussed only incidentally, but some apparent errors in computation in Marshall's arithmetical illustration.

[5]Ibid., p. 149.

[6]Ibid., p. 150.

[7]And, it should be noted, taking account simultaneously of “producer's rent,” which the domestic-trade theory concept does not do.

[8]In the consumer's-surplus concept, as modified here, it is true, however, that with every change in the amount of surplus measured in G-bales as we move along the OG curve from O, there occurs a change in the average utility significance of a G-bale if no change has meanwhile occurred in G's utility functions. What the direction of this change will be will depend on the elasticity of the OG curve, i.e., on whether a movement along the OG curve from O (and therefore an increase of surplus) is associated with an increase or a decrease in the amount of G-bales expected.