Front Page Titles (by Subject) IV. Net Benefit in International Trade: Marshall - Studies in the Theory of International Trade
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IV. “ Net Benefit” in International Trade: Marshall - Jacob Viner, Studies in the Theory of International Trade 
Studies in the Theory of International Trade (New York: Harper and Brothers, 1965).
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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 OG1, such that at any point on it, P1,
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 M1,M1P11 = Ap1, 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 P1, starting from O, is made to move along OG1, then P11 will start from U and trace out a curve ending at A1, 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 — SAA1, 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
Marshall, Money credit & commerce, 1923, pp. 160–63, 338–40.
Chart XVI is a slightly simplified reproduction of Marshall's fig. 9, ibid., p. 339.
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.
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.
Ibid., p. 149.
Ibid., p. 150.
And, it should be noted, taking account simultaneously of “producer's rent,” which the domestic-trade theory concept does not do.
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.