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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

IX. Some Elaborations on the Basis of Pigou's Analysis

Duties on imports, however, whether levied by the paying or the receiving country, and a fortiori when levied by both, do tend to result in higher initial utilities in each country for native than for imported commodities, and although they also tend to result in an excess of expenditures on native over expenditures on foreign commodities, they operate to make reparations turn the terms of trade in favor of, instead of against, the paying country. Import duties, regardless of which country levies them, operate to make the imported commodity relatively dearer than the native commodity in each country, as compared to what the situation would be in the absence of the duties. If in each country the units of the two commodities are so chosen as to be equal in price before the imposition of the duty, then, with the units used for the English commodity in England and the German commodity in Germany left unaltered, after the imposition of the duty the size of the unit used for the German commodity in England and the size of the unit used for the English commodity in Germany will both have to be decreased if the units used for the two commodities within each country are to be kept equal to each other in price. In terms of the graphical illustrations here used, it will follow that the initial utility of the imported commodity will be lower in each country after the duty than before, the initial utility of the native commodity remaining unaltered. A situation with respect to “dissimilarities” of the utility functions within each country corresponding in kind to that illustrated in chart IV will thus tend to result.

This reasoning is illustrated, for the case of an English import duty, in chart V. It is there assumed that initially there are no trade restrictions in either England or Germany, that there are no “domestic” commodities, and that in each country the representative consumer spends as much on imported as on native commodities. It is also assumed that in each country the utility functions are linear and originally “similar,” so that when commodity units are so chosen as to be equal in their original prices, the utilities of initial units are also equal. Then so that Germany could make reparations payments to England without affecting the terms of trade.

Suppose, however, that before the obligation to pay reparations comes into effect, England imposes a revenue import duty of 50 per cent ad valorem on the German commodity. Let us assume that as a result the price of the German commodity to the English consumer rises by one-third relative to the price of the English commodity, i.e., one unit of the English commodity now has the same price in England as three-fourths of a unit of the German commodity, duty-paid. If, while the unit used for the English commodity in England is left unchanged, a new unit three-fourths as large as the old one is now used for the imported commodity so as to make units of the two commodities equal in value at the new relative prices, there will be a new utility function, a'c', for the imported commodity, with oa' 75 per cent of oa, and oc' 33 ⅓ per cent greater than oc.

If the levy of a 50 per cent duty on the German commodity

causes its price in England duty-paid to rise by one-third relative to the price of the English commodity in England, then in Germany, with units unchanged, the price of the English commodity must rise one-eighth relative to the price of the German commodity, i.e., one unit of the German commodity now has the same price in Germany as eight-ninths of a unit of the English commodity.1 If the unit used for the German commodity in Germany is left unchanged, but a new unit eight-ninths as large as the original one is now used for the English commodity in Germany so as to make the units of the two commodities equal in value at their new relative prices, there will be a new utility function, a'₁c'₁, for the English commodity in Germany, with o₁a'₁ eight-ninths of o₁a₁, and o₁c′₁ nine-eighths of o₁c₁. Since ⊘' and F' are now both smaller numerically and therefore greater algebraically than they were before the imposition of the duty, while ƒ′ and ψ′ are unaltered, therefore in the new situation, and, even in the case illustrated by chart V, where the imposition of the duty causes the representative consumer in each country to spend more on native than on imported commodities,2 the levy of the duty creates a situation in which reparations payments would make the terms of trade turn in favor of Germany.

It can be similarly shown that export taxes levied by either or both countries and an excess of international over internal transportation costs for the commodities of either or both countries, even when they result in an excess in each country of expenditures on native over expenditures on foreign commodities, by tending to make native commodities relatively cheap in each country and thus tending to make the initial utility of native commodities greater in each country than the initial utility of imported commodities of equal price, tend likewise, given linear functions, to create a situation in which reparations payments will turn the terms of trade in favor of the paying country. Export or import subsidies, granted by either or by both countries, and an excess of internal over international transportation costs for the commodities of either or both countries, tend, on the other hand, by making native commodities dear in each country relative to imported commodities, to create a situation in which reparations will turn the terms of trade in favor of the receiving country in spite of an excess in each country of expenditures on foreign over expenditures on native commodities.

The existence of “domestic” commodities also operates to create a presumption that reparations payments will turn the terms of trade against the paying country, but in this case by increasing the proportion of expenditures in each country on native commodities without affecting the relative utilities of initial units of native and imported commodities. To adapt Pigou's analysis to the existence of domestic commodities, the utility functions for a representative consumer of the products of his own country must be interpreted as representing the marginal utility curve of a composite commodity made up of one or more units of each of the different native commodities, with the units so chosen as to be equal in pre-reparations price, and with the number of units of each commodity entering into the composite commodity made proportional to their respective importance in domestic consumption. If the assumptions of constant costs and of similarity and linearity of utility functions for “representative” consumers are adhered to, and if the possibility that reparations payments may change the identity of the “representative” consumer is disregarded, the weighting of the different native commodities in making up the composite native commodity presents no difficulty, since under these assumptions relative variations in the prices or the volume of consumption of the constitutent items of the composite native commodity cannot result merely from a change in the total expenditures of the representative consumer. The introduction in either country of domestic commodities will operate with respect to that country to reduce the slope of the curve of marginal utility to a representative individual of the composite native commodity, i.e., the existence of domestic commodities will operate to reduce the relevant ƒ′ and/or ψ′. Since and it follows, therefore, that where there are only two countries, the existence of “domestic” commodities in either country will tend to make and therefore will tend to make reparations payments turn the terms of trade against the paying country.

If either of the countries is incompletely specialized, i.e., if it imports a portion of its consumption of some commodity, say cloth, which it also produces at home, a special case arises where the ratio of to does not suffice to determine the effect of reparations on the terms of trade even on the assumptions of linearity and “similarity” within each country of the various utility functions. Regardless of the ratio of to the incompletely specialized country, whether it be the paying or the receiving country, can check any tendency for the terms of trade to move against it by cutting down on its exports and shifting the productive resources thus freed to the production of cloth. Under constant costs the prices of other foreign commodities could not rise relative to cloth as long as cloth was still being produced abroad, and the prices of other native commodities could not fall relative to cloth as long as more cloth could be produced at home. Before the terms of trade could turn against the country which before reparations had been incompletely specialized, it would be necessary therefore that she should be producing nothing except (“domestic” commodities and) cloth and that the other country should have completely abandoned the production of cloth.3

If the assumption of linearity of the utility functions is abandoned the solution of the problem becomes much more difficult. But in the two-country case, the departures from linearity are as likely a priori to be in directions strengthening the presumption that reparations payments will cause the terms of trade to turn against the paying country as to weaken it, and Pigou has shown in effect that if is much greater numerically than it will take substantial deviations from linearity in directions working favorably for the terms of trade of the paying country to keep reparations payments from turning the terms of trade against her.4

The use of the concept of a “representative” German or Englishman in utility analysis raises familiar difficulties. Its use in this particular problem involves a tacit evasion of the difficulty arising if the payment of reparations results in a redistribution of the available spending power within either or within both communities of such a nature that the individual who could reasonably be taken as “representative” before the payments began was no longer “representative” after they had begun. Any redistribution in spending power in Germany resulting from the making of reparations payments would operate to make the terms of trade move unfavourably or favorably to Germany according as the reduction in spending power fell relatively more heavily or less heavily on individuals for whom, as compared to other Germans, the ratio, or the ratio of the slope of their utility curve for German goods to the slope of their utility curve for English goods, was large or small numerically. Similarly, any redistribution in spending power in England resulting from the receipt of reparations payments would operate to make the terms of trade move favourably or unfavourably to Germany according as the increase in spending power accrued more heavily or less heavily to individuals for whom, as compared to other Englishmen, the ratio, or the ratio of the slope of their utility curve for German goods to the slope of their utility curve for English goods, was small or large numerically. In the absence of special information, it is hard to see any basis for any presumption that the changes in distribution of spending power in either country would be in one direction rather than the other.

I have so far assumed that there are only two countries. If in addition to the countries directly participating in the reparations payments there are other countries connected with them through trade relations, additional complications arise which Pigou, who does not differentiate “England” from “non-Germany,” but takes his “representative Englishman,” with his significant ratio as representative of all non-Germany, fails to mention. If there are three or more countries, there is no longer only one significant set of commodity terms of trade, but there are at least four distinct sets, namely, the terms of trade: (1) between Germany and the rest of the world, including England; (2) between England and the rest of the world, including Germany; (3) between Germany and England, and (4) between the neutral area and the rest of the world.

Since the reparations payments go only to Englishmen proper, the change in the relative distribution of spending power as between Englishmen and other non-Germans as the result of reparations will, even with the assumptions of linearity and of “similarity” of the utility functions within the entire non-German area, prevent Pigou's ratio, although adequately representative of the utility functions of all non-Germany before reparations, from being representative after reparations, and will render inadequate Pigou's criterion for the effect of reparations payments on the terms of trade of Germany, unless before reparations the ratios corresponding to Pigou's ratio were identical for both the representative Englishman and the representative neutral. If before reparations the ratio for the representative Englishman corresponding to Pigou's for all non-Germany was smaller algebraically than the similar ratio for the representative neutral, then the terms of trade would turn against Germany as the result of reparations not only when before reparations Pigou's condition of was met, but also if and even, within limits, if On the other hand, if before reparations the ratio for the representative Englishman corresponding to Pigou's was greater algebraically than the similar ratio for the representative neutral, the terms of trade would turn in favor of Germany as the result of reparations not only when before reparations , but also if , and even, within limits, if . But since, a priori, the probability that the ratio corresponding to Pigou's will be greater algebraically for the representative Englishman than for the representative neutral is no greater than the probability that it will be smaller, and, because of the existence of “domestic” commodities, Pigou's is likely to be much smaller algebraically than the presumption that the terms of trade will turn against the paying country survives the introduction of third countries into the problem. If England and the third country produce the same commodity (or commodities), there is no basis for trade between these two countries, and the terms of trade between Germany and the outside world as a whole must be identical with those between Germany and England. The third country, therefore, will share with England any improvement or impairment in the terms of trade with Germany which may result for England as the result of her receipt of reparations from Germany.

If the third country produces the same commodity (or commodities) as Germany, similar conclusions would be reached as in the preceding case, except that the fortunes of the neutral country would now be pooled with those of the paying country instead of with those of the receiving country. If either England or Germany produces “domestic” commodities as well, this would operate, in the manner already explained, to make reparations payments result in the terms of trade turning against Germany, but whether or not the neutral country produced “domestic” commodities would not affect the direction of change in the terms of trade of Germany with the outside world as the result of reparations.

If the third country, however, produces distinctive exportable commodities of its own, the method of approach needs to be modified somewhat. To take first the terms of trade of Germany with the outside world, “non-German” data are to be used wherever in the case of only two countries English data would be used, and the problem will then correspond to the case where England and the neutral country produce identical commodities, except that given the pre-reparations ratio of representative of all non-Germany, the greater numerically the slope of the representative Englishman's utility curve for the neutral country's commodity as compared to the slope of his curve for the German commodity, the more favorable will be the situation for Germany with respect to the terms of trade. Similarly, for the terms of trade of England with the rest of the world, “non-English” data are to be used wherever in the case of only two countries German data would be used, and the problem will then correspond to the case where Germany and the neutral country produce identical commodities, except that, given the pre-reparations ratio representative of all non-England, the greater numerically the slope of the representative German's utility curve for the neutral country's commodity as compared to the slope of his curve for the English commodity, the less favorable will be the situation for England with respect to the terms of trade. To take next the terms of trade of England with Germany, they will remain unchanged, move in favor of England, or move in favor of Germany, given Pigou's assumptions, according as =, <, or > where Φ′ and ƒ′ relate to the slopes of the utility curves of the representative Englishman for English and German commodities, respectively, and ψ′ and F′ relate to the slopes of the utility curves of the representative German for English and German commodities, respectively, i.e., regardless of the slopes of their respective utility curves for neutral country commodities or of the slopes of the utility curves of the representative neutral for the commodities of England and Germany.

To take, finally, the terms of trade of the neutral country with the rest of the world, the payment of reparations by Germany to England will leave them unchanged, will move them in favour of the neutral country, or will move them against the neutral country, caeteris paribus, according as the slope of the utility curve for the neutral country's commodity is numerically equal, smaller, or greater for the representative Englishman than for the representative German, and, caeteris paribus, according as the pre-reparations volume of imports of neutral commodities is equal, greater, or smaller for England as a whole than for Germany as a whole, in proportion to their total expenditures.

[1]In this illustration, the reasonable assumption has been made that in the duty-levying country the imposition of the duty will result in the price of the imported commodity rising relative to the price of the native commodity by less than the amount of the duty. This assumption, that the terms of trade move in favor of the duty-levying country as the result of the duty, affects the degree, but not the direction, of change in the terms of trade to be expected from reparations payments. If the duty caused no change in the termsof trade, there would be no change in a1c1 as the result of the duty, but ac would move further toward the horizontal than indicated in chart V, i.e., there would be no change in F′, but the numerical reduction of ⊘' would be greater than there indicated.

[2]The duty has these results only if d'f',d'1f'1, are above the intersections of ac and a'c' and a1c1 and a'1c'1, respectively. It should be explained that d'f', which represents the new income of the Englishman measured in units of English goods or their (new) value equivalent in German goods, must be drawn so as to be equal to df+⅓ e'f'. On d'f',d'e' represents the number of English goods and e'f' the number of German goods (in their new units) which would be purchased by the representative Englishman with his new income. Measured in units of English goods alone, the new income would be the same as the old, or df. But since on all purchases of German goods the government collects one-third of the duty-paid price (=one-half of the price before duty), which is presumably not lost to the representative Englishman but returns to him as remission of other taxes or in some other form, d'f' must equal df + ⅓ e'f'. In the German section of the diagram d'1f'1 must be drawn so as to be equal to d1f1.

[3]Cf. infra, pp. 448 ff.

[4]Pigou, Economic journal, XLII (1932), 535.