Studies in the Theory of International Trade

Chapter VI

THE INTERNATIONAL MECHANISM UNDER

A SIMPLE SPECIE CURRENCY

I. INTRODUCTORY

In this chapter an account will be presented of the history and the present status of the theory of the mechanism of adjustment of international balances, in terms throughout of the simplifying assumption of an international simple specie currency, i.e., with the circulating medium consisting solely of standard metallic money. It was in terms of this assumption that the theory was first presented, and it has served ever since as a convenient device whereby to segregate for separate treatment different problems connected with the mechanism. It should be noted that in this chapter, as throughout the book, the term “balance of payments” is used in its original sense of an excess of immediate claims on abroad over obligations to abroad, or vice versa, which must be liquidated by specie. It should be noted also that by a “disturbance” to international equilibrium will be meant a change in
one of the elements in a preexisting equilibrium such as to require a new equilibrium, and that this change, whether it takes the form of a series of crop failures, of international tributes or loans, of new import duties, or of a relative change in the demands of the two countries for each other’s products, is presumed to continue indefinitely, and its cessation is treated as a new change in the reverse direction. A wide variety of disturbances can be used to
illustrate the theory of the mechanism of international trade, and each has its own sequence of stages and to some extent its own set of special problems. A selection must be made, therefore, and the reader is asked not to attribute to me or to the writers cited generalization of the conclusions reached from the analysis of cases specifically dealt with beyond what the context clearly shows to be intended.

II. THE MECHANISM ACCORDING TO HUME

In so far as the classical theory of the mechanism of international trade had one definite originator, it was David Hume.
*1 His main objective in presenting his theory of the mechanism was to show that the national supply of money would take care of itself, without need of, or possibility of benefit from, governmental intervention of the mercantilist type. He started out with the hypothesis that four-fifths of all the money in Great Britain was annihilated overnight, and proceeded to trace the consequences. Prices of British commodities and British wages would sink in proportion; British commodities would consequently overwhelm foreign competition in foreign markets, and the increase in exports would be paid for in money until the “level of money” in Great Britain was again equal to that in neighboring countries. Assuming next that the money in Great Britain were multiplied fivefold overnight, he held that prices and wages would rise so high in England that no foreign countries could buy British commodities, while foreign commodities, on the other hand, would become comparatively so cheap that they would be imported in great quantities. Money would consequently flow out of England until it was again at a level with that of other countries. The same causes which would bring about this approach to a common international level when disturbed “miraculously” would prevent any great inequality in level from occurring “in the common course of nature.” The same forces also would preserve an approximately equal level as between different provinces of the same country. An additional, though minor, factor, operating to correct “a wrong balance of trade,” was the fluctuations in the foreign exchanges within the limits of the specie points. If the trade balance was unfavorable, the exchanges would move against England, and this would become a new encouragement to export. The entire mechanism was kept in operation by the profit motive of individuals, “a moral attraction, arising from the interests and passions of men,” acting under the stimulus of differences in prices.

The mechanism, therefore, was according to Hume automatically
self-equilibrating, was intranational as well as international, was bilateral, involving adjustments both at home and abroad, and consisted of such changes in the volume of exports and imports, resulting chiefly from changes in relative prices but also in minor degree from fluctuations in exchange rates, as would bring about or maintain an even balance of trade, so that no further specie need move to liquidate a balance.

III. AN OMITTED FACTOR? RELATIVE CHANGES IN DEMAND AS AN EQUILIBRATING FORCE

It will be conceded at once that, in the case, for instance, of the initiation of continuing unilateral remittances, the aggregate demand for commodities, in the sense of the amounts buyers are willing to purchase at the prevailing prices, will, in the absence of price changes, fall in the paying country and rise in the lending
country,
*2 and that unless there is an extreme and unusual distortion of the relative demands for different classes of commodities from their previous proportions this shift in demands will of itself contribute to an adjustment of the balance of payments to the remittances. The problem is rather to explain why this fairly obvious proposition should not sooner have received general recognition and to determine to what extent its recognition constitutes, as some contend, a major revolution in the theory of the mechanism requiring wholesale rejection of what the older writers had to say. To the first question, even though I have sinned in this connection myself, I have no answer, except that it is difficult to judge, after something has been clearly pointed out to us, how obvious it would or should be to others not so circumstanced. While, however, the account of the mechanism given by Hume and by many later writers gives no indication of recognition that the direct influence on the trade balance of relative changes in demands in the two countries would be an equilibrating factor, such recognition was by no means wholly lacking on the part of the major writers of the nineteenth century.

That imports pay for exports, and that an increase in imports, by providing foreigners with increased means of payment, would operate to increase exports, was pointed out even during the mercantilist period. But the following account will disregard incidental recognition of the relationship between amount of income and extent of demand, which has always been common, even with laymen, and will deal only with cases where such recognition is to be found incorporated as an integral part of a more or less formal exposition by nineteenth-century writers of the mechanism of adjustment of international balances.
*3

Wheatley, Ricardo.

Henry Thornton, in 1802, had applied the Hume type of explanation generally to any type of disturbance of the balance of payments, and specifically to the disturbance resulting from a crop failure which made necessary greatly increased imports of grain,
*4 and to a change in the English demand for foreign commodities as compared to the foreign demand for English commodities.
*5 Wheatley and Ricardo, on the other hand, denied that this explanation was applicable to such disturbances of a non-currency nature and offered different explanations of the mechanism of adjustment to such disturbances. While Wheatley’s discussion was in part earlier, Ricardo’s was less significant for the point at issue, and it will be convenient to dispose of it first. Ricardo denied that crop failures or the payment of subsidies would disturb the balance of payments at all and denied, therefore, that any mechanism of adjustment would be necessary.
*6 The only justification for this position which he offered was that if a crop failure should be permitted to disturb the balance of payments, since the disturbance would prove to be temporary and after it was over things would be as they had been before, any movement of specie—and presumably also any corresponding change in relative price levels—would have to be offset later by a return movement of equal size, a waste of effort which would not be indulged in:

The ultimate result then of all this exportation and importation of money, is that one country will have imported one commodity in exchange for another, and the coin and bullion will in both countries have regained their natural level. Is it to be contended that these results would not be foreseen, and the expense and trouble attending
these needless operations effectually prevented, in a country where capital is abundant, where every possible economy in trade is practiced, and where competition is pushed to its utmost limits? Is it conceivable that money should be sent abroad for the purpose merely of rendering it dear in this country and cheap in another, and by such means to insure its return to us?
*7

This exaggerates the extent to which individual traders can foresee whether a drain of gold would be temporary or not, or would find it in their interest to check it even if they were convinced that it was temporary.
*8 Seasonal movements of specie are still permitted to occur, even though their seasonal character is generally known.

Wheatley defended his denial that crop failures or foreign subsidy payments would disturb the balance of payments by more adequate reasoning. He maintained that crop failures, or the payment of subsidies, would immediately alter the relative demands of the two regions for each other’s products in such manner and degree that the commodity balance of trade would at once undergo the manner and degree of change necessary to maintain equilibrium in the balance of payments. This shift in relative demand would result from the alteration brought about by the crop failure or the subsidy in the relative ability of the two countries to buy each other’s commodities:

If, then, it be correct in theory, that the exports and imports to and from independent states have a reciprocal action on each other, and that the extent of the one is necessarily limited by the extent of the other, it is obvious, that if no demand had subsisted in this country from 1793 to 1797 for corn and naval stores, the countries that furnished the supply would have possessed so much less means
of expending our exports, as an inability to sell would of course have created an equal inability to buy. It is totally irregular, therefore, to infer, that our exports would have amounted to the same sum, had the import of the corn and naval stores been withheld, as those who provided the supply would have been utterly incapable of purchasing them.
*9

On similar grounds, Wheatley held that under an inconvertible paper currency the exchanges would not be affected by a crop failure or the payment of a subsidy, and could move against a country only if there had developed a relative redundancy of currency in that country.
*10 Wheatley carried his doctrine so much further than he clearly showed to be justified that even the bullionists rejected it, and in doing so overlooked the important element of validity underlying it.

Longfield, Torrens, Joplin.

A certain equilibrium exists between our average exports and imports. This is disturbed by the importation of corn. England suddenly demands a large quantity, perhaps six millions worth of corn. She may be ready to pay for them by her manufactures, but will those who sell it be willing to take those manufactures in exchange? Will the Prussian or Russian landowner, whose wealth has been suddenly increased, be content to expend his increased wealth in the purchase of an increased amount of English manufactures? We say that the contrary will take place, and that his habits will remain unchanged, and his increase of wealth will be spent in nearly the same manner as his former income, that is to say, not one fiftieth part in the purchase of English goods. His countrymen will, in the first instance, have the advantage of his increased expenditure. It will not be felt in England until after a long time, and passing through many channels…. Thus the English have six millions less than usual to expend in the purchase of the commodities which they
are accustomed to consume, while the inhabitants of the corn exporting countries have six millions more…. The commodities, therefore, which the Russians and Prussians consume, will rise in price, while those which the English use will undergo a reduction. But a very great proportion, much more than nineteen-twentieths of the commodities consumed in any country, are the productions of that country. English manufactures will therefore fall, while Russian and Prussian goods will rise in price. The evil, after some time, works its own cure.
*11

Torrens, in 1841-42, in the course of an attempt to demonstrate that retaliation against foreign tariffs would be beneficial to England even if such retaliation did not lead foreign countries to reduce their tariffs, placed main emphasis on the role of relative price changes in adjusting the international balances to tariff changes, but in his well-known Cuban illustration the restoration of equilibrium was made to result directly from the relative shift in the amounts of means of payment, as well as indirectly from the relative shift in prices resulting from this shift in means of payment. He assumed, first, that all the demands for commodities in terms of money in each country had unit elasticity, and that Cuba was exporting to England 1,500,000 units of sugar, at a price of 30 shillings per unit, in return for 1,500,000 units of English cloth, at a price also of 30 s. per unit. Cuba then imposes a duty of 100 per cent on cloth, with the result that the price of cloth rises to 60 s. in Cuba, and the Cuban consumption falls by 50 per cent, to 750,000 units. Sugar continues for a time to flow to England at the original price and in the original quantity. There results an unfavorable balance of payments for England, and specie moves from England to Cuba. The price of sugar rises, and the price of cloth falls. The Cuban consumption of cloth increases to more than 750,000 units, apparently because of both the fall in the price of cloth and the increase in the amount of money available for the purchase of cloth in Cuba. Conversely, the rise in the price of sugar and the decrease in the quantity of money in England result in a decline in the English consumption of sugar to less than 1,500,000 units. Specie continues to flow from England to Cuba, the amount of money to fall in England and rise in Cuba, the price of cloth to fall and the price of sugar
to rise, until the exports of cloth to Cuba had expanded and the exports of sugar to England contracted sufficiently to restore equilibrium in the balance of payments between the two countries. Under this final equilibrium, Cuba would be importing annually 1,500,000 units of cloth, at a price before duty of 20 s., and after duty of 40 s. per unit, and would be exporting 750,000 units of sugar at a price of 40 s. per unit.
*12 These results, it is to be noted, could not have resulted from the changes in prices alone, given the postulated elasticities of demand. They imply changes in money incomes in each country, and consequent changes in each country, the same in direction as the changes in money incomes, in the quantities which would be demanded of both commodities if the prices had remained unaltered.

Joplin, in his many tracts, repeatedly expounded the mechanism of adjustment of international balances in terms only of relative price changes, but in one passage, by exception, he stressed the direct influence on the course of trade of the relative change in demand for each other’s commodities resulting from the transfer of money from one of the countries to the other, with the change in relative prices mentioned only as a by-product of, rather than as an essential factor in, the equilibrating process:

Now, when the balance of payments is against one and in favor of another nation, it arises from the inhabitants of the former having a greater demand for the productions of the latter, than the inhabitants of the latter have for the productions of the former. But after a transmission of the balance in money, an alteration must necessarily be experienced in the state of this demand. The inhabitants of the country from whence the money was sent would be unable, from their reduced monetary incomes, to purchase so large a quantity of the products of the money-importing country as before; while they, the inhabitants of the importing country, would be enabled, by the increase in their monetary incomes, to purchase more of the commodities of the nation from which the money had been received. Thus the trade would again be brought to a balance in money, and be thereby rendered an exchange of commodity for commodity: the nation receiving the money gaining by the improved terms on which the barter would be thereafter conducted.
*13

J. S. Mill, Cairnes.

John Stuart Mill, in the exposition of the mechanism which he gives in his
Principles, appears to attribute to relative changes in prices sole responsibility for bringing about a trade balance such as would restore equilibrium in a disturbed balance of payments.
*14 At one point, in fact, he appears explicitly to say so. Discussing a case where “there is at the ordinary prices a permanent demand in England for more French goods than the English goods required in France at the ordinary prices will pay for,” he states that “the imports require to be permanently diminished, or the exports to be increased;
which can only be accomplished through prices.”
*15 At another point, however, he expressly includes, as a factor operating to restore equilibrium, the relative shift in the amount of monetary income in the two countries resulting from the transfer of specie. He is tracing the consequences of a cheapening of the cost of production of a staple article of English production:

The first effect is that the article falls in price, and a demand arises for it abroad. This new exportation disturbs the balance, turns the exchanges, money flows into the country…and continues to flow until prices rise. This higher range of prices will somewhat check the demand in foreign countries for the new article of export; and will diminish the demand which existed abroad for the other things which England was in the habit of exporting. The exports will thus be diminished;
while at the same time the English public, having more money, will have a greater power of purchasing foreign commodities. If they make use of this increased power of purchase, there will be an increase of imports: and by this, and the check to exportation, the equilibrium of imports and exports will be restored.
*16

The ordinary interpretation of Mill’s theory as explaining the adjustment of international balances solely in terms of relative
price changes probably should be accepted, and this passage therefore regarded as indicating only an accidental perception by Mill at one moment of the presence in the mechanism of an additional factor rather than as a statement of an integral element in his theory. But it may be an error to do so. The exposition in the
Principles is a restatement, in some respects less detailed, of an earlier exposition by Mill,
*17 in which the relative change in monetary income in the two countries resulting from a movement of specie is expressly incorporated in the exposition of the mechanism as, together with the elasticities of demand in terms of money prices, determining the extent of the response to price changes of the volume of purchases of each other’s commodities by the two countries. Even here the emphasis is mainly on relative price changes, but this can in part be explained by the fact that Mill treats a rise in the prices of a country’s own products as necessarily involving also a rise in its money incomes,
*18 as well as by the fact that he is here primarily concerned with the effects of disturbances on the “gains” from trade, rather than with the mechanism
qua mechanism.
*19

Cairnes, in his better known expositions of the mechanism of international trade,
*20 makes no reference to the relative shift in means of payment, or in demands for commodities in terms of money, as a factor contributing to the adjustment of international balances. But in an earlier essay he emphasized the role it plays, and showed that he was aware that he was adding something not in the usual version:

[In the cases of crop failures, military remittances abroad, etc.] The transference of so much gold from this country to foreign countries—though it need not interfere to any great extent with the proceedings of commerce at home—yet alters the disposable wealth comparatively of this and other countries; their means of expenditure is proportionally altered, and consequently their demand for each other’s goods. There is thus, in the circumstances attending a transmission of gold from this country, a provision made for its return, quite independently of the state of prices,
or of the circulation….
*21

Bastable, Nicholson.

Suppose that A owes B £1,000,000 annually. This debt is a claim in the hands of B, which increases her purchasing power, being added to the amount of that power otherwise derived…. [It is also doubtful whether in case of interest payments or repayments of previous loans] Mill is correct in asserting that the quantity of money will be increased in the creditor and reduced in the debtor country. The sum of money incomes will no doubt be higher in the former; but that increased amount may be expended in purchasing imported articles obtained by means of the obligations held against the debtor nation…. Nor does it follow that the scale of prices will be higher in the creditor than in the debtor country. The inhabitants of the former, having larger money incomes, will purchase more
at the same price, and thus bring about the necessary excess of imports over exports.
*22

A few years later Nicholson presented a similar criticism of Mill’s reasoning, worked out in some detail, and accompanied by a denial, based on crudely fallacious reasoning, that price changes and specie movements played
any part in the mechanism.
*23

A number of the most important nineteenth-century writers on the theory of international trade thus recognized that relative shifts in the amounts of means of payment, or of incomes, exercised, independently of relative price changes, an equilibrating role in the mechanism of adjustment of international balances to disturbances.
*24 But there were important divergences of doctrine between these writers. It was common doctrine for all of them that a change in relative money incomes resulting, say, from loans would contribute to the adjustment of the balance of payments to the loans through its influence on the relative demands of the two countries for each other’s commodities. But one group
(i.e., Ricardo, Longfield, J. S. Mill, Cairnes) either explained this shift in relative incomes as resulting from a prior transfer of money or conceded that a transfer of money would result from it, whereas another group (Wheatley, Bastable, and Nicholson, and, at one point, Cairnes) denied that any transfer of money need take place. One group (Longfield, Joplin, Cairnes, J. S. Mill) left an important place in the mechanism for relative price changes, whereas another group (Wheatley, Ricardo, Bastable, Nicholson) denied, or questioned, the necessity of relative price changes for the restoration of equilibrium.

Taussig, Wicksell.

In an article published in 1917, and dealing primarily with the mechanism of adjustment under a paper standard currency, Taussig argued that in the case of an international loan under a metallic standard that part of the proceeds not used immediately by the borrowers in purchase of foreign goods would enter the borrowing country in the form of goods only after a remittance of specie from lender to borrower had raised prices in the borrowing country and lowered them in the lending country.
*25 In a reply to this article, Wicksell claimed that the increased demand for commodities in the borrowing country, and the decreased demand for commodities in the lending country, would “in the main” be sufficient to call forth the changes in the trade balance necessary to restore equilibrium in the balance of payments. He held that it would not make any difference if the increased power of purchase in the borrowing country were directed toward its own products rather than imported products:

…this of course would diminish the imports, but if the value of imports surpasses the value of exports by precisely the amount borrowed
during the same time, there would be no occasion for sending or receiving gold.

Gold
would move to the borrowing country, but only because, and
after, it had acquired additional commodities, and not before the transfer of the loan in the form of goods.
*26

Taussig, in his brief rejoinder, confined his discussion in the main to other points and did not adequately meet the fundamental issue raised by Wicksell as to the role played by changes in demand in the equilibrating process. To Wicksell’s denial of the necessity of specie movements at an early stage of the process of adjustment, he made an effective reply: “I find it difficult to conceive how ‘increased demand for commodities’ will cause a rise in the price of commodities, unless more money is offered for them; and no more money can be offered for them unless the supply of money is larger.”
*27 This may seem to imply an acceptance by Taussig of Wicksell’s doctrine at least to the extent of recognition that changes in demand do play an equilibrating part aside from price changes, for if there is an increase in demand it operates to increase the amount taken at the
same prices as well as to increase the prices, but I cannot find a clear statement to this effect either here or in his later writings. Taussig also pointed out that Wicksell’s denial of the possibility that relative price changes could be an important equilibrating factor, since, transportation costs aside, commodities tend to have uniform prices everywhere, overlooked the existence of “domestic” commodities not entering into international trade, whose price movements could diverge from the movements of the prices of international commodities and thus contribute to the establishment of a new international equilibrium.
*28

“Canada’s Balance.”

In 1924, reviewing this discussion between Wicksell and Taussig, I conceded, as had Taussig in his original article, that to the extent that the new spendable funds
in the borrowing country resulting from the loan were used in the purchase of foreign commodities which otherwise would not have been imported there would be a contribution to adjustment independent of relative price changes. I also accepted the argument, which I attributed to Wicksell,
*29 that the use of the proceeds of the loans to purchase home-produced commodities which otherwise would have been exported would similarly contribute to adjustment. I concluded, however, that there was no
a priori reason to expect that these two factors would suffice to bring about adjustment, on the grounds that: (1) the theoretical expectation would be that in the absence of price changes the same percentage of the additional, as of the original, spendable funds would be used in the purchase of “domestic” or non-international commodities; and (2) unless in the absence of price changes
none of the borrowed funds would be used in the purchase of “domestic” commodities, there could not be adjustment of the balance of payments without relative price changes.
*30 As will appear later, this last proposition was an error, resulting from my failure, at this point,
*31 to bear in mind that a diversion of productive factors from production of exportable commodities for export to production of domestic commodities for domestic consumption would, by restricting the volume of exports, contribute as much to the adjustment of the balance of payments as would an
equivalent increase of imports or of domestic consumption of products hitherto exported.

Keynes, Ohlin.

The discussion of the transfer aspect of the German reparations problem gave rise to intensified discussion of this issue, but the contributions of Ohlin and Keynes can alone be dealt with here. Ohlin, in an article published in 1928, laid strong emphasis on the role which a relative shift in demand for commodities, in terms of money, upward in the receiving countries, downward in Germany, would play in adjusting the German balance of payments to the reparations payments, thus making relative price changes adverse to Germany a subsidiary and probably unnecessary part of the mechanism, and easing the task of transfer of the reparations in the form of goods.
*32 In this article, it appears to me, he took a position with respect to the lack of significance of relative price changes in the international mechanism more extreme than the treatment in his later book (which still seems extreme to me). He argued that when international unilateral remittances occurred a change in price favorable to the paying country was as likely to take place as one unfavorable to that country, and that in the absence of knowledge of the particular circumstances it must be presumed that no relative change in prices will occur.
*33 He further claimed that even if a relative price change unfavorable to the paying country did occur, it would only be at the beginning of the payments, and would not persist long enough to be significant.
*34

In 1929, Keynes, in a pessimistic article on the possibility of transfer of the German reparations, which stressed the difficulties which Germany would encounter even if she succeeded in providing for the payments in her government budget, did not take into account, as a factor facilitating economic transfer of the payments, the shift in the demands for commodities which would result from an initial transfer of means of payment from Germany to the receiving countries. Ohlin replied, invoking this shift as a
factor which would lessen the seriousness of the transfer problem, and there resulted a further exchange of views between the two writers, in which neither succeeded in converting the other.
*35 Ohlin did not state his views as clearly as he has since presented them, and on one essential point he made an unnecessary concession to Keynes.

Keynes reasoned throughout, on the conventional lines, as if the only factor tending to adjust the German trade balance to its reparations obligations could be an increase in German exports relative to imports resulting from a fall in German prices relative to outside prices. Taking an extreme case to emphasize his point, namely, where the foreign (simple “Marshallian”) elasticity of demand for products of Germany was assumed to be less than unity, and abstracting from the possibility of a reduction in the value of German imports, he concluded that “in this case, the more she exports, the smaller will be the aggregate proceeds. Again the transfer problem will be a hopeless business”—i.e., the reparations in this case could not be transferred even if relative price changes did occur. Keynes therefore concluded that the elasticities of demand of the two countries might be such as to make transfer in kind wholly impossible, and that for such transfer to take place in any case, “the expenditure of the German people must be reduced, not only by the amount of the reparation-taxes which they must pay out of their earnings, but also by a reduction in their gold-rate of earnings below what they would otherwise be,” that is, German money wages, etc., must fall even aside from taxation thereof.
*36 This Ohlin denied.

At a later stage of the controversy, Keynes explained that he had attributed little (no?) importance to changes in demand conditions, because he had assumed that Germany was not in a position to export large quantities of gold, and because if Germany did ship gold her products would have to share the benefits of the resultant increase in demands outside Germany with the products of the rest of the world, so that the gain to her export trade
would be negligible.
*37 To this it could be replied that the ratio of gold shipments to aggregate reparations payments over the entire period would not have to be large, since a given transfer of gold will continue to keep up the level of foreign demand in terms of money for German goods by some fraction (or multiple) of itself per unit period as long as the gold stays abroad; it will operate not only to raise the foreign demand for German goods but to decrease the German demand for foreign goods; and if in the first instance all, or most, of the receiving country’s increase in demand is directed to the products of third countries, these countries will acquire the specie surrendered by Germany, and their demands for foreign commodities, including those of Germany, will rise. But Keynes, apparently to the last, failed to understand Ohlin’s argument that the initial transfer of specie, or its equivalent, would result in a relative shift in an equilibrating direction of the demands in terms of money prices of the two countries for each other’s products, regardless of their elasticities. He still argued that if the world’s demand for German goods had an elasticity of less than unity, “there is
no quantity of German-produced goods, however great in volume, which has a sufficient selling-value on the world market, so that the only expedient open to Germany would be to cut down her imports.”
*38 But elasticity of demand of less than unity for German exports would set a definite limit on the value of such exports only if no increase in the foreign demand for German commodities in terms of money
resulted directly from the transfer abroad by Germany of specie.
*39

The failure of the two writers to make themselves clear to each other, and especially the failure of Ohlin to convert Keynes, was probably due in part to an ambiguous and otherwise unsatisfactory use by both writers of the treacherous term “purchasing power.” Ohlin’s argument that a relative shift in demand for each other’s products would occur rested on the doctrine that the payment of reparations would commence with a transfer of “purchasing power” from Germany to the receiving countries and that the resultant relative change in the amounts of “purchasing power” in the respective areas would bring about this relative shift in demands for commodities. In reply, Keynes presents a hypothetical case, where Germany, having succeeded by some means in developing a net export surplus of £25,000,000, meets her reparations obligations to the extent of £25,000,000 out of the proceeds of this export surplus. Exploiting to the full the ambiguities of the term “buying power,” he then claims that “the increased ‘buying power,’ due to the fact of Germany paying something…will have been
already used up in buying the exports, the sale of which has made the reparation payments possible,” whereas “Professor Ohlin has to maintain that the ‘increased buying power’ is
more than £25,000,000, and—if his repercussion is to be important—appreciably more.”
*40 Ohlin, instead of pointing out that the increase of “buying power” in France which could be counted on to bring about real transfer of
reparations would precede rather than follow the real transfer, and would not be “used up” by the French import surplus of a particular year, merely replied: “Surely it is easier to sell many goods to a man who has got increased buying power, even though after buying them he has no longer greater buying power than he used to have!”
*41 a reply which conceded too much to Keynes, and left his argument intact instead of refuting it.

For Keynes, the real transfer of £25,000,000 of reparations was due to a fortuitous development of an export surplus by Germany, payment for which Germany was willing to accept in credits against her reparations liabilities. Suppose, however, that Germany’s first step in her attempt to meet her reparations obligations was the payment of £25,000,000
in gold to France, and that in France this increase in gold had its normal effects on the total volume of means of payments. Suppose also that thereafter at each reparations payment date, Germany credited France anew with £25,000,000 in German funds at German banks. Frenchmen would now have both increased willingness to buy German goods at the same prices and increased power to pay for them in French currency, and there would therefore tend to be recurrent French import surpluses with respect to Germany. These import surpluses could be liquidated internationally by drafts against the reparations credits in favor of France periodically set up by the German government in German banks. As long as Germany continued, in the narrow financial sense, to meet her reparations obligations, the increase in the French willingness to buy and power to pay, as compared to the pre-reparations situation, would never be “used up,” but would be everlasting. But the question of the place of willingness to buy and power to pay for foreign commodities in the mechanism of transfer of unilateral payments will be dealt with in a more fundamental manner later, after a needed digression on the role of price changes in the mechanism.

IV. PRICES IN THE MECHANISM: THE CONCEPT OF “PRICE LEVELS”

An adequate exposition of the role of price changes in the mechanism of international trade as it affects a particular country
would explain both what would be the necessary relationship under equilibrium between prices in that country and prices abroad, and in what manner if any fluctuations of prices would contribute to, or would be associated with, the restoration of equilibrium when it had been disturbed. In tracing the development of doctrine on these questions, it is once more convenient to begin with Hume. For our present purposes it is convenient to accept as the predominant criterion of equilibrium in international trade under an international metallic standard a situation in which there is an even balance of payments, i.e., no flow, and no tendency to flow, of bullion or specie from country to country.
*42

Hume held that when the balance of payments of England with the outside world was even, the “level of money” in England and in neighboring countries would also be equal, subject to minor qualifications. The mechanism of international trade operated to bring money to a common level in all countries, just as “all water, wherever it communicates, remains always at a level.” Hume meant by “level of money” the proportion between money and commodities:

It must carefully be remarked, that throughout this discourse, whenever I speak of the level of money, I mean always its proportional level to the commodities, labor, industry, and skill, which is in the several states. And I assert that where these advantages are double, triple, quadruple, to what they are in the neighboring states, the money infallibly will also be double, triple, quadruple.
*43

Modern usage makes it tempting to translate “level of money” by average value or purchasing power of money as against commodities in general, with some statistical average of prices as its reciprocal. But this would be an anachronism as far as Hume, or even as the classical school as a whole, was concerned. Hume wrote before the first attempt in England, that of Evelyn in 1798, to measure changes in price levels by means of statistical averages.
*44 Even after 1798, the leading economists until the time of
Jevons either revealed no acquaintance with the notion of representing, by means of statistical averages, either a level of prices, or changes in such level, or found it inacceptable for various reasons, good and bad.
*45 While a number of crude index numbers were constructed during the first half of the nineteenth century, none of the classical economists, with the single exception of Wheatley, would have anything to do with them.
*46

Hume’s use of the term “level” troubled some of the classical economists. Wheatley claimed that Hume was inconsistent in arguing both that money everywhere maintained its level and that one country might retain a greater relative quantity than another, “which is incompatible with the nature of a level.”
*47 Ricardo, in his published writings, seems to have avoided the use of the term “level” for the general state of prices, although he used it in this sense freely in his private correspondence.
*48 He refused to acknowledge that there was any satisfactory way of comparing the value of money, or of bullion, in different countries:

When we speak of the high or low value of gold, silver, or any other commodity in different countries, we should always mention some medium in which we are estimating them, or no idea can be attached to the proposition. Thus, when gold is said to be dearer in England than in Spain, if no commodity is mentioned, what notion does the assertion convey? If corn, olives, oil, wine, and wool, be at a cheaper price in Spain than in England, estimated in those commodities, gold is dearer in Spain. If, again, hardware, sugar, cloth, &c., be at a lower price in England than in Spain, then, estimated in those commodities, gold is dearer in England. Thus gold appears dearer or cheaper in Spain, as the fancy of the observer may fix on the medium by which he estimates its value.
*49

Malthus denied that money necessarily maintained a uniform level in different countries, if by uniformity of level was to be understood necessary equality of the prices of some specified commodity or of the “mass of commodities.”
*50

What then were the views of the classical writers with respect to the relationship of prices and of the value of gold in different countries? The following seems to be a correct interpretation of their general position: (1) When they speak of the value of money or of the level of prices without explicit qualification, they mean the array of prices, of both commodities and services, in all its particularity and without conscious implication of any kind of statistical average; (2) when they postulate a tendency for the uniformity of the value of money, or of prices, in different countries, they have reference only to particular identical commodities taken one at a time, and only to transportable commodities, and they claim such a tendency for uniformity only subject to allowance for transportation costs both for the commodities and for the specie; (3) where the monetary units are not the same, or where different standards are in use, they postulate uniformity in the prices of identical commodities only after conversion into a common currency unit at the prevailing rate of exchange, and they postulate uniform ratios between the prices of different transportable commodities in the currencies of the respective countries.
*51

The only circumstance that can obstruct the exactness of these proportions, is the expense of transporting the commodities from one place to another; and this expense is sometimes unequal. Thus the corn, cattle, cheese, butter, of Derbyshire, cannot draw the money of London, so much as the manufactures of London draw the money of Derbyshire. But this objection is only a seeming one; for so far as the transport of commodities is expensive, so far is the communication between the places obstructed and imperfect.
*52

In spite of the obscurity of his exposition, it seems clear that Ricardo would have subscribed to these propositions, and that where occasional statements in his writings appear to conflict with them the inconsistency is only apparent. Thus Ricardo says at one point that “the value of money is never the same in any two countries” and that “the prices of the commodities which are common to most countries are also subject to considerable difference”
*53 but the context shows that he had in mind the differences in different countries in the purchasing power of gold over particular commodities which were due to the cost of transporting gold, to bounties and tariffs, to the cost of transporting goods, and to the existence of non-transportable “home commodities” which, according to him, would be higher in price in countries where the effectiveness of labor in export industries and therefore also the wages of labor were comparatively high, and he included as an element in the value of money its purchasing power in terms of labor, which he assumed to be a non-transportable commodity.
*54 In a letter to Malthus, Ricardo conceded that the situation suggested by Blake, where gold moved from France to England although the value of gold in terms of commodities was constant in France and rising in England, was possible though improbable, and explained the possibility of such divergent trends of the value of gold by reference to the transportation costs of commodities and the existence of non-transportable commodities.
*55

Wheatley held that in the absence of tariff barriers “corn and manufactures…would always be brought, or have a constant tendency to be brought to the same proportion and price in all countries, with the exception of the charge of transit between them. A difference to the extent of this charge might always exist; but if trade were open, the difference in the price of corn and manufactures, in any two countries, could never exceed the expense of bringing in the one and taking out the other.”
*56

The classical school and its important followers all held the same views on this point: after allowance for transportation costs, the market prices of identical transportable commodities must everywhere be equal or tend to be equal when expressed in or converted to a common currency.
*57 When, therefore, critics of the classical theory have taken it to task on the ground that it explained the adjustment of international balances by the influence on the course of trade of divergent market prices in different markets of identical transportable commodities,
*58 or
when followers of the classical theory have attempted to defend it although themselves giving it such an interpretation,
*59 they have misinterpreted the classical doctrine.

When costs connected with transportation, including tariff duties as such, are taken into account, prices in two markets for identical commodities can vary independently of each other within the limits of the transportation costs in either direction between these markets, except as a connection of both markets with a third market may impose narrower limits. Assuming only two markets, A and B, a cost of transportation from A to B of
m, and from B to A of
n, and a technological possibility of the production of the commodity in either A or B, and it is possible, (1) when
P_a is the price in A, for the price in B to be anywhere from
P_a+
m to
P_a–
n, and (2) when
P_b is the price in B, for the price in A to be anywhere from
P_b+
n to
P_b–
m. If the commodity is regularly moving from one market to the other, the price in the buying market must obviously be higher than the price in the selling market by exactly the cost of transportation, but the possibility of reversal of direction of movement, or of cessation or initiation of movement because of substitution in one country of domestic production for import or of import for domestic production, makes the double-transportation-cost range of possible relative variation in price potentially of practical significance.
*60

V. THE “TERMS-OF-TRADE” CONCEPT

In the classical theory, the discussion of the role of variations in prices in the mechanism of adjustment of international balances relates not to relative variations in prices of identical commodities in different markets, but to relative variations in prices of different commodities in the same markets, and primarily to relative variations in prices as between export and import commodities. It concerns itself, therefore, with the effect of disturbances on what are now called the “terms of trade.” Changes in the terms of trade were discussed, however, with reference to two essentially distinct though related problems; first, their role in the mechanism of adjustment and, second, their significance as measures of gain or loss from foreign trade. It is only the former of these problems that concerns us in this chapter.
*61

The most familiar concept of the terms of trade measures these terms by the ratio of export prices to import prices, what Taussig has called the “net barter terms of trade,” and I prefer to designate as the “commodity terms of trade.” The classical economists, however, had also another concept of terms of trade, for which they tacitly accepted the commodity terms of trade as an accurate measure, so that they used the two concepts as quantitatively identical although logically distinct. This second concept, which I would designate as the “double factoral terms of trade,” is the ratio between the quantities of the productive factors in the two countries necessary to produce quantities of product of equal value in foreign trade.

From Hume on, there was general agreement that some or all types of disturbances in international balances would result in changes in the terms of trade, and that these changes would contribute to the restoration of equilibrium. As has been shown, Hume held that a relative change in the quantity of money in one country as compared to other countries would result in a rise in the prices of its products relative to the prices of foreign products, until, as the result of the influence of this relative change in prices on the course of trade and on the flow of specie, the “level of money” had again been equalized internationally.
This was almost universally accepted doctrine during the next century. Thornton and Malthus claimed, with Wheatley and Ricardo dissenting, that a similar change in relative prices would occur and would operate to restore equilibrium in the balance of payments when it had been disturbed by a crop failure or the remittance of a subsidy, and this also came to receive wide acceptance, under the erroneous designation of the “Ricardian theory.” Ricardo conceded, however, that there were some types of disturbance in an existing international equilibrium other than those originating in the currency which would affect the terms of trade, and he specified an original change in the relative demand of two countries for each other’s products and a tariff change as disturbances of this sort.
*62 There is ground for distinguishing in this connection between different types of disturbances, and Ricardo’s distinctions have some measure of validity. In the account which follows of later treatments of the question, only the historically most important controversies are referred to.

Irish Absenteeism.

When it is considered that, if in the natural order of things, undisturbed by such a measure as the restriction on specie, the remittances to absentees, by causing a balance of pecuniary intercourse
against Ireland, would force an export from thence wherewith to pay it, and restore the level, it may be fairly concluded that the absentees, by bringing over their money to England, force the manufacture or produce to follow them, which, but for their coming, they would necessarily have caused to be used at home, the only difference is, that the produce or manufactures which their incomes naturally promote, would come to be consumed or used in England, in the stead of being consumed or used in Ireland; and thus the encouragement to the productive industry of Ireland may be said to operate in both cases…
*63

Longfield
*64 introduced into the controversy the question of the effect of absenteeism on the Irish terms of trade, apparently for the first time in print.
*65 He insisted that it was important to examine whether the increase in Irish exports resulting from absenteeism took place “in consequence of a diminished demand [for Irish products] at home, or an increased demand abroad,” and claimed that the former was the case, because Irish landlords living abroad would not have the same demand for Irish commodities and services as would the same landlords if living in Ireland. In order to induce acceptance of the rents in goods instead of money, therefore, the Irish tenants would have to offer more
goods to liquidate their indebtedness to absentee landlords than would be necessary if the landlords lived in Ireland, i.e., there would have to be a fall in the prices of Irish export products relative to the prices of imports.
*66

Tariff Changes.

Torrens’s discussion of the effect of a tariff on the terms of trade has already been referred to.
*67 In his basic illustration, Torrens assumed unit elasticities of demand for sugar and cloth in both countries, production of sugar only in Cuba and of cloth only in England, and production under conditions of constant costs for both countries, and he concluded that both the commodity and the factoral terms of trade would move in favor of Cuba, the tariff-levying country. His argument was on the whole received unsympathetically by most of the economists of his time, because it seemed to them to undermine the case for free trade.
*68 But their criticisms, in so far as they were deserving of consideration at all, bore only on the conformity of the assumptions to real conditions. Of these criticisms, the most important was the argument by Merivale that if sugar could be produced in England as well as in Cuba, or if a third country which could produce sugar were brought into the hypothesis, the English elasticity of demand for
Cuban sugar would be greatly increased, and the shift in the terms of trade in favor of Cuba would in consequence be much lessened in degree.
*69 The only favorable comments on Torrens’s argument were by an anonymous writer in the
Dublin University magazine,*70 who may perhaps have been Longfield, and by J. S. Mill, who made the publication of Torrens’s
The budget the occasion for the publication of his own
Essays on some unsettled questions, which had been written some fifteen years before, and of which the first essay presented a similar argument as to the effect of import duties on the terms of trade.

VI. THE PRICES OF “DOMESTIC” COMMODITIES

While the distinction between “domestic” commodities and those entering into international trade dates at least from Ricardo,
*71 and subsequent writers made clear that international uniformity in the prices of identical commodities after allowance for transportation costs was a necessary condition under equilibrium only for “international” commodities,
*72 Taussig was the first to lay emphasis on the significance for the mechanism of adjustment of international balances to disturbances of changes in the level of domestic commodity prices as compared to the prices of international commodities. In 1917, Taussig argued that some of the proceeds of an international loan would ordinarily be directed in the first instance to the purchase of domestic commodities, instead of import commodities. But in order that the loan should be transferred wholly in the form of goods, it was necessary that there should develop an excess of imports over exports equal to the amount of the borrowings, and this could not occur if part of the proceeds of the borrowings continued to be directed to purchases of domestic goods. The increased purchases of domestic goods would raise their prices, however, relative to other commodities, and the rise in prices of domestic commodities as compared to international commodities, as well as the rise in export prices as compared to import prices, would operate to decrease exports, increase imports, sufficiently to effect a transfer of the loan in the form of goods.
*73

In my
Canada’s balance, I conceded that the increase in means
of payment in the borrowing country would, even in the absence of price changes, result in both a decrease in exports and an increase in imports. I claimed, however, that in the absence of price changes and of special circumstances it was to be expected that the borrowings abroad would not disturb the proportions in which the total purchasing power in the borrowing country, including that derived from the loan, would be used in buying domestic and foreign commodities; and I claimed further that without a change in these proportions the direct effect of the transfer of means of payment would not suffice fully to adjust the balance. I held, therefore, that there would have to occur relative price changes of the type postulated by Taussig, namely, for the borrowing country, a rise of export prices relative to import prices and of domestic commodity prices relative to both export and import prices.
*74

To my statement that, in the absence of price changes, it was theoretically to be expected that increase in the amounts available for expenditure by the borrowing country would not result in a change in the proportions in which these expenditures were distributed among the different classes of commodities, it has been objected that “there are ample grounds to dispute this view,”
*75 and that “there is every reason to believe, on the contrary, that borrowings abroad would disturb the proportions.”
*76 But this statement was not intended to be a denial of the obvious fact that there were an infinite number of proportions in which the increased funds could conceivably be divided among the three classes of commodities, nor even as an assertion that in the absence of price changes the probability that the proportions in which the expenditures were divided among the three classes of commodities would not be disturbed was greater than the probability that these proportions would be disturbed, i.e., was greater than all the other probabilities combined. The probability that the
proportions would be disturbed is obviously infinitely greater than the probability that they would not be. If an indifferent marks-man aims at a distant target, the probability that he will hit the bull’s-eye is, on the basis of experience, small. But it is nevertheless much greater than the probability that he will hit any other single spot in the universe, and if a forecast of his shot must be made, the probable error will be minimized if, in the absence of a known bias in his marksmanship or in the conditions governing his shooting, it is forecast that he will hit the bull’s-eye.
*77 The assumption that, in the absence of price changes and of known evidence to the contrary, the amounts available for expenditure in each country would after their increase or decrease be distributed among the different classes of commodities in the same proportions as before still seems to me more reasonable than any other specific assumption. It represents what Edgeworth in another connection described as “a neutral condition between two conditions of which neither is known to prevail.”
*78 But this assumption was not sufficient to justify such definite conclusions as I drew from it, and in occupying themselves with the assumption instead of with the partly erroneous inferences I based upon it my critics have directed their ammunition at the wrong target.

The existence of domestic commodities affects the mechanism of adjustment only as it affects the manner in which the amounts available for expenditure are apportioned as between native
*79 and foreign products. The assumption of the existence of domestic commodities is not essential to any valid theory of the general mechanism of adjustment of international balances to disturbances; and certainly no quantitative proposition as to their importance relative to international commodities need be incorporated in an abstract explanation of the mechanism. But if “domestic” commodities do exist, certain important consequences ensue, and it becomes necessary to take specific account of them in the analysis. For a commodity to be a “domestic” commodity, be it noted, it is not necessary that its prices be wholly
independent of the prices of similar commodities abroad, or of the prices of competitive or of complementary international commodities at home. If this were the case, there could obviously be no “domestic” commodities in a world in which all prices are parts of an interrelated system. It suffices to make a commodity a “domestic” commodity if it ordinarily does not cross national frontiers and if its price is not tied directly to the prices of similar commodities abroad in such manner that there is always a differential between them approximating closely to the cost of transportation between the two markets.
*80

That in the United States, for instance, there is an extensive and important range of commodities (including services) available for purchase whose prices are capable of varying within substantial limits while the prices of identical or similar products or services in other countries remain unaltered, seems to me so obvious that it would not require restatement had it not been disputed. One writer
*81 has claimed, however, not only that the existence of a substantial range of domestic commodities is a vital assumption of the ordinary theory of the mechanism but that such an assumption is contrary to the facts. But the evidence he offers in support of his argument consists only of an irrelevant demonstration that the prices in different markets of identical commodities actually moving in international trade in constant directions are bound together in a close relationship.

VII. THE MECHANISM OF TRANSFER OF UNILATERAL PAYMENTS

IN SOME RECENT LITERATURE

Recent discussion of the problem of the effect of international unilateral payments on the terms of trade has made it clear that the older writers (including myself) had not sufficiently explored
the problem and had failed to realize its full complexity. There follows an account of some recent attempts at a more definitive solution of the problem.
*82

Wilson.

Wilson examines the effects on relative prices, and especially on the commodity terms of trade, of trade, of a continued import of capital, with the aid of an elaborate series of arithmetical illustrations of an ingenious type.
*83He concludes that relative price changes will ordinarily be necessary for restoration of equilibrium, but that the type of change will depend on the particular circumstances of each case, and may be unfavorable the paying country. He believes that he demonstrates that the changes in export and import prices,
relative to each other, make no direct contribution to bringing about a transfer of the loan in the form of goods instead of in money, but that the role of these changes is solely to determine for each country to what extent the transfer shall take place through a change in exports or a change in imports, and to bring the two countries to a uniform decision, and that it is the relative changes in prices between domestic and international commodities which, together with the shift in demands resulting from the transfer of means of payment from lender to borrower, brings about the transfer of the loan in the form of goods.
*84 Wilson’s account marks a distinct advance over previous attempts, because it takes more of the variables simultaneously into account and deals with some of them with a greater measure of precision of analysis than had previously been achieved. While he carries the problem forward toward a solution, there are, however, some defects in his mode of analysis which seriously detract from the significance of the concrete results which he obtains.

Wilson’s mode of analysis and the nature of the results which he obtains can for present purposes be made sufficiently clear by reference to two of his arithmetical examples, I and IV,
*85 which are here presented in somewhat modified form to simplify the exposition. It is assumed in both examples that production is under conditions of constant cost; that in the absence of price changes the transfer of the payments will not change the proportions in which either country would desire to distribute its expenditures as between the classes of commodities available to it; and that the amount to be paid is 9 monetary units. In Wilson’s example I there are no domestic commodities in either country, while in his example IV there are domestic commodities in each country. Purchases are measured in monetary units uniform for both countries. The paying country’s export commodity is represented by P, and its domestic commodity by D
_p; the receiving country’s export commodity is represented by R, and its domestic commodity by D
_r.

Granted Wilson’s assumptions, his example I is an adequate demonstration of the possibility that payments can be transferred without resulting in any movement of the terms of trade. Under the conditions given, the receiving country is willing in the absence of price changes to increase its purchases of each of the commodities to an extent just sufficient to offset the decreases in
purchases by the paying country, and therefore no price changes are necessary for the restoration of equilibrium. This example suggests a general principle already formulated by a previous writer in this connection that “If the borrower wants what the lender does without, no change in prices is necessary.”
*86 It is to be noted, however, that in example I one of the countries spends a substantially larger amount on foreign than on native commodities. It will be found upon experimentation that, given the assumption that in the absence of price changes the international loan or tribute will not cause either country to desire a change in the proportions in which it had hitherto distributed its expenditures between native and imported commodities, the transfer of the loan or tribute will necessarily result in a movement of the terms of trade unfavorable to the paying country unless before reparations the unweighted average ratio of expenditures on native to expenditures on foreign commodities for the two countries combined is unity or less, an improbable situation when there are domestic commodities.

In example I there were assumed to be no domestic commodities. To show that his conclusion—that the transfer of payments will not necessarily involve a movement of the terms of trade against the paying country and may even involve a movement of the terms of trade in its favor—is not dependent on the assumption that there are no domestic commodities, Wilson presents his example IV, in which domestic commodities are introduced for both countries but otherwise the same assumptions are followed as for example I.

Comparing separately for each commodity the amounts which in the absence of price changes the two countries combined would be willing to purchase after the payments with the amounts they purchased before the payments, Wilson concludes that while the price of the receiving country’s domestic commodity would rise, and the price of the paying country’s domestic commodity would fall, the aggregate demand for the receiving country’s export commodity will at unaltered prices have fallen more (from 60 to 58) relatively than the aggregate demand for the paying country’s export commodity (from 50 to 49) and therefore the price of the former will probably have to fall relatively to the price of the
latter to restore equilibrium. For the relations of the price levels of the internationally-traded commodities, he reaches the general conclusion that: “No matter what be the original proportions of total demand,
that class of goods will be higher relatively in price to the other, for which the borrowing country has the greater relative demand as compared with the lending country.”*87

No significance can be attached, for constant cost conditions, to the results derived by Wilson from his example IV, since it fails to take into consideration the necessary relationship between the prices in each country of domestic and export commodities resulting from their competition for the use of the same factors of production. If in either country the prices of domestic commodities rose or fell relative to export commodities, factors of production would be diverted from the low-price to the high-price industry until the earning power of the factors in the two industries was equalized, and under constant costs this would mean that in neither country could there be relative changes between the prices of domestic and export commodities. What the direction of relative change of the prices of the products of the respective countries will be as the result of international payments will depend on what effect the payments have on the relative aggregate demands of the two countries for
all the products, and therefore for the factors of production, of the respective
countries. In Wilson’s example IV, the payment results, in the absence of price changes, in an increase in the aggregate demand for the products of the receiving country (275 after the payment as compared to 270 before the payment) and in a decrease in the aggregate demand for the products of the paying country (85 after the payment as compared to 90 before the payment). The prices of the factors, and consequently the commodity terms of trade, must therefore move against the paying country if equilibrium is to be restored.

To an objection to his analysis made by some unspecified person
*88 to the effect that the flow of gold from lending to borrowing country, by raising money prices and incomes generally in the borrowing country, and lowering them generally in the lending country, will make the prices of the productive services and therefore also of their products, in domestic and export industries alike, rise in the borrowing country and fall in the lending country, Wilson replies that: “mere changes in money costs of production are not sufficient in themselves to cause a change in prices. If prices are to be affected by changes in costs of production, it can only come about through a change in the relative demand and supply of those goods whose money costs of production are affected,” and that the relative changes in price which such changes in cost would tend to produce would tend to be checked by diversion of expenditures to or from other classes of goods not so affected.
*89 This reply bears only on the
degree of relative price changes needed, whereas the issue is whether
any price changes are needed, and if so, in what directions. It, moreover, misses the character of the valid objection to which his analysis is open, which is not the common but fallacious argument that relative changes in the amounts available for expenditure in the two countries must necessarily result in changes in the same direction in the prices of the productive services and therefore also in the money costs of production of the two countries,
*90 but that changes in the relative aggregate demands for the commodities of the respective countries will do so. If, as is possible, but, as will later
be shown, improbable, a transfer of funds on loan from country A to country B results in an increase in the aggregate demand of the two countries for A’s products and a decrease in their aggregate demand for B’s products, it will be the prices of A’s, and not of B’s, factors of production which will rise.

Yntema.

Yntema applies to the problem a powerful mathematical technique, and analyzes it on the basis of a wide range of assumptions.
*91 For cases such as those contemplated by the older writers, he reaches conclusions substantially in accord with theirs, especially with reference to the relative movement of the prices of the domestic commodities of the two countries and of their double factoral terms of trade.
*92 But Yntema’s analysis rests throughout on certain assumptions which seriously limit the significance of his results. He assumes that when a relative change in the amount of money in two countries occurs as a result of loans or tributes or other disturbances in the international balances, there will occur in the country whose stock of money has increased a rise not only in all of that country’s demand schedules (in the simple Marshallian sense), but also in the prices of the factors of production and in the supply schedules of that country’s products, and that there will similarly occur in the country whose stock of money has decreased a fall not only in all of that country’s demand schedules, but also in the prices of its factors of production and in the supply schedules of that country’s products, though these rises or falls need not be uniform in degree within each country. But a rise in all the demand schedules of a country does not necessarily lead to or require a rise in its supply schedules or in the prices of its factors of production. What will be the effect of an international transfer of income on the
direction of the relative movement of the prices of the factors in the two countries is itself the question relating to the equilibrating process awaiting solution, but in Yntema’s analysis it is unfortunately decided by arbitrary assumption. Yntema’s conclusion that under constant cost the terms of trade must necessarily shift in favor of the receiving country results from his assumption that the prices of the factors and the money costs of production will necessarily
rise in the receiving country. As had been argued above, this is not a valid assumption.

Ohlin.

In his important treatise,
*93 Ohlin gives an elaborate account of the mechanism, whose most important contribution is the convincing demonstation that not price changes only but also relative shifts in demands resulting from the transfer of means of payment, are operative in restoring a disturbed equilibrium in the balance of payments. On the question immediately at issue, i.e., the specific mode of operation of relative changes in sectional price levels in the mechanism of adjustment, he is extremely critical in tone in his treatment of the older writers, although as long as he adheres to the traditional assumptions he follows the traditional reasoning and conclusions only too closely. Ohlin claims that the older writers exaggerated the importance of relative price changes in the equilibrating process both because they overlooked the direct influence on purchases of the shift in means of payment and because the ordinarily high elasticity of foreign demand for a particular country’s exportable products makes a small change in price exert a large influence on the volume of trade. Subject to the qualification that I believe I have shown that recognition of its validity was not nearly as rare among the classical expositors of the theory of international trade as he appears to take for granted, I concede his first point. But on the second point, at least a partial defense can be made of the position of the older writers. When two factors are necessarily associated in a complex economic process, there is rarely a satisfactory criterion for measuring their relative importance, even if all the quantitative data that could be desired were available. Ohlin appears to regard the relative degree of price change as between different classes of commodities as an appropriate measure of the importance of such price changes in the equilibrating process. A more appropriate criterion, if it could be applied, would be the proportion of (1) the equilibrating change in the trade balance which results from relative price changes to (2) the total change in the trade balance necessary to restore equilibrium. Since foreign demands for a particular country’s products ordinarily have a high degree of elasticity, small price changes in the right direction can exert great equilibrating influence. But the emphasis
which Ohlin gives to the question of the degree of change seems to me a novel one, as far as discussion of mechanism is concerned, and I cannot recall a single instance in the older literature where a definite position was taken as to the extent of the price changes necessary to restore a disturbed equilibrium.

Taking the case of international loans,
*94 Ohlin assumes, as a first approximation, that “all goods produced in a country require for their manufacturing ‘identical units of productive power’ consisting of a fixed combination of productive factors.” The lending country B must make initial remittances to the borrowing country A. The assumptions as to the effects on demands are not clearly stated, but seem to be as follows: the aggregate demands in terms of money prices of the two countries combined (1) for the export goods of A and (2) for the export goods of B, are each assumed to remain unaltered;
*95 (3) the demand in A for A “domestic” goods increases; (4) the demand in B for B “domestic” goods decreases. This “implies” a shift in demand from B factors to A factors, which “raises the [relative] scarcity of the A unit, which means that every commodity produced in A becomes dearer than before compared with every commodity produced in B. The terms of exchage between A’s export goods and B’s change in favor of A.”
*96 So far, therefore, there is no correction of the older doctrines with respect to the
kind of price changes necessary to restore equilibrium. But Ohlin attributes these results to the assumption that all industries use identical “units of productive power,” and remarks that it is because they have expressed costs in such units that “men like Bastable, Keynes, Pigou, and Taussig have stopped at the preliminary conclusion in §5 and have found a variation in the terms of trade certain in all cases, at least where the direction of demand is not of a very special sort.”
*97

These results, however, arise not from the assumption of the use in each country of identical “units of productive power,” but from Ohlin’s assumption that the transfer of funds does not of itself lead to any alteration in the aggregate monetary demand for the export commodities of the respective countries. Even with both these assumptions, they are not
necessary results, if it be granted that, without price changes, the increase in funds in A may lead to a
decrease in the demand for A “domestic” goods, or that the decrease in the funds in B may lead to an
increase in the demand for B “domestic” goods, or both, consequences by no means inconceivable, as, for instance, if A’s and B’s domestic goods are both predominantly low-grade necessaries of the sort heavily consumed only when there is economic pressure.
*98 But Ohlin would probably regard—and not without justification—such movements of demand as “of a very special sort” and therefore not calling for consideration.

Abandoning the assumption of identical “units of productive power” and substituting the assumption that different industries use different factors, and use the same factors in different proportions, Ohlin shows that by introducing additional assumptions of non-competing factoral groups, the existence of idle resources, the tendency of the prices of the products to rise more rapidly than the prices of the factors in an expanding industry, and so forth, instances are possible where the commodity terms of trade turn against rather than in favor of the borrowing country.
*99

It is to be noted that some of these assumptions are of a non-equilibrium nature, i.e., can be valid only temporarily. But granted that Ohlin has shown the
possibility that the terms of trade, when such assumptions are made, will turn
against the borrowing country, what about the probabilities? Every one of these added factors is as likely,
a priori, to accentuate the movement of the terms of trade in favor of the borrowing country as to operate to move them against the borrowing country. Take only one example, sufficiently representative of the others: Ohlin argues that the factors used relatively largely in expanding industries are
likely to rise in price, while those used relatively largely in declining industries are likely to fall in price; in the borrowing country, the domestic commodity industries will be expanding, because of the increased demand for their products, while the export commodity industries will be declining, presumably because of decreased demand in the lending country for their products; the prices of the factors used largely in the domestic commodity industries therefore will rise, while those used largely in the export commodity industries will fall. In the lending country, reverse trends will be operating. The export commodities of the borrowing country therefore will decline in price relative to the prices of the export commodities of the lending country; i.e., the terms of trade will move against the borrowing country. But the export commodity industries of the borrowing country are not,
a priori, more likely to decline than to expand. The foreign demand for their products, it is true, will tend to fall, but Ohlin overlooks that the home demand for their products will tend to rise, and that there is no obvious reason why the latter tendency should be expected to be less marked than the former and to be insufficient to offset the former.

Pigou.

In a recent article Pigou has attacked the problem in terms of marginal utility functions, and has reached the conclusion that, under constant costs, there is a strong presumption, but not a necessity, that the commodity terms of trade (which he calls the “real ratio of international interchange”) will turn against the paying country as the result of reparations.
*100 Pigou’s results, it will later be shown, can in part at least be reached by an alternative procedure which is simpler and has the additional virtue that it does not involve resort to utility analysis. But Pigou’s analysis can be made to serve the useful function of bringing into clear view the utility implications of this alternative procedure, and thus warrants detailed examination and elaboration.

In order that the new terms of trade should be equal to the old, it would therefore be necessary that

which, for linear functions, implies
*101 that

It can similarly be shown that reparations will cause the terms of trade to turn in favor of Germany if
and to turn against Germany if

VIII. A GRAPHICAL EXAMINATION OF PIGOU’S ANALYSIS
*102

The examination of Pigou’s algebraic analysis, and especially of its economic implications, can be facilitated by the use of
graphical illustrations. In chart III the left-hand diagram relates to the representative Englishman and the right-hand diagram to the representative German. Commodity units of the respective commodities are so chosen, for each country separately, as to be equal in price prior to reparations. For the English and the German “representative” consumer, respectively, the quantity purchased before reparations of his own country’s commodity is measured on the
df or
d₁f₁axis, to the left from the
oa or
o₁a₁axis, and the quantity purchased before reparations of the imported commodity is measured on the same axis but to the right from the
oa or
o₁a₁, axis. For the representative consumer in each country the marginal utilities of the different commodities are measured vertically from the
bc, or
b₁c₁, axis. The curve of marginal utility to the representative English consumer is, therefore,
ab for the native commodity and
ac for the imported commodity, and
a₁b₁and
a₁c₁are similarly the curves of marginal utility to a representative German of the German and the English
commodities, respectively. Since the utility functions are assumed to be linear,
ab, ac,a₁b₁and
a₁c₁, are all drawn as straight lines.

In chart III there is substituted, for the two “marginal
disutility of surrendering” functions which Pigou uses (i.e.,
ƒ(
nX) and ψ(
mY)), the corresponding marginal
utility curves,
ab and
a₁b_1. The substitution does not call for a change in the numerical value of the slope, and by placing the
ab and
a₁b₁ curves on the left side of
oa, o₁a₁ axes, i.e., by making their inclinations positive, change of signs is also avoided. Since ø = the slope of
ac,ƒ’ = the slope of
ab,ψ’ = the slope of
a₁b₁ and
F’ = the slope of
a₁c_1, Pigou has demonstrated that the terms of trade of Germany will not change, will move against Germany, or will move in favour of Germany according as

Unless, however, some presumptions can be established as to the relative slopes of the various utility curves, no progress has been made toward determining the probable effects of reparations payments on the terms of trade. To establish such presumptions Pigou resorts to two additional sets of presumptions, first, that before reparations each country spends more on native than on imported goods, and second, that the utility functions within each country are “similar.”

The presumption that each country before reparations spends more on its own products than on foreign products is equivalent to making
de > efand
d₁e₁ >
e₁f₁ in chart III. Pigou adopts it, presumably, on the ground that such is almost invariably the actual situation. The general prevalence of this situation results, however, chiefly from restrictions on foreign trade, from the existence—by no means universal—of greater international than internal costs of transportation from producer to consumer, and, above all, from the fact that included in the native commodities of each country are “domestic” commodities, or commodities which because of regional differences of taste or non-transport-ability cannot find a market outside their country of production. But Pigou presumably abstracts from trade restrictions and transportation costs, and he explicitly excludes “domestic” commodities by his assumption that “there is only one sort of good made in the reparation paying country and only one sort made in the rest
of the world.” In the absence of these factors, there would be no
a priori presumption that there was any difference in either area in the amounts spent for native and for imported commodities if the two areas were equal in size, size being measured in terms of the pre-reparations value of output or of consumption. If the two areas were unequal in size, the most reasonable assumption would appear to be that, at the pre-reparations equilibrium, prices of the commodities would be such as to induce each country to spend more on the larger country’s than on the smaller country’s product. To justify acceptance of a general presumption that each country spends more on its own than on imported products it is necessary to recognize the existence of trade restriction, transportation costs, and above all, “domestic” commodities. It will be shown, moreover, that while an excess in each country before reparations of expenditures on native over expenditures on imported commodities, of itself, whatever its cause, tends to make
, i.e., to contribute toward a situation in which reparations will make the terms of trade turn against the paying country, to the extent that such excess is due to higher international than internal transportation costs or to import duties this tendency
unfavourable to the paying country will, given linear utility functions, be more than offset by the counter-tendency of the transportation costs and import duties to cause deviations from “similarity” of the utility functions within each country in directions
favorable to the paying country.

For the two-country case, the assumptions of linearity and of
“similarity” within each country of the utility functions turn out to involve as a corollary the familiar assumption in other discussions of this problem that, in the absence of relative price changes, changes in the amounts available for expenditure in the respective countries resulting from reparations payments will not affect in either country the proportions in which these expenditures are apportioned between native and foreign commodities. Before reparations the representative Englishman bought
ed units of English commodities and
ef units of German commodities. Since the commodity units in chart III have been so chosen as to make the pre-reparations prices of the two commodities equal, their marginal utilities must have been equal to a representative English purchaser of both, i.e.,
kd =
lf. Therefore,
d, e, f, must be points on a horizontal straight line. Suppose that in the absence of relative price changes the representative Englishman, after reparations, buys
hg units of English commodities and
hj units of German commodities. If no changes have occurred in their relative prices, the two commodities must still have equal marginal utilities to him, i.e.,
g, h, j, must be points on a horizontal straight line. From the geometry of triangles it follows that
i.e., that in the absence of relative price changes, changes in the amount of his aggregate expenditures will not affect the proportions in which the representative Englishman distributes them as between English and German commodities. Similarly,
i.e., in the absence of relative price changes, changes in the amount of his aggregate expenditures will not affect the proportions in which the representative German distributes them as between German and English commodities.

That for the two-country case the assumptions of linearity and of similarity within each country of the utility functions plus the assumption of an excess before reparations for the representative consumer of each country of his purchases of native over his purchases of foreign commodities suffice to establish Pigou’s conclusion that reparations will necessarily cause the terms of trade to turn against the paying country, i.e., that
can also readily be demonstrated from chart III. Suppose that in chart III,
ed >
ef and
e₁d₁ >
e₁f₁. Then, since: numerically, φ’ :
ƒ’ ::
ed :
ef;numerically, ψ’ :
F’ ::
e
₁f₁ :
e
₁d
₁; and

It can be seen from chart IV that, other things equal, the greater before reparations the average ratios of excess of the consumption of native over the consumption of imported commodities in the two countries, the greater must be the average ratio of excess in the two countries of the initial utility of the imported commodity over the initial utility of the native commodity if the terms of trade are not to be turned against the
paying country by reparations payments. Although the pre-reparations ratios of consumption of native to consumption of imported commodities assumed in chart IV are much lower than would ordinarily be found in practice, the ratio of excess of the initial utility of native over the initial utility of imported commodities had to be substantial for each country (or on the average for the two countries combined) if reparations payments were not to turn the terms of trade against the paying country. If with uniform commodity units in both countries the ratio between the prices of the two commodities was identical in both countries—as would be the rule for internationally traded commodities in the absence of trade barriers or transportation costs—it would be difficult, if not impossible, to find plausible grounds for holding that such substantial “dissimilarities” of utility functions were likely to prevail in practice.

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.

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 1/3 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.
*103 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 ø’ 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,
*104 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.
*105

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.
*106

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
land 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
muchsmaller 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, 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.

X. AN ALTERNATIVE SOLUTION

That it is possible to attack the problem without resort to utility analysis is demonstrated in chart VI in terms of a two-country case, based on the assumptions that in each country before reparations more is spent on native than on imported commodities, that
the proportions in which expenditures are distributed between native and imported commodities remain unaltered in both countries, in the absence of relative price changes, as the amount available for expenditures changes, that production is carried on under constant cost conditions, and that there are no trade barriers or transportation costs. The “amount available for expenditure,” it is to be noted, is measured not in money but in units of the native commodity, or their equivalent in value, which can be bought with the money available at the prevailing prices.

Through any point,
e, on a vertical line
mn draw a horizontal line
df, such that the distance
df, represents the aggregate number of units of commodities which England can purchase with her national income before reparations at the prevailing prices, when the physical units of the commodities are so chosen that the English and the German commodity are equal in price, and such that
de, and
ef, represent the amounts of German commodities, respectively, which the English would consume before reparations at the prevailing prices. Through any point on
mn below
e draw another line
gj such that, in the absence of price changes,
gj-df would represent the amount of reparations received
by England, and
gh and
hj would represent the amounts of English and of German commodities, respectively, which the English would consume after reparations. Draw lines connecting
g with
d and
j with
f, and project them until they intercept
mn. If a change in the amount England has available for expenditure does not, in the absence of price changes, and within the range of observation, change the proportions in which England would divide her expenditures between English and German commodities, i.e., if
gh:hj::de:ef, then the projections of
gd and
jf will intercept
mn at some common point
a, above
e.

If in either or in both countries the proportion in which expenditures between native and imported commodities, in the absence of relative price changes, varies with variations in the aggregate amount of spendable funds, such variations will operate favorably or unfavorably for Germany’s terms of trade according as, in the case of Germany, the proportion spent on German goods increases or decreases with a
decrease in the amount of spendable funds and as, in the case of England, the proportion spent on German goods increases or decreases with an
increase in the amount of spendable funds. Deviation in the proportions of the expenditures in a direction favorable to Germany in either or in both countries will not suffice, however, to turn the terms of trade in favor of Germany, given an excess before reparations in the
expenditures of each country (or in both combined) on native commodities over their expenditures on imported commodities, unless such deviations are sufficiently marked to make reparations payments result in the aggregate for both countries, in the absence of relative changes in prices, in a relative increase in the demand for German commodities over the demand for English commodities.
*107

A concrete case may be cited to illustrate the type of situation in which the terms of trade might turn in favor of the paying country as the result of reparations. First, suppose that the paying country, Germany, produces two kinds of commodities, one a “domestic” commodity, primarily a necessary, and the other a luxury, which is exported but is not consumed heavily at home, and imports from England what is essentially a luxury commodity. As the spendable funds of Germany are cut down by reparations payments, there would probably occur, in the absence of relative price changes, a proportionately greater reduction in the German purchases of the luxury import than of the necessary “domestic” commodity. Suppose, in turn, that England also produces two kinds of commodities, one a “domestic” commodity, primarily a necessary, and the other a luxury, which is exported but is not consumed heavily at home, and imports from Germany what is a luxury commodity. As the spendable funds of England are increased by the reparations receipts, there would probably occur, in the absence of relative price changes, a proportionately greater increase in the English purchases of the imported luxury than of the necessary “domestic” commodity. These deviations from proportionality, both working in favor of Germany, could conceivably be sufficiently marked to make the terms of trade turn in favor of Germany as the result of reparations, even if before reparations each country spent much more on native than on foreign commodities. This would be certain to be the situation if the English demand for native commodities was such that, with prices unchanged, the English purchases of native commodities would fall absolutely when the English incomes increased, and if the German demand for native commodities was such that, with
prices unchanged, the German purchases of native commodities would rise absolutely when the German incomes decreased, demand phenomena which are no doubt highly improbable, but are not inconceivable.
*108

Demand and supply curves in terms of money prices of the ordinary Marshallian type cannot legitimately be used in the solution of the reparations transfer problem, since they abstract from the interrelationships between demands, supplies, and incomes.
*109 Nor can the problem be solved through the use of Marshallian reciprocal-demand curves without additional information, since the problem turns on what happens as the result of reparations payments to the position and shape of the reciprocal-demand curves, and this depends on the utility functions in both countries, and cannot be determined without reference, direct or indirect, to these functions.
*110

It has so far been assumed that in every industry production is carried on under conditions of constant costs. By virtue of this assumption, it has been possible to carry out the analysis without explicit reference to costs without impairing the validity of the conclusions reached. Under constant technological costs money costs can change only as the prices of the factors of production change, and, assuming no change in the supplies of the factors, their prices can change only as the aggregate demands for them from all the industries using them change. It was therefore necessary to take account only of the apportionment by the two countries of their expenditures as between their own products and foreign
products, and their mode of apportionment of their expenditures as between their “domestic” and their export commodities had no bearing on the problem. Under constant costs, moreover, the double factoral terms of trade would be affected by reparations payments in precisely the same way, both as to direction and as to degree, as the commodity terms of trade. But if some, or all, industries operate under varying costs as their output is varied, it is possible in each country for the prices of domestic and of export commodities, respectively, to move in different degrees and even in different directions as the result of a change in the volume of expenditures, so that the movement of the prices of the “domestic” commodities of the two countries may differ in direction or in degree from the movement of their export commodity prices, and the factoral terms of trade may move differently, in degree, and when the commodity terms of trade move
against the receiving country, even in direction, from the commodity terms of trade. This will hold even if there is effective mobility of the factors within each country, i.e., if the marginal value productivity and the rate of remuneration of each factor are equal in all industries in which it is employed, provided different industries use the factors in different and variable combinations. But if prices at which any factor is available are for any reason not uniform in all industries, or if there are factors which are specialized for certain industries, then the range of possible relative variation of the prices of “domestic” and of export commodities in each country will be still greater.

I venture the prediction, therefore, that when the problem is
solved for more complex cases involving varying costs as output is increased, the following conclusions derived from analysis of the simpler cases dealt with above will be found not to require substantial modification: (1) that a unilateral transfer of means of payment may shift the commodity terms of trade in either direction, but is much more likely to shift them against than in favor of the paying country; (2) that the double factoral terms of trade will ordinarily shift in the same direction as the commodity terms of trade, but under increasing costs in all industries, when the commodity terms of trade shift in favor of the paying country, the double factoral terms of trade will nevertheless shift in favor of the receiving country, or will shift in less degree than the commodity terms of trade in favor of the paying country; and (3) that the tendency of the terms of trade to move against the paying country will be more marked,
caeteris paribus, the greater the excess in each country, prior to the transfer, of consumption of native products to consumption of imported products, to the extent that such excess is not due to trade barriers or to higher international than internal transportation costs.

XI. TYPES OF DISTURBANCE IN INTERNATIONAL EQUILIBRIUM

In the examination of the probable effects on the terms of trade of a lasting disturbance of a preexistent international equilibrium, there is one basis of distinction between types of disturbances which calls for special emphasis. Disturbances are to be distinguished according as they originate in a relative change in the amounts, measured in units of constant purchasing power over native goods, available for expenditure in the two areas, or as they originate in a relative change in the demands of the two countries for each other’s products in terms of their own products resulting from changes in taste or in conditions of production, or from changes in tariffs, subsidies, internal taxes, or transportation costs.
*111 The analysis presented above of the effects on the terms of trade of reparations payments is applicable without serious modification to all lasting disturbances of the first class, i.e., involving an initial relative shift in the amounts available for expenditure, whether this shift is due to loans, tribute, or subsidy,
but is not applicable to disturbances of the second class, where, however, analysis in terms of reciprocal demand curves is appropriate in most cases.

Two consequences will follow: (1) Germany will have an adverse balance of payments with England, and specie will move from Germany to England; (2) the price of the German commodity
will fall in both countries relative to the English, so that in England it will, without duty, be lower than it was before the duty was imposed, and, including duty, will exceed the pre-duty price by less than the amount of the duty. In other words, the commodity terms of trade will have moved against Germany, with an international transfer of specie as part of the process whereby this comes about. The effect of the duty on the terms of trade is illustrated in chart VII, an application in a slightly modified
*112 form of Marshall’s foreign trade curves.

The quantity of the English commodity is measured from
o on the
ox axis, and the relative price of the English commodity, in terms of number of units of the German commodity for one unit of the English commodity, is measured from
o on the
oy axis. The curve
ae represents the quantities of the English commodity which before the duty England would be willing to export at the indicated rates of exchange of the English for the German commodity, and the curve
bg represents the quantities of the English commodity which Germany would be willing to import at the indicated rates of exchange of the English for the German commodity. Equilibrium will be established at the terms of trade
of
mn or
ot units of the German commodity for one unit of the English commodity.

An endless variety of further distinctions between types of disturbances can of course be drawn. Tributes and loans, for instance, are to be distinguished from each other by the fact that, since the former are as a rule involuntary and the latter voluntary, the problem of adjustment in the “paying” country is likely to be more serious in the former than in the latter case. Loans, moreover, call almost immediately for interest payments and eventually for amortization payments in the opposite direction from the loans, whereas this is not true of tributes. Loans are to be distinguished according to whether they are made out of income or out of capital, and according to whether the proceeds are used in the borrowing country for immediate
consumption or for investment, since the nature of the source and of the mode of use of the loan will affect the manner in which adjustment is made to the change in the amount of funds available for expenditure, and will affect also the relative availability of the different classes of commodities toward which the expenditures are directed. In actual experience the initial disturbances may come in various combinations, or may originate at home or abroad, or simultaneously in both, and, depending on the nature of the original disturbance and perhaps on other circumstances, what at one time operates as the source of the disturbance and gives rise to the need for adjustment may at other times be the equilibrating factor, with corresponding changes in the time-sequence of phenomena. Thus price changes, capital movements, changes in demand, for example, may at one time be disturbing factors, at other times equilibrating ones, and except when there are drastic disturbances whose origin is fairly obviously to be associated with contemporary events external to the mechanism of international trade itself, it will ordinarily be fruitless to try to distinguish equilibrating from adjusting factors. Some writers have attempted to generalize, however, as to the “disturbing” or “equalizing” character of specific elements in international balances. Thus Keynes, for instance, has maintained that historically the international movement of long-term capital has adjusted itself to the trade balance rather than the trade balance to capital movements,
*113 whereas Taussig
*114 has supported the opposite, and traditional, view. There is no apparent
a priori reason why the dependence should not be as much in one direction as the other, and the question of historical fact can be settled only, if at all, by comprehensive historical investigation. It is possible, however, to set forth theoretically the types of circumstances which would tend to make the one or the other the more probable direction, and to find striking historical illustrations in support of such analysis. It seems clear to me, for instance, that in the case of Canada before the war the fluctuations in the trade balance were much more the effect than the cause of the fluctuations in the long-term borrowings abroad, whereas in the case of New Zealand the fluctuations in her balance of indebtedness
since the war seem to be clearly the result rather than the cause of the fluctuations in her trade balance. In New Zealand a marked degree of dependence of the national income on the state of the crops and the world-market prices of a few export commodities, with sharp year-to-year fluctuations in the crops and in prices, makes it necessary to choose between highly unstable expenditures on consumption or domestic investment, on the one hand, and substantial fluctuations in the net external indebtedness of the country, on the other, and the choice seems to be predominantly in favor of the latter. Examination of such data as are readily available strongly confirms, however, the orthodox doctrine that, at times when “fear” movements of capital are not important, short-term capital movements are much more likely than long-term capital movements to be “equilibrating,” and that major long-term capital movements have, as Taussig maintains, mainly been “disturbing” rather than “equilibrating” in nature.

XII. SPECIE MOVEMENTS AND VELOCITY OF MONEY

The classical economists were agreed that (abstracting from the process of distribution of newly-mined bullion) there were no specie movements under equilibrium conditions, and that specie moved only to restore and not to disturb equilibrium, or, as Ricardo put it, gold was “exported to find its level, not to destroy it.”
*115 But on the range of circumstances which could disturb equilibrium in the balance of payments so as to require corrective specie movements they were, as we have seen, not in agreement. Wheatley, as much later Bastable and Nicholson, held that the balance of payments would adjust itself immediately, and without need of specie movements, to disturbances of a non-currency nature, through an immediate and presumably exactly equilibrating relative shift in the demand of the two regions for each
other’s commodities. Granted that a relative shift in demand as between the two countries may, without the aid of relative price changes, restore an equilibrium disturbed, say, by an international tribute, it is an error to suppose that the shift in demand can ordinarily occur, under the assumption, be it remembered, of a simple specie currency, without involving a prior or a supporting transfer of specie from the paying to the receiving country. The new equilibrium requires that more purchases measured in money be made per unit of time in the receiving country and less in the paying country; as has been shown above, it is by its effect on the relative monetary volume of purchases in the two countries that the relative shift in demands exercises its equilibrating influence. Unless as and because one country becomes obligated to make payments to the other velocity falls in the paying country and rises in the receiving country, these necessary relative changes in purchases and in demands will not occur except after and because of a relative change in the amount of specie in the two countries, and such changes in velocity are at least not certain to occur, nor to be in the right directions if they do occur. Acceptance of the doctrine that a relative shift in demand schedules may suffice, without changes in relative prices, to restore equilibrium in a disturbed international balance does not involve as a corollary that specie movements are unnecessary for restoration of equilibrium, as Wheatley, Bastable, Nicholson, and others seem to have supposed. The error arises from acceptance of a too simple version of the quantity theory of money, in which price levels and quantities of money must move together and in the same direction regardless of what variations may occur in other terms of the monetary equation. In its most extreme application this erroneous doctrine has led to the conclusion that if unilateral payments should perchance result in a relative shift in price levels in favor of the
paying country, the movement of specie will be from the receiving to the paying country!
*116

Under the assumption of a simple specie currency, the significant velocity concept for the analysis of the mechanism of international trade is accordingly the ratio of final purchases per unit of time to the amount of specie in the country, which we will call the “final purchases velocity of money.” This concept
is to be distinguished not only from the familiar velocity concept, or the “transactions velocity of money,” but also from the “income” or “circuit” velocity of money concept. This latter is for our purposes a more serviceable concept than the “transactions velocity,” since it disregards many kinds of transactions which are of no direct significance for the international mechanism. It is nevertheless not a wholly satisfactory concept for the present purpose. For any limited period of time “income” is not only difficult of measurement but almost incapable of definition. It does not matter, moreover, for the mechanism of international adjustment whether what is spent comes from current net income or from disposable capital funds, borrowings, internal or external, or “negative income” or business losses eventually to be defrayed by the creditors. Nor does it matter whether the expenditures are for consumption or for maintenance or expansion of investment, except indirectly as this may affect the productive resources of the country or the apportionment of expenditures as between different classes of commodities. What matters for present purposes is primarily the ratio to the volume of money of the expenditures per unit of time which, for that unit of time, make an equivalent reduction in the willingness to spend of the purchasers.
*117 The final purchases velocity of money will of course necessarily be much smaller than the transactions velocity. It may be smaller or larger than the income velocity. It will tend to be smaller than the income velocity in so far as the latter covers income not spent or invested at home but hoarded or lent abroad. It will tend to be larger than the income velocity in so far as the latter fails to take account of maintenance and replacement expenditures, disinvestment expenditures, or expenditures of the proceeds of external or internal borrowings.

Since the relative change in the amount of final purchases in the two areas is an important equilibrating factor in the process of adjustment to a disturbance in their international balances, then, assuming no change to occur in either country in the final purchases velocity of money, the greater is the weighted average final purchases velocity of money in the two countries combined, the smaller will be the amount of money necessary to be transferred to restore a disturbed equilibrium, other things remaining
the same. If, as the result of a transfer of specie to meet the first instalments of new and periodic obligations of one country to the other, a sudden change occurs in the amount of money in each country, and the volume of final purchases in each country does not immediately respond proportionately to the change in the amount of money, the amount of transfer of money to the receiving country will for a time have to be greater than the amount of such transfer ultimately necessary, and after the velocities in the two countries have recovered their normal levels, but before the periodic payments have terminated, a partial return of money to the paying country will occur. If, on the other hand, change in the amount of money tends to be accompanied with change in its velocity in a corresponding direction, a smaller initial transfer of money will suffice for the time being, but as the velocities recede to their normal levels more money will have to be transferred from the paying to the receiving country to maintain their relative volumes of final purchases at the new equilibrium level. In all cases, the amount of specie transfer necessary for adjustment to a disturbance will depend on the velocities of money in the two areas as well as on the manner in which the demands for different classes of commodities behave as the amounts of money are varied. Except under very unusual conditions, however, adjustment of the balance of payments to new and continuing unilateral remittances will require some initial transfer of specie from the paying to the receiving country.

The final purchases velocities in the two countries not only help to determine the amount of specie transfer necessary for adjustment, but they also help to determine what effects the remittances shall have on the
absolute price levels in the two countries combined. If in the receiving country money has a higher velocity than in the paying country, the transfer of means of payment will result in a higher level of prices for the two countries combined, and vice versa. It is even conceivable, though not of course probable, that reparations payments may result in higher (or in lower) prices in
both of the countries. Failure to take into account the possibility of different velocities in the two countries has led some writers to deny this even as a theoretical possibility.
*118

In case A, the final purchase velocity of money per month, both before and after
*119 the beginning of the reparations payments is unity in both countries, and prior to the transfer the final purchases per month are 3000 in the receiving country and 1500 in the paying country. There must therefore have been, in the initial equilibrium situation, 3000 monetary units in the former, and 1500 in the latter, country. A transfer of 600 monetary units from the paying to the receiving country takes place when the payments begin, and the resultant shifts in demands bring about an adjustment of the balance of payments of the two countries to the tribute without necessitating any change in prices. In case B the velocity of money per month both before and after the beginning of the tribute payments is 2 in the receiving country and 1 in the paying country, and prior to the transfer there are 1500 units of money in each of the countries. To restore equilibrium; a transfer of only 450 units of money is necessary. But since the
transfer of money is from a low-velocity to a high-velocity country, it results in an increase in the world level of prices and of money incomes. As in case A, however, equilibrium is restored without any change in the terms of trade. In case C the velocity of money is ½ in the receiving country and 1 in the paying country, and prior to the transfer there are 6000 units of money in the receiving country and 1500 in the paying country. To restore equilibrium a transfer of 720 units of money is necessary. But since the transfer of money is from a high-velocity to a low-velocity country, it results in a decrease in the world level of prices and of money incomes. As in the previous cases, however, equilibrium is restored without any change in the terms of trade. Whatever other cases were chosen, the same conclusion would be indicated that the effect of a transfer of payments on
relative prices is independent of the velocities, provided that such changes in money incomes as are offset by corresponding changes in prices are assumed not to affect the apportionment of expenditures among different classes of commodities.
*120

In the older literature, analysis of this sort of the role of velocity of money in the mechanism of adjustment of international
balances is to be found, if at all, only by implication. In the more recent literature, also, discussion of this phase of the mechanism is scanty. Ohlin’s treatment of velocity is imbedded in his exposition of the mechanism as a whole, but there seems to me to be agreement between our accounts in so far as they cover the same ground. D. H. Robertson, in a short essay,
*121 which nevertheless contains in germ much of what has here been more elaborately expounded with reference to the transfer mechanism, also treats the velocity factor, in so far as he carries his analysis, in the same manner in which it is here treated. But concerned presumably more with establishing certain possibilities than with surveying the range of probabilities, he applies his analysis only to assumptions so extreme as to lead him to highly improbable conclusions. In an analysis of the effects of reparations payments by Germany to America on specie movements, terms of trade, and aggregate income in the two countries, he introduces an annual velocity of money factor, assumed to be unity and invariable in each country, and which represents the ratio of annual income, or annual expenditure, to the stock of money. From an arithmetical illustration he concludes that the payment by Germany of reparations need involve no transfer of money, no alteration in the terms of trade, and no change in “gross monetary income” in either country. Substituting “final purchases” for “gross monetary income,” and taking only the data which he presents for America, his illustration is as follows:

America

Before Reparations Payments

Final purchases of £1,600 buy 900 American goods + 100 German goods and pay £600 taxes.

Gold stock £1,600.
V = 1.

Price of American goods = £1.

During Reparations Payments at the rate of £600 per year

Final purchases of £1,600 buy 900 American goods + 700 German goods.

Gold stock £1,600.
V = 1.

Price of American goods = £1.

How extreme the assumptions are on which all of these results
depend is not made apparent only because they are not brought clearly into the open in either the illustration or the accompanying text. The illustration assumes that the government of America uses the proceeds of the reparations payments to remit taxation, but it presumably continues to render the same services to the community, for otherwise £600 of spending power would be unaccounted for. As far as final purchases or “gross money incomes” are concerned, the apparent absence of an increase when reparations are received is due solely to the fact that real income in the form of government services for which previously £600 was paid by individuals in taxes is now met by the reparations income of the government and therefore does not appear in the accounts of
private monetary income. As far as money stocks are concerned, the absence of any increase in the receiving country can be explained only if the periodic receipt of the reparations payments and their use by the government in hiring personnel and buying materials with which to carry out its functions requires no use of the country’s stock of money, whereas collection of taxes equal in amount to the reparations plus use of the tax receipts in the identical fashion in which the proceeds of the reparations are used would involve the use of £600 throughout the year. As far as the commodity terms of trade are concerned, the absence of any change is to be explained by the assumption that although in the receiving country no prices have changed and spending power has increased by £600, no increase will occur in that country in the amount of its own goods or governmental services demanded by its people.

XIII. COMMODITY FLOWS AND RELATIVE PRICE LEVELS

Graham and Feis hold that the explanation of the mechanism of adjustment of international balances to capital borrowings offered by the classical economists and their modern followers omits reference to a factor operating to bring about relative shifts in price levels in the direction opposite to that posited in this explanation. Graham claims that since the effect of a loan is to shift goods from the lending to the borrowing country, the volume of goods relative to the volume of gold will be increased in the borrowing country and decreased in the lending country, and therefore the prices will tend to fall in the former and rise in
the latter. On the assumption that the first phase of the mechanism is a transfer of gold from the lending country to the borrowing country unaccompanied by a transfer of goods, and that the transfer of goods is a later phase, Graham, calling the former the “short-range” effect of capital movements and the latter the “long-range” effect, concludes that “the short and long range effects of borrowings will run in opposite directions.”
*122 He had earlier applied the same reasoning to the problem of the adjustment of international balances to capital imports under an inconvertible paper currency, on the assumption that the quantity of money in each country is held constant.
*123 Feis accepts Graham’s argument:

The effects of the goods movements upon price levels would, therefore, tend to be in the opposite direction to those produced by changes in the volume of purchasing power in each of the countries concerned, as Professor Graham has pointed out. Apparently, two conflicting tendencies are present in each country during the process of adjustment. These tendencies may or may not be simultaneous and equal in strength.
*124

This reasoning seems erroneous to me. The conclusion of these writers results from a mechanical application of the
formula of price determination to the international trade mechanism, on the implicit assumptions that the price level is result and not cause, and that the changes in
M and the changes in
T are unrelated and independent factors in the mechanism,
*125 and
Feis, at least, explicitly attributes the same assumptions to the classical school.
*126 But in the classical theory, as in the preceding exposition, the establishment of international equilibrium is regarded as primarily a problem of international adjustment of prices, and the direction and extent of flow of specie, and therefore also the relative amounts of money in the two countries, instead of being treated as independent factors, are held to be determined by the relative requirements for money of the two countries given their equilibrium price levels and their respective physical volumes of transactions requiring mediation through money. The bearing of the commodity flows in the mechanism, therefore, is not their influence on the relative price levels, but is, instead, their influence on the quantity of specie flow necessary to support the price relations required for equilibrium.

Let us suppose that when the lending first begins the lending country ships sufficient commodities on consignment to the borrowing country to bring its export surplus to equality with its volume of lending per unit period, but that, in consequence of the influx of goods, prices as a whole fall in the borrowing country to a level lower than is consistent with the maintenance of its import surplus at the required amount. A new or intensified flow of specie must thereupon occur from lending to borrowing country, so as to bring prices (and demands) in the borrowing country to a level adequately high to result in a continuing import surplus equal to the borrowings.
*127

XIV. EXCHANGE RATES

Hume conceded that the fall in the exchange value of a country’s currency when for any reason there was adverse pressure on its balance of payments tended to exercise an equilibrating influence by providing an extra incentive to commodity export and a deterrent to commodity import. He held, however, that this could be but a minor factor in the process of adjustment, and although he gave no reasons it may be presumed that he saw that under a metallic standard the maximum possible range of variation of the exchanges, i.e., between the specie export and import points, was so limited as to make it extremely unlikely that such variation could exert an appreciable direct influence on the course of trade.
*128 Since his time the maximum range of variation has become still narrower under normal conditions because of reduction in the cost of transporting specie, and scarcely anyone today would dispute that under an international metallic standard exchange variations are a negligible factor as far as their direct
influence on commodity trade is concerned.
*129 It has sometimes been suggested, however, that this narrowing of the range between the gold points has not been an unalloyed benefit, since by its facilitation of specie shipments it has contributed to the instability of national credit structures. Proposals have been made, starting with Torrens in 1819,
*130 artificially to widen the margin between the specie points, by seigniorage charges, premiums on gold for export, different buying and selling prices for gold at the Central Bank, generous tolerance for underweight in the internal specie circulation, differential buying or selling prices for the gold of the particular degrees of fineness most in supply or demand abroad, and other similar devices, and such practices have, for this or other reasons, been followed. To the extent that such practices exist, the range of possible exchange fluctuations under a metallic standard, and therefore the possible influence of exchange variations on the course of trade, can of course be somewhat increased. In effect this is an attempt to retain the advantages of an international metallic standard while escaping in part one of its incidents, namely, the direct dependence of the national stock of money, or of the specie reserves upon which it rests, on the state of the foreign exchanges. But the same advantages of partial freedom of the quantity of the circulating medium from dependence on the vagaries of the exchanges can be more safely, and especially for an important financial center whose effectiveness depends largely on its ability to attract foreign short-term funds, more cheaply obtained, by the maintenance of excess specie reserves, than by artificial widening of the range between the gold points. Even with such widening, moreover, unless it were carried to much greater lengths than has ever been customary, the direct influence of exchange rate fluctuations on the course
of commodity trade would still be negligible. But even small variations in the exchanges can exert an appreciable influence on the movement of short-term capital funds, and through them on the mechanism of adjustment. This phase of the mechanism is discussed in the next chapter, in connection with the discussion of the relation of banking processes to the mechanism.

In their discussion of the foreign exchanges, the writers on the theory of international trade with apparently almost complete unanimity expound a particular error of minor practical importance but revealing lack of due precision in exposition or thought. They hold that when the balance of payments is even, the exchanges will be at their mint par.
*131 The correct statement is that when the balance of payments is even the exchanges will be somewhere within the export and import points. The mint par has significance for the exchanges only as a base point from which to determine the specie export and import points. Equilibrium between the amount of foreign bills demanded and offered is as likely to be reached at any one as at any other rate within the limits of the specie points. Except for the approximately fixed limits to the range of possible fluctuation of the exchanges under an international metallic standard, there is no basis for differentiating the theory of the foreign exchanges between two currencies having a common metallic standard, on the one hand, and between two currencies on different standards, on the other hand.

XV. A CRITICISM OF THE PURCHASING-POWER PARITY THEORY
*132

Owing more, probably, to good fortune than to superior insight, the classical economists escaped almost completely the fatal
error of formulating their theory of the international relationships of prices in terms of simple quantitative relationships between average price levels. But since 1916, Professor Gustav Cassel has expounded, and obtained wide acceptance of, a simple formula purporting to express the relationship to each other of national statistical price levels, which he called the purchasing-power parity theory. Some writers have found in this formula nothing but a restatement of the English classical theory, but it differs substantially from any version of the classical theory known to me.

Given a normal freedom of trade between two countries, A and B, a rate of exchange will establish itself between them and this rate will, smaller fluctuations apart, remain unaltered as long as no alterations in the purchasing power of either currency is made and no special hindrances are imposed upon the trade. But as soon as an inflation takes place in the money of A, and the purchasing power of this money is, therefore, diminished; the value of the A-money in B must necessarily be reduced in the same proportion…. Hence the following rule: when two currencies have been inflated, the new normal rate of exchange will be equal to the old rate multiplied by the quotient between the degrees of inflation of both countries. There will, of course, always be fluctuations from this new normal rate, and in a period of transition these fluctuations are apt to be rather wide. But the rate calculated in the way indicated must be regarded as the new parity between the currencies. This parity may be called the
purchasing power parity, as it is determined by the quotients of the purchasing powers of the different currencies.
*133

Cassel has expounded the theory primarily in terms of paper currencies and with special bearing on the effects of currency inflation on exchange rates. But if true for paper currencies, there is no apparent reason why it should not apply equally to gold standard currencies. Since under an international gold standard the possible range of variation of the exchanges is narrowly limited by the gold points, it should follow that under such a standard the possibility of substantial divergence of movement of price levels, in direction or in degree, in different countries is correspondingly limited. It would seem further that if substantial relative changes in the purchasing power of two currencies must generally result in corresponding inverse changes in the rates at which these currencies exchange for each other, then under equilibrium conditions metallic standard currencies must have equal purchasing power in terms of units of identical gold content,
*134 unless adequate reason can be found for holding that all the factors other than relative price levels capable of exerting an enduring influence on the exchanges were already present in the year arbitrarily chosen as the base year, had already exercised all of their possible influence on the exchange rates, and would never disappear or weaken. It is easy to conceive, however, of changes in cost or demand conditions or both, in one or the other countries, or both, which so change the relative demands of the two countries for each other’s products in terms of their own as to bring about an enduring and substantial relative change in their levels of prices, including the prices of domestic commodities and services, even under the gold standard. The existence of non-transportable goods and services in one country which have no exact prototype in the other, moreover, makes it difficult to see not only how there could be any necessity under the gold standard that the price levels be identical in the two countries, but how the two price levels could be compared at all with any approach to precision.

Cassel nevertheless accepts readily the corollaries of his doctrine:

Even when both countries under consideration possess a gold standard,
the rate of exchange between them must correspond to the purchasing power parity of their currencies. The purchasing power of each currency has to be regulated so as to correspond to that of gold; and when this is the case, the purchasing power parity will stand in the neighborhood of the gold parity of the two currencies. Only when the purchasing power of a currency is regulated in this way will it be possible to keep the exchanges of this currency in their parities with other gold currencies. If this fundamental condition is not fulfilled, no gold reserve whatever will suffice to guarantee the par exchange of the currency. Under stable currency conditions and when no radical alterations in the conditions of international trade take place, no great or lasting deviation from purchasing power parity is possible.
*135

Some writers have held that the purchasing-power parity theory is invalid if applied to
general price levels, but that it could be made acceptable, and in fact reduced to the status of a truism, if it were confined to the price levels of commodities directly entering into international trade, and if abstraction were made, as does Cassel, from relative changes in transportation costs or tariff rates. The following quotation from Heckscher is representative of this point of view:

The conception that the exchanges represent relative price levels, or, what is the same thing, that the monetary unit of a country has the same purchasing power both within the country and outside it, is correct only upon the never existing assumption that all goods and services can be transferred from one country to another without cost. In this case, the agreement between the prices of different countries is even greater than that which is covered by the conception of an identical purchasing power of the monetary unit; for not only average price levels but also the price of each particular commodity or service will then be the same in both countries, if computed on the basis of the exchanges.
*136

Cassel, however, rejects this view, and insists that the doctrine will not hold if applied to international commodities alone, since if the prices of all B’s export commodities were doubled, all other prices in B and all prices in A remaining unchanged, the exchange value of B’s currency would fall by much less than
half. Before the exchange could fall to this level, other commodities hitherto produced only for home consumption could be profitably exported by B, and its imports of A’s commodities would have fallen, and thus a further drop in its exchanges would be prevented.
*137

Cassel is right in maintaining that the doctrine need not hold if applied to the price levels of a
variable range of international commodities. But it need not hold even if applied to a fixed assortment of international commodities. Suppose that there are only two countries, that no new commodities enter into international trade, that no commodities already in international trade change the direction of their flow or disappear from trade, and that there are no tariffs or freight costs, so that all international commodities command idential prices in all markets, in terms of the standard currency when this is uniform and exchange is at par, or in terms of the currency of either of the countries converted from the other, when necessary, at the prevailing rate of exchange. Even in this case, the doctrine that the exchange rates will vary in exact inverse proportion with the relative variations in the index number of prices of international commodities in the two countries would not only not be atruism, but would not necessarily or ordinarily be true if, as would be most appropriate,
weighted index numbers were used and the basis for the weighting were, not the relative importance of the commodities in international trade (which, with only two countries, would mean identical weights for both countries) but their relative importance in the consumption or the total trade, external and internal, of the respective countries. In fact, it would be possible for the exchange rate under these conditions to change even if no change
occurred in any price, provided there were changes in the weights in the two countries, or even if no change occurred in any weight, provided there were any changes in prices, notwithstanding the necessity under the conditions assumed that any price changes should be identical in both countries.

The one type of case which would meet the requirement of exact inversely proportional changes in price levels and in exchange rates would be a monetary change in one country, such as a revaluation of the currency, which would operate to change all prices and money incomes in that country in equal degree, while every other element in the situation, in both countries, remained absolutely constant.
*138 Cassel, however, argues for at least the practical validity of his theory, as applied to actual history, on the ground that it is substantially confirmed by the facts, since under the gold standard there do not occur even over long periods wide divergences in the trends of the indices of different countries, and under fluctuating paper currencies the divergences between the actual trends of the indices and the purchasing-power parities calculated in accordance with his formula are not great and tend to disappear. He claims that the disturbances such as capital flows or tariff changes which operate to prevent purchasing-power parity from establishing itself are rarely powerful enough, as compared to the influence of the comparative purchasing power of the respective currencies, to result in a wide divergence from purchasing-power parity and are moreover likely to be temporary in character. His defense of the theory is essentially empirical rather than analytical.

It is no doubt true that the comparative purchasing power of two paper currencies in terms of all the things which are purchasable in their respective countries is at least ordinarily the most
important single factor in determining the exchange rate between the two currencies and must ordinarily be powerful enough to keep divergences of the exchange rate and purchasing power parity from reaching such lengths as, say, a rate only 50 per cent or as much as 200 per cent of the rate called for by the purchasing-power parity formula. It is also true that the exchange rate, which means approximately the comparative mint prices of gold, is ordinarily the most important single factor in determining the price levels of countries on an international gold standard. But the divergences between actual exchange rates and those required by the purchasing-power parity formula are in fact frequently substantial, and the “disturbances” from which such divergences result need not by any means be temporary in character, so that a longer period would lessen the divergence, but may in fact be progressive in character through time. Nor can these divergences be satisfactorily explained by defects in the available index numbers. On the contrary, the indices ordinarily used are unweighted wholesale price indices, and these are notoriously heavily loaded with the staple commodities of international commerce, whose prices are most likely to have uniform trends in different countries. Examination of such few indices as are constructed on a broad enough basis to give some representation to domestic commodities and services indicates, what is to be expected, that the more comprehensive the index the wider tends to be the divergence of the actual exchange rate from the purchasing-power parity rate. Use of weighted indices also ordinarily results in a widening of the indicated deviation of the exchanges from the purchasing-power parity rate.

Cassel’s theory purports to be not merely a statement of relations between quantities, but also an explanation of the order of causation, with exchange rates being determined by relative price levels, rather than vice versa. Under an international metallic standard in the long run, for any one country, and especially if it is a small country, its price level will be determined for it largely by factors external to it and impinging upon it through specie movements.
*139 Under paper standards not substantially pegged to gold, whether
de jure or
de facto, it is impossible to formulate the issue intelligently without reference to the principles
on which the quantity of money in each country is regulated, and if, as is, however, rarely the case, there is no clear governing principle, and the play of circumstances, such as the state of the national budget, pressure from business, or more or less arbitrary or traditional discount policies, are allowed to be the determining factors, there will be mutual influence of prices on exchange rates and of exchange rates on prices, with no satisfactory way of apportioning to each set of influences its share of responsibility for the actually resultant situation.

The art of economic theory to a great extent consists in the ability to judge which of a number of different factors cooperating in a certain movement ought to be regarded as the most important and essential one. Obviously in such cases we must choose a factor of permanent character, a factor which must always be at work. Other factors which are only of a temporary character and may be expected to disappear, or at any rate can be theoretically assumed to be absent, must for that reason alone be put in a subordinate position.
*140

No objection can be made to this, if it is to be understood to mean merely that minor factors should be treated as minor factors. But if it is presented as justification for the omission of mention of minor factors, and even for express denial that they are operative, on the ground that their recognition weakens the persuasive power of one’s argument, then this amounts merely to saying that bad theory may make good propaganda, and is a debatable proposition at that.
*141

101.

Pigou says that these implications are very simple
(ibid., p. 534) and does not trouble to demonstrate them. A demonstration may not be superfluous for some readers:

From (iii)

and

133.

Gustav Cassel, “Memorandum on the world’s monetary problems,” International Financial Conference, Brussels, 1920,
Documents of the Conference, V, 44-45. (Italics in the original.)

If
a and
b represent two countries,
E represents the number of units of
b‘s money which exchanges for one unit of
a‘s money,
P represents the index number of prices, and
o and
r the base and the given years, respectively, then according to Cassel:

134.

I.e., using the same symbols as in note 2,
supra: