CHAPTER XVI.
The Turnover of Variable Capital .
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The Annual Rate of Surplus-Value .
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THE TURNOVER OF VARlABLE CAPlTAL
I. THE ANNUAL RATE OF SURPLUS-VALUE
Let us assume a circulating capital of £2,500 four-fifths of which, or £2,000, are constant capital (materials of production) and one-fifth, or £500, is variable capital invested in wages.
Let the period of turnover be 5 weeks: the working period 4 weeks, the period of circulation 1 week. Then capital I is £2,000, consisting of £1,600 of constant capital and £400 of variable capital; capital II is £500, £400 of which are constant and £100 variable. In every working week a capital of £500 is invested. In a year of 50 weeks an annual product of 50 times 500, or £25,000, is manufactured. Capital I of £2,000, constantly employed in the working period, is therefore turned over 12 1/2 times. 12 1/2 times 2,000 makes £25,000. Of these £25,000 four-fifths, or £20,000, are constant capital laid out in means of production, and one-fifth, or £5,000, is variable capital laid out in wages. The total capital of £2,500 is thus turned over 25,000/2,500 , or 10, times.
The variable circulating capital expended in production can serve afresh in the process of circulation only to the extent that the product in which its value is reproduced has been sold, converted from a commodity-capital into a money-capital, in order to be once more laid out in payment of labour-power. But the same is true of the constant circulating capital (materials of production) invested in production, the value of which reappears in the product as a portion of its value. What these two portions -- the variable and the constant part of the circulating capital -- have in common and what distinguishes them from the fixed capital is not that the value transferred from them to the product is circulated by the commodity-capital, i.e., through the circulation of the product as a commodity. One portion of
A sum of £2,500 has been advanced and the value of the annual product is £25,000. But the variable portion of the circulating capital is £500; therefore the variable capital contained in £25,000 amounts to 25,000 divided by 5, or £5,000. If we divide these £5,000 by £500, we find that the number of turnovers is 10, just as it is in the case of the total capital of £2,500 Here, where it is only a question of the production of sur-
That refers to the annual rate of surplus-value. As for the amount of surplus-value obtained during a specified period of turnover, it is equal to the value of the variable capital ad-
In the case of both capitals A and B, we have invested a variable capital of £100 a week. The degree of self-expansion, or the rate of surplus-value, is likewise the same, 100%, and so is the magnitude of the variable capital, £100. The same quantity of labour-power is exploited, the volume and degree of exploitation are equal in both cases, the working-days are the same and equally
Only the capital actually employed in the labour-process produces surplus-value and to it apply all laws relating to surplus-value, including therefore the law according to which the quantity of surplus-value, its rate being given, is determined by the relative magnitude of the variable capital.[*]
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The labour-process itself is measured by time. If the Iength of the working-day is given (as here, where we assume all conditions relating to A and B to be equal, in order to elucidate the difference in the annual rate of surplus-value), the working week consists of a definite number of working-days. Or we may consider any working period, for instance this working period of 5 weeks, as one single working-day of, say, 300 hours, if the working-day has l0 hours and the week 6 days. We must further multiply this number by the number of labourers who are employed conjointly every day simultaneously in the same labour-process. If that number is taken as 10, there will be 60 times 10 or 600 hours in one week, and a working period of 5 weeks would have 600 times 5, or 3,000 hours. The rate of surplus-value and the length of the working-day being the same, variable capitals of equal magnitude are therefore employed, if equal quantities of labour-power (a labour-power of the same price multiplied by the number of labourers) are set in motion in the same time.
Let us now return to our original examples. In both cases, A and B, equal variable capitals of £100 per week are invested every week throughout the year. The invested variable capitals actually functioning in the labour-process are therefore equal, but the advanced variable capitals are very unequal. In the case of A, £500 are advanced for every 5 weeks, of which £100 are employed every week. In the case of B, £5,000 must be advanced for the first 5-week period, of which only £100 per week, or £500 in 5 weeks, or one-tenth of the advanced capital, is employed. In the second 5-weck period £4,500 must be advanced, but only £500 of this is employed, etc. The variable capital advanced for a definite period of time is converted into employed, hence actually functioning and operative variable capital only to the extent that it really steps into the sections of that period of time taken up by the labour-process, to the extent that it really functions in the labour-process. In the intermediate time, in which a portion of it is advanced in order to be employed later, this portion is practically non-existent for the labour process and has therefore no influence on the formation of either value or surplus-value. Take for instance capital A, of £500. It is advanced for 5 weeks, but every week only £100 enter successively into the labour-process. In the first week one-fifth of this capital is employed; four-fifths are advanced without being employed, although they must be in stock, and therefore advanced, for the labour-processes of the following 4 weeks.
The circumstances which differentiate the relation between
Let us consider the first 5-week productive period of capital B. At the end of the fifth week £500 have been employed and consumed. The value of the product is £1,000, hence 500s/500v=100%. Just the same as with capital A. The fact that, in the case of capital A, the surplus-value is realised together with the advanced capital, while in the case of B it is not, does not concern us here, where it is only a question of the production of surplus-value and of its ratio to the variable capital advanced during its production. But if on the contrary we calculate the ratio of surplus-value in B, not to that portion of the advanced capital of £5,000 which has been employed and hence consumed during its production, but to this total advanced capital itself, we find that it is 500s/5,000v or 1/10, or 10%. Hence it is 10% for capital
Rate of Surplus-Value of Capital B 10% ____________________________ = _____ Rate of Surplus-Value of Capital A 100%
Annual Rate of Surplus-Value of Capital B 100% __________________________________ = _______ Annual Rate of Surplus-Value of Capital A 1,000%
But 10% :100 % = 100% :1,000%, so that the proportion is the same. But now the problem has changed. The annual rate of capital B, 5,000s/5,000v=100%, offers not the slightest deviation -- not even the semblance of a deviation -- from the laws of production
Secondly: The 5-week period of turnover of capital A comprises only one-tenth of the year, so that one year contains ten such turnover periods, in which capital A of £500 is succes-
quantity or surplus-value produced annually _____________________________________ variable capital turned over annually
This is the only consequence of the laws of production of surplus-value and of the determination of the rate of surplus-value.
Let us now see further what is expressed by the ratio
Capital turned over annually _______________________ capital advanced
In the case of capital A we have:
£5,000 of capital turned over annually ________________________________ £500 of capital advanced
In the case of capital B we have:
£5,000 of capital turned over annually ________________________________ £5,000 of capital advanced
In both ratios the numerator expressed the advanced capital multiplied by the number of turnovers; in the case of A, 500 times 10; in the case of B, 5,000 times 1. Or it may be multiplied by the inverted time of turnover calculated for one year. The time of turnover for A is 1/10 of a year; the inverted time of turn over is 10/1, years; hence 500 times 10/1, or 5,000. In the case of B, 5,000 times 1/10, or 5,000. The denominator expresses the turned over capital multiplied by the inverted number of turnovers; in the case of A, 5,000 times 1/10; in the case of B, 5,000 times 1/1
The respective quantities of labour (the sum of the paid and unpaid labour), which are set in motion by the two variable capitals turned over annually, are equal in this case, because the turned-over capitals themselves are equal and their rates of self-expansion are likewise equal.
The ratio of the variable capital turned over annually to the variable capital advanced indicates 1) the ratio of the capital to be advanced to the variable capital employed during a definite working period. If the number of turnovers is 10, as in the case of A, and the year assumed to have 50 weeks, then the period of turnover is 5 weeks. For these 5 weeks variable capital must be advanced and the capital advanced for 5 weeks must be 5 times as large as the variable capital employed during one week. That is to say, only one-fifth of the advanced capital (in this case £500) can be employed in the course of one week. On the other hand, in the case of capital B, where the number of turnovers is 1/1, the time of turnover is 1 year, or 50 weeks. The ratio of the advanced capital to the capital employed weekly is therefore 50:1. If matters were the same for B as they are for A, then B would have to invest £1,000 per week instead of £100. 2) It follows that B has employed ten times as much capital
A) The annual rate of surplus-value is equal to the
quantity of surplus-value produced during the year __________________________________________ variable capital advanced
But the quantity of the surplus-value produced during the year is equal to the real rate of surplus-value multiplied by the variable capital employed in its production. The capital employed in the production of the annual quantity of surplus-value is equal to the advanced capital multiplied by the number of its turnovers, which we shall call n. Formula A is therefore transformed into the following:
B) The annual rate of surplus-value is equal to the
real rate of surplus-value x variable capital advanced x n ________________________________________________ variable capital advanced
For instance, in the case of capital B = ,[€] or 100%.
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Only when n is equal to 1, that is, when the variable capital advanced is turned over only once a year, and hence equal to the capital employed or turned over during a year, the annual rate of surplus-value is equal to its real rate.
Let us call the annual rate of surplus-value S', the real rate of surplus-value s', the advanced variable capital v, the number of turnovers n. Then S' = s' v n/v = s'n. In other words, S' is equal to s'n, and it is equal to s' only when n =1, and hence S' = s' times 1, or s'.
It follows furthermore that the annual rate of surplus-value is always equal to s'n, i.e., to the real rate of surplus-value produced in one period of turnover by the variable capital consumed during that period, multiplied by the number of turnovers of this variable capital during one year, or (what amounts to the same) multiplied by its inverted time of turnover calculated for one year. (If the variable capital is turned over ten times per year, then its time of turnover is 1/10 of a year; its inverted time of turnover therefore 10/1, or 10.)
It follows furthermore that S' = s' when n is equal to 1. S' is greater than s' when n is greater than 1; i.e., when the advanced capital is turned over more than once a year or the turned-over capital is greater than the capital advanced. Finally, S' is smaller than s' when n is smaller than 1, that is, when the capital turned over during the year is only a part of the advanced capital, so that the period of turnover is longer than one year.
Let us dwell a moment on this last case.
We retain all the premises of our former illustration, except that the period of turnover is lengthened to 55 weeks. The labour-process requires a variable capital of £100 per week, hence £5,500 for the period of turnover, and produces every week 100s; s' is therefore 100%, as before. The number of turnovers, n, is here 50/55 or 10/11, because the time of turnover is 1 plus 1/10 of the year (of 50 weeks), or 11/10 years.
.[€] It is therefore smaller than 100%. Indeed, if the annual rate of surplus value were 100%, then during the year 5,500v would produce 5,500s, whereas 10/11 years are required for that. The 5,500v produce only 5,000s during one year, therefore the annual rate of surplus-value is 5,000s/5,500v, or 10/11, or 90 10/11%.
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The annual rate of surplus-value, or the comparison between the surplus-value produced during one year and the variable capital advanced in general (as distinguished from the variable capital turned over during the year), is therefore no merely subjective comparison; the actual movement of the capital itself gives rise to this contraposition. So far as the owner of capital A is concerned, his advanced variable capital of £500 has returned to him at the end of the year, and £5,000 of surplus-value in addition. It is not the quantity of capital employed by him during the year, but the quantity returning to him periodically that expresses the magnitude of his advanced capital. It is immaterial for the present issue whether at the end of the year the capital exists partly as a productive supply, or partly as money- or commodity-capital, and in what proportions it may have been divided into these different parts. So far as the owner of capital B is concerned, £5,000, his advanced capital, has returned to him besides £5,000 in surplus-value. For the owner of capital C (the last considered, worth £5,500) surplus-value to the amount of £5,000 has been produced during the year (£5,000 invested and rate of surplus-value 100%), but his advanced capital has not yet returned to him, nor has his produced surplus-value.
S' = s'n indicates that the rate of surplus-value valid for the variable capital employed during one period of turnover, to wit,
quantity of s produced in one turnover period _____________________________________ , v employed in one turnover period
We have already seen (Buch I, Kap. IV[*]) (The Transformation of Money into Capital), and furthermore (Buch I, Kap. XXI[**]) (Simple Reproduction), that the capital-value is in general advanced, not expended, as this value, having passed through the various phases of its circuit, returns to its point of departure, and at that enriched by surplus-value. This characterises it as advanced. The time that elapses from the moment of its departure to the moment of its return is the time for which it was advanced. The entire circular movement described by capital-value, measured by the time from its advance to its return, constitutes its turnover, and the duration of this turnover is a
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period of turnover. When this period has expired and the circuit is completed, the same capital-value can renew the same circuit, can therefore expand anew, can create surplus-value. If the variable capital is turned over ten times in one year, as in the case of capital A, then the same advance of capital begets in the course of one year ten times the quantity of surplus-value that corresponds to one period of turnover.
One must get a clear conception of the nature of this advance from the standpoint of capitalist society.
Capital A, which is annually turned over ten times, is advanced ten times during one year. It is advanced anew for every new period of turnover. But at the same time, during the year A never advances more than this same capital-value of £500 and in actual fact never disposes of more than these £500 for the productive process examined by us. As soon as these £ 500 have completed one circuit A makes them start anew the same circuit; by its very nature capital preserves its character of capital only because it always functions as capital in successive production processes. It is, moreover, never advanced for more than five weeks. Should the turnover last longer, it proves inadequate. Should the turnover be curtailed, a part becomes superfluous. Not ten capitals of £500 are advanced, but one capital of £500 is advanced ten times at successive intervals. The annual rate of surplus-value is therefore not calculated for ten advances of a capital of £500 or for £5,000, but for one advance of a capital of £500. It is the same as if one shilling circulates ten times and yet never represents more than one single shilling in circulation, although it performs the function of 10 shillings. But in the pocket which holds it after each change of hands it retains the same identical value of one shilling as before.
In the same way capital A indicates at each successive return, and likewise on its return at the end of the year, that its owner has operated always with the same capital-value of £500. Hence only £500 return to him each time. His advanced capital is there fore never more than £500. Hence the advanced capital of £500 forms the denominator of the fraction which expresses the annual rate of surplus-value. We had for it the above formula S' = s'vn/v = s'n. Since the real rate of surplus-value, s', equals s/v the quantity of surplus-value divided by the variable capital
"Whatever the form of the process of production in a society, it must be a continuous process, must continue to go periodically through the same phases. . . . When viewed therefore as a connected whole and as flowing on with incessant renewal, every social process of production is, at the same time, a process of reproduction. . . . As a periodic increment of the capital advanced, or periodic fruit of capital in process, surplus-value acquires the form of a revenue flowing out of capital." (Buch I, Kap. XXI, pp. 588, 589.)[*]
In the case of capital A we have 10 five-week turnover periods. In the first period of turnover £500 of variable capital are advanced; i.e., £100 are weekly converted into labour-power, so that £500 are spent on labour-power at the end of the first turnover period. These £500, originally a part of the total capital advanced, have ceased to be capital. They are paid out in wages. The labourers in their turn pay them out in the purchase of means of subsistence, consuming means of subsistence worth £500. A quantity of commodities of that value is therefore annihilated; (what the labourer may save up in money, etc., is not capital either). As far as concerns the labourer, this quantity of commodities has been consumed unproductively, except inasmuch as it preserves the efficacy of his labour-power, an instrument indispensable to the capitalist.
In the second place however these £500 have been transformed, for the capitalist, into labour-power of the same value (or price). Labour-power is consumed by him productively in the labour-process. At the end of 5 weeks a product valued at £1,000 has been created. Half of this, £500, is the reproduced value of
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Let us take the third period of turnover. Here it is evident that the capital of £500, advanced for a third time, is not an
But in the case of B the value-product, which replaces the advanced variable capital and adds to it a surplus-value, is not in the form in which it can function anew as productive, or variable, capital. It is in such a form in the case of A. And up to the end of the year B does not possess the variable capital expended in the first 5 and every subsequent 5 weeks (although it has
In the cases of both A and B new labour-power is consumed in the second 5-week period and a new capital of £500 is spent in payment of this labour-power. The means of subsistence of the labourers, paid with the first £500, are gone; at all events their value has vanished from the hands of the capitalist. With the second £500 new labour-power is bought, new means of subsistence withdrawn from the market. In short, it is a new capital of £500 that is being expended, not the old. But in the case of A this new capital of £500 is the money-form of the newly produced substitute for the value of the formerly expended £500, while in the case of B, this substitute is in a form in which it cannot function as variable capital. It is there, but not in the form of variable capital. For the continuation of the process of production for the next 5 weeks an additional capital of £500 must therefore be available and advanced in the here indispensable form of money. Thus, during 50 weeks, both A and B expend an equal amount of variable capital, pay for and consume an equal quantity of labour-power. Only, B must pay for it with an advanced capital equal to its total value of £5,000, while A pays for it successively with the ever renewed money-form of the value-substitute, produced every 5 weeks, for the capital of £500 advanced for every 5 weeks. In no case is more money-capital advanced here than is required for 5 weeks, i.e., never more than that advanced for the first 5 weeks, viz., £500. These £500 last for the entire year. It is therefore clear that, the degree of exploitation of labour and the real rate of surplus-value being
The difference is due to the difference in the periods of turnover, i.e., the periods in which the value-substitute of the variable capital employed for a definite time can function anew as capital, hence as a new capital. In the case of B as well as A, there is the same replacement of value for the variable capital employed during the same periods. There is also the same increment of surplus-value during the same periods. But in the case of B, while every 5 weeks there is a replacement of the value of £500 and a surplus-value of £500, this value-substitute does not constitute new capital, because it does not exist in the form of money. In the case of A the old capital-value is not only replaced by a new one, but is rehabilitated in its money-form, hence replaced as a new capital capable of performing its function.5,000s 5,000s A: ______ = 1,000%; B: ______ = 100%. 500v 5,000v But 500v : 5,000v = 1:10 = 100%:1,000%.
The conversion, sooner or later, of the value-substitute into money, and thus into the form in which variable capital is advanced, is obviously an immaterial circumstance, so far as the production of surplus-value itself is concerned. This production depends on the magnitude of the variable capital employed and the degree of exploitation of labour. But that circumstance modifies the magnitude of the money-capital which must be advanced in order to set a definite quantum of labour-power in motion during the year, and therefore it determines the annual rate of surplus-value.
Let us look at this matter for a moment from the point of view of society. Let the wages of one labourer be £1 per week, the working-day 10 hours. In case of A as well as B 100 labourers are employed during a year (£100 for 100 labourers per week, or £500 for 5 weeks, or £5,000 for 50 weeks), and each one of them works 60 hours per week of 6 days. So 100 labourers work 6,000 hours per week and 300,000 hours in 50 weeks. This labour-
The shorter the period of turnover of capital -- the shorter therefore the intervals at which it is reproduced throughout the year -- the quicker is the variable portion of the capital, originally advanced by the capitalist in the form of money, transformed into the money-form of the value (including, besides, surplus-value) created by the labourer to replace this variable capital; the shorter is the time for which the capitalist must advance money out of his own funds, and the smaller is the capital advanced by him in general in proportion to the given scale of production; and the greater comparatively is the quantity of surplus-value which he extracts during the year with a given rate of surplus-value, because he can buy the labourer so much more frequently with the money-form of the value created by that labourer and can so much more frequently set his labour into motion again.
Second -- and this is interlinked with the first difference -- the B and A labourers pay for the means of subsistence which they buy with the variable capital that has been transformed in their hands into a medium of circulation. For instance they not only withdraw wheat from the market, but also replace it with an equivalent in money. But since the money wherewith the B labourer pays for his means of subsistence, which he withdraws from the market, is not the money-form of a value produced and thrown by him on the market during the year, as it is in the case of the A labourer, he supplies the seller of the means of subsistence with money, but not with commodities -- be they means of production or means of subsistence -- which this seller could buy with the proceeds of the sale, as he can in the case of A. The market is therefore stripped of labour-power, means of subsistence for this labour-power, fixed capital in the form of instruments of labour used in the case of B, and of materials of production, and to replace them an equivalent in money is thrown on the market; but during the year no product is thrown on the market with which to replace the material elements of productive capital withdrawn from it. If we conceive society as being not capitalistic but communistic, there will be no money-capital at all in the first place, nor the disguises cloaking the transactions arising on account of it. The question then comes down to the need of society to calculate beforehand how much labour, means of production, and means of subsistence it can invest, without detriment, in such lines of business as for instance the building of railways, which do not furnish any means of production or subsistence, nor produce any useful effect for a long time, a year or more,
On the other hand pressure on society's available productive capital. Since elements of productive capital are for ever being withdrawn from the market and only an equivalent in money is thrown on the market in their place, the effective demand rises without itself furnishing any element of supply. Hence a rise in the prices of productive materials as well as means of subsistence. To this must be added that stock-jobbing is a regular practice and capital is transferred on a large scale. A band of speculators, contractors, engineers, lawyers, etc., enrich themselves. They create a strong demand for articles of consumption on the market, wages rising at the same time. So far as foodstuffs are involved, agriculture too is stimulated. But as these foodstuffs cannot be suddenly increased in the course of the year, their import grows, just as that of exotic foods in general (coffee, sugar, wine, etc.) and of articles of luxury. Hence excessive imports and speculation in this line of the import business. Meanwhile, in those branches of industry in which production can be rapidly expanded (manufacture proper, mining, etc.), climbing prices give rise to sudden expansion soon followed by collapse. The same effect is produced in the labour-market, attracting great numbers of the latent relative surplus-population, and even of the employed labourers, to the new lines of business. In general such large-scale undertakings as railways withdraw a definite quantity of labour-power from the labour-market, which can come only from such lines of business as agriculture, etc., where only strong lads are needed. This still continues even after the new enterprises have become established lines of business and the migratory working-class needed for them has already been formed, as for instance in the case of a temporary rise above the average in the
scale of railway construction. A portion of the reserve army of labourers, which kept wages down, is absorbed. A general rise in wages ensues, even in the hitherto well employed sections of the labour-market. This lasts until the inevitable crash again releases the reserve army of labour and wages are once more depressed to their minimum, and lower.[32]
Inasmuch as the length, great or small, of the period of turnover depends on the working period proper, that is, the period necessary to get the product ready for the market, it is based on the existing material conditions of production specific for the various investments of capital. In agriculture they assume more of the character of natural conditions of production, in manufacture and the greater part of the mining industry they vary with the social development of the process of production itself.
Inasmuch as the length of the working period depends on the size of the supply (the quantitative volume in which the product is generally thrown upon the market as commodities), it is conventional in character. But the convention itself has its material basis in the scale of production, and is therefore accidental only when examined singly.
Finally, inasmuch as the length of the turnover period hinges on that of the period of circulation, it is partly dependent on the incessant change of market conditions, the greater or lesser ease of selling, and the resultant necessity of disposing of part of the product in nearer or remoter markets. Apart from the volume of the demand in general, the movement of prices is here of cardinal importance since sales are intentionally restricted when prices are falling, while production proceeds; vice versa, production and sales keep pace when prices are rising or sales can be made in advance. But we must consider the actual distance of the place of production from the market as the real material basis.
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For instance English cotton goods or yarn are sold to India. Suppose the exporter himself pays the English cotton manufacturer (the exporter does so willingly only if the money-market is strong. But when the manufacturer himself replaces his money-capital by some credit transaction, things are not so good). The exporter sells his cotton goods later in the Indian market, from where his advanced capital is remitted to him. Up to this remittance the case runs the very same course as when the length of the working period necessitated the advance of new money-capital to maintain the production process on a given scale. The money-capital with which the manufacturer pays his labourers and renews the other elements of his circulating capital is not the money-form of the yarn produced by him. This cannot be the case until the value of this yarn has returned to England in the form of money or products. It is additional money-capital as before. The only difference is that instead of the manufacturer, it is advanced by the merchant, who in turn may well have obtained it by means of credit operations. Similarly, before this money is thrown on the market, or simultaneously with this, no additional product has been put on the English market that could be bought with this money and would enter the sphere of productive or individual consumption. If this situation continues for a rather long period of time and on a rather large scale, it must have the same effect as the previously mentioned prolongation of the working period.
Now it may be that in India the yarn is again sold on credit. With this credit products are bought in India and sent as return shipment to England or drafts remitted for this amount. If this condition is protracted, the Indian money-market comes under pressure and the reaction on England may here produce a crisis. This crisis, in its turn, even if connected with bullion export to India, calls forth a new crisis in that country on account of the bankruptcy of English firms and their Indian branches, which had received credit from Indian banks. Thus a crisis occurs simultaneously in the market in which the balance of trade is favourable, as well as in the one in which it is unfavourable. This phenomenon may be still more complicated. Assume for instance that England has sent silver bullion to India but India's English creditors are now urgently collecting their debts in that country, and India will soon after have to ship its silver bullion back to England.
It is possible that the export trade to India and the import trade from India may approximately balance each other,