The Turnover of Variable Capital Chap. 2.16.1 by Karl Marx Lyrics
Chapter 16: The Turnover of Variable Capital
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 £2,500, is manufactured. Capital I of £2,000, constantly employed in the working period, is therefore turned over 12½ times. 12½ 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 £25,000 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 the value of the product, and thus of the product circulating as a commodity, of the commodity-capital, always consists of the wear and tear of the fixed capital, that is to say, of that portion of the value of the fixed capital which is transferred to the product during the process of production. The difference is really this: The fixed capital continues to function in the process of production in its old use-form for a longer or shorter cycle of turnover periods of the circulating capital (equal to constant circulating plus variable circulating capital), while every single turnover is conditioned on the replacement of the entire circulating capital passing from the sphere of production — in the form of commodity-capital — into the sphere of circulation. The constant circulating and variable circulating capital have the first phase of circulation, C' — M, in common. In the second phase they separate. The money into which the commodity is reconverted is in part transformed into a productive supply (constant circulating capital). Depending on the different terms of purchase of its constituent parts, one portion of the money may sooner, another later, be converted from money into materials of production, but finally it is wholly consumed that way. Another portion of the money realised by the sale of the commodity is held in the form of a money-supply, in order to be gradually expended in the payment of the labour-power incorporated in the process of production. This part constitutes the variable circulating capital. Nevertheless the entire replacement of either portion always originates from the turnover of capital, from its conversion into a product, from a product into a commodity, from a commodity into money. This is the reason why, in the preceding chapter, the turnover of the circulating capital, constant and variable, was treated jointly and separately without paying any regard to the fixed capital.
In the question which we shall now take up, we must go a step farther and proceed with the variable portion of the circulating capital as though it along constituted the circulating capital. In other words, we leave out of consideration the constant circulating capital which is turned over together with it.
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 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 surplus-value, it is absolutely correct to make this average calculation, according to which the value of the annual product is divided by the value of the advanced capital and not by the value of that portion of this capital which is employed constantly in one working period (thus, in the present case not by 400 but by 500, not by capital I but by capital I plus capital II). We shall see later that, from another point of view, the calculation is not quite exact, just as this average calculation generally is not quite exact. That is to say, it serves well enough for the practical purposes of the capitalist, but it does not express exactly or properly all the real circumstances of the turnover.
We have hitherto ignored one part of the value of the commodity-capital, namely the surplus-value contained in it, which was produced during the process of production and incorporated in the product. To this we have now to direct our attention.
Suppose the variable capital of £100 invested weekly produces a surplus-value of 100%, or £100, then the variable capital of £500 invested over a 5-week turnover period produces £500 of surplus-value, i.e., one half of the working day consists of surplus-labour.
If £500 of variable capital produce a surplus-value of £500, then £5,000 produce ten times £500, or £5,000 in surplus-value. But the advanced variable capital amounts to £500. The ratio of the total surplus-value produced during one year to the sum of value of the advanced variable capital is what we call the annual rate of surplus-value. In the case at hand it is 5,000 to 500 or 1,000%. If we analyse this rate more closely, we find that it is equal to the rate of surplus-value produced by the advanced variable capital during one period of turnover, multiplied by the number of turnovers of the variable capital (which coincides with the number of turnovers of the entire circulating capital).
The variable capital advanced in the case before us for one period of turnover is £500. The surplus-value produced during this period is likewise £500. The rate of surplus-value for one period of turnover is therefore 500s/500v or 100%. This 100%, multiplied by 10, the number of turnovers in one year, makes 5,000s/500v, or 1,000%.
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 advanced during this period, of £500 in the present case, multiplied by the rate of surplus-value, in the present case therefore 500 times 100/100, or 500 times 1, or £500. If the advanced variable capital were £1,500, then with the same rate of the surplus-value the amount of surplus-value would be 1,500 times 100/100, or £1,500.
We shall apply the term capital A to the variable capital of £500, which is turned over ten times per year, producing an annual surplus-value of £5,000 for which, therefore, the yearly rate of surplus-value is 1,000%.
Now let us assume that another variable capital, B, of £5,000, is advanced for one whole year (i.e., here for 50 weeks), so that it is turned over only once a year. We assume furthermore that at the end of the year the product is paid for on the same day that it is finished, so that the money-capital, into which it is converted, returns on the same day. The circulation period is then zero, the period of turnover equals the working period, namely, one year. As in the preceding case there is to be found in the labour-process each week a variable capital of £100, or of £5,000 in 50 weeks. Let the rate of surplus-value be the same, or 100%, i.e., let one half of the working-day of the same length consist of surplus-labour. If we consider 5 weeks, the invested variable capital is £500, the rate of surplus-value 100% and therefore the amount of surplus-value produced in 5 weeks £500. The quantity of labour-power here exploited, and the intensity of its exploitation, are assumed to be exactly the same as those of capital A.
Each week the invested variable capital of £100 produces a surplus-value of £100, hence in 50 weeks the invested capital of 50 × 100 = £5,000 produces a surplus-value of £5,000. The amount of surplus-value produced annually is the same as in the previous case, £5,000, but the yearly rate of surplus-value is entirely different. It is equal to the surplus-value produced in one year divided by the advanced variable capital: 5,000s/5,000v, or 100%, while in the case of capital A it was 1,000%.
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 divided into necessary labour and surplus-labour. The amount of variable capital employed in the course of the year is £5,000 in either case; it sets the same amount of labour in motion, and extracts the same amount of surplus-value, £5,000, from the labour-power set in motion by these two equal capitals. Nevertheless there is a difference of 900% in the annual rate of surplus-value of the two capitals A and B.
This phenomenon creates the impression, at all events, that the rate of surplus-value depends not only on the quantity and intensity of exploitation of the labour-power set in motion by the variable capital, but besides on inexplicable influences arising from the process of circulation. And it has indeed been so interpreted, and has — if not in this its pure form, then at least in its more complicated and disguised form, that of the annual rate of profit — completely routed the Ricardian school since the beginning of the twenties.
The strangeness of this phenomenon disappears at once when we place capitals A and B in exactly the same conditions, not only seemingly but actually. These equal conditions exist only when the variable capital B in its entire volume is expended for the payment of labour-power in the same period of time as capital A.
In that case the £5,000 of capital B are invested for 5 weeks, £1,000 per week makes an investment of £50,000 per year. The surplus-value is then likewise £50,000, according to our premises. The turned-over capital of £50,000 divided by the advanced capital of £5,000 makes the number of turnovers 10. The rate of surplus-value, 5,000s/5,000v, or 100%, multiplied by the number of turnovers, 10, makes the annual rate of surplus-value 50,000s/5,000v, or 10/1, or 1,000%. Now the annual rate of surplus-value are alike for A and B, namely 1,000%, but the amounts of the surplus-value are £50,000 in the case of B, and £5,000 in the case of A. The amounts of the surplus-value produced are now in the same proportion to one another as the advanced capital-values B and A, to wit: 5,000:500 = 10:1. But capital B has set in motion ten times as much labour-power as capital A within the same time.
Only the capital actually employed in the labour-power 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. [See Karl Marx, Capital, Ch. XI. — Ed.]
The labour-process itself is measured by time. If the length 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 10 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-week 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 the advanced and the employed variable capital affect the production of surplus-value — the rate of surplus-value being given — only to the extent, and only by reason of the fact that they differentiate the quantity of variable capital which can be really employed in a stated period of time, for instance in one week, 5 weeks, etc. The advanced variable capital functions as variable capital only to the extent and only during the time that it is actually employed, and not during the time in which it remains in stock, is advanced, without being employed. But all the circumstances which differentiate the relation between the advanced and the employed variable capital come down to the difference of the periods of turnover (determined by the difference of either the working period, or the circulation period, or both). The law of production of surplus-value states that equal quantities of functioning variable capital produce equal quantities of surplus-value if the rate of surplus-value is the same. If then, equal quantities of variable capital are employed by the capitals A and B in equal periods of time with equal rates of surplus-value, they must generate equal quantities of surplus-value in equal periods of time, no matter how different the ratio of this variable capital employed during a definite period of time to the variable capital advanced during the same time, and no matter therefore how different the ratio of the quantities of surplus-value produced, not to the employed but to the advanced variable capital in general. The difference of this ratio, far from contradicting the laws of the production of surplus-value that have been demonstrated, rather corroborates them and is one of their inevitable consequences.
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 of 1/10, or 10%. Hence it is 10% for capital B and 100% for capital A, i.e., ten-fold. If it were said that this difference in the rate of surplus-value for equal capitals, which have set in motion equal quantities of labour equally divided at that into paid and unpaid labour, is contrary to the laws of the production of surplus-value, the answer would be simple and prompted by a mere glance at the actual relations: In the case of A, the actual rate of surplus-value is expressed, i.e., the relation of a surplus-value produced in 5 weeks by a variable capital of £500, to the variable capital of £500. In the case of B on the other hand the calculation is of a kind which has nothing to do either with the production of surplus-value or with the determination of its corresponding rate of surplus-value. For the £500 of surplus-value produced by a variable capital of £500 of variable capital advanced during their production, but with reference to a capital of £5,000, nine-tenths of which, or £4,500, have nothing whatever to do with the production of this surplus-value of £500, but are on the contrary intended to function gradually in the course of the following 45 weeks, so that they do not exist at all so far as the production of the first 5 weeks is concerned, which alone is at issue in this instance. Hence in this case the difference in the rates of surplus-value of A and B presents no problem at all.
Let us now compare the annual rates of surplus-value for capitals B and A. For capital B it is 500s/500v = 100%; for capital A it is 5,000s/500v = 1,000%. But the ratio of the rates of surplus-value is the same as before. There we had
(Rate of Surplus-Value of Capital B) / (Rate of Surplus-Value of Capital A)
= 10% / 100%
Now we have
(Annual Rate of Surplus-Value of Capital B) / (Annual Rate of Surplus-Value of Capital A)
= 100% / 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 known to us and of the rate of surplus-value corresponding to this production. During the year 5,000v have been advanced and productively consumed, and they have produced 5,000s. The rate of surplus-value therefore equals the above fraction, 5,000s/5,000v = 100%. The annual rate agrees with the actual rate of surplus-value. In this case it is therefore not capital B but capital A which presents the anomaly that has to be explained.
We have here the rate of surplus-value 5,000s/500v = 1,000%. But while in the first case 500s, the product of 5 weeks, was calculated for an advanced capital of £5,000, nine-tenths of which were not employed by its production, we have now 5,000s calculated for 500v, i.e., for only one-tenth of the variable capital actually employed in the production of 5,000s; for the 5,000s are the product of a variable capital of £5,000 productively consumed during 50 weeks, not that of a capital of £500 consumed in one single period of 5 weeks. In the first case the surplus-value produced in 5 weeks had been calculated for a capital advanced for 50 weeks, a capital ten times as large as the one consumed during the 5 weeks. Now the surplus-value produced in 50 weeks is calculated for a capital advanced for 5 weeks, a capital ten times smaller than the one consumed in 50 weeks.
Capital A, of £500, is never advanced for more than 5 weeks. At the end of this time it returns and can renew the same process in the course of the year ten times, as it makes ten turnovers. Two conclusions follow from this:
Firstly: The capital advanced in the case of A is only five times larger than that portion of capital which is constantly employed in the productive process of one week. On the other hand capital B which is turned over only once in 50 weeks and must therefore be advanced for 50 weeks, is fifty times larger than that one of its portions which can constantly be employed for one week. The turnover therefore modifies the relation between the capital advanced during the year for the process of production and the capital constantly employable for a definite period of production, say, a week. Here we have, then, the first case, in which the surplus-value of 5 weeks is not calculated for the capital employed during these 5 weeks, but for a capital ten times larger, employed for 50 weeks.
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 successively re-invested. The employed capital is here equal to the capital advanced for 5 weeks, multiplied by the number of periods of turnover per year. The capital employed during the year is 500 times 10, or £5,000. The capital advanced during the year is 5,000/10, or £500. Indeed, although the £500 are always re-employed, the sum advanced every 5 weeks never exceeds these same £500. On the other hand in case of capital B only £500 are employed during 5 weeks and advanced for these 5 weeks. But as the period of turnover in this case is 50 weeks, the capital employed in one year is equal to the capital advanced for 50 weeks and not to that advanced for every 5 weeks. The annually produced quantity of surplus-value, given the rate of surplus-value, is however commensurate with the capital employed during the year, not with the capital advanced during the year. Hence it is not larger for this capital of £5,000, which is turned over once a year, than it is for the capital of £500, which is turned over ten times a year. And it is so big only because the capital turned over once a year is itself ten times larger than the capital turned over ten times a year.
The variable capital turned over during one year — hence the portion of the annual product, or of the annual expenditure equal to that portion — is the variable capital actually employed, productively consumed, during that year. It follows therefore that if the variable capital A turned over annually and the variable capital B turned over annually are equal and the employed under equal conditions of self-expansion, so that the rate of surplus-value is the same for both of them, then the quantity of surplus-value produced annually must likewise be the same for both of them. Hence the rate of surplus-value calculated for a year must also be the same, since the amounts of capital employed are the same, so far as the rate is expressed by (quantity of surplus-value produced annually) / (variable capital turned over annually). Or, expressed generally: Whatever the relative magnitude of the turned-over variable capitals, the rate of the surplus-value produced by them in the course of the year is determined by the rate of surplus-value at which the respective capitals have worked in average periods (say, the average of a week or day).
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 see further what is expressed by the ratio
(Capital turned over annually) / (capital advanced)
(taking into account, as we have said before, only the variable capital). The division shows the number of turnovers made by the capital advanced in one year.
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 turnover is 10/1 years; hence 500 times 10/1, or 5,000. In the case of B, 5,000 times 1/1, 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 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 (£5,000) as A to set in motion the same quantity of variable capital and hence — the rate of surplus-value being given — of labour (paid and unpaid), and thus to produce also the same quantity of surplus-value during the year. The real rate of surplus-value expresses nothing but the ratio of the variable capital employed during a definite period to the surplus-value produced in the same time; or the quantity of unpaid labour set in motion by the variable capital employed during this time. It has absolutely nothing to do with that portion of the variable capital which is advanced during the time in which it is not employed. Hence it has likewise nothing to do with the ratio between that portion of capital which is advanced during a definite period of time and that portion which is employed during the same period of time — a ratio that is modified and differentiated for different capitals by the turnover period.
It follows rather from what has been set forth above that the annual rate of surplus-value coincides only in one single case with the real rate of surplus-value which expresses the degree of exploitation of labour; namely in the case when the advanced capital is turned over only once a year and the capital advanced is thus equal to the capital turned over in the course of the year, when therefore the ratio of the quantity of the surplus-value produced during the year to the capital employed during the year in this production coincides and is identical with the ratio of the quantity of surplus-value produced during the year to the capital advanced during the year.
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 × variable capital advanced × n) / (variable capital advanced)
For instance, in the case of capital B = 100 × 5,000 × 1 / 5,000 , or 100%.
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'vn/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 turnover 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.
S' = 100% × 5,500 × 10/11 / 5,500 = 100 × 10/11 = 1000/11 = 90 10/11%. 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%.
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 not 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) / (variable capital employed in one turnover period)
must be multiplied by the number of turnover periods, or of the periods of reproduction of the advanced variable capital, by the number of periods in which it renews its circuit.
We have already seen (Buch I, Kap. IV [English edition: Part II. — Ed.]) (The Transformation of Money into Capital), and furthermore (Buch I, Kap. XXI [English edition: Ch. XXIII. — Ed.]) (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 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 therefore 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 which produced it, we may substitute s/v for the value of s' in s'n, and get the other formula S' = sn/v.
But by its ten-fold turnover and thus the ten-fold renewal of its advance, the capital of £500 performs the function of a ten times larger capital, of a capital of £5,000, just as 500 shillings which circulate ten times per year perform the same function as 5,000 shillings which circulate only once.
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 £2,500, is manufactured. Capital I of £2,000, constantly employed in the working period, is therefore turned over 12½ times. 12½ 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 £25,000 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 the value of the product, and thus of the product circulating as a commodity, of the commodity-capital, always consists of the wear and tear of the fixed capital, that is to say, of that portion of the value of the fixed capital which is transferred to the product during the process of production. The difference is really this: The fixed capital continues to function in the process of production in its old use-form for a longer or shorter cycle of turnover periods of the circulating capital (equal to constant circulating plus variable circulating capital), while every single turnover is conditioned on the replacement of the entire circulating capital passing from the sphere of production — in the form of commodity-capital — into the sphere of circulation. The constant circulating and variable circulating capital have the first phase of circulation, C' — M, in common. In the second phase they separate. The money into which the commodity is reconverted is in part transformed into a productive supply (constant circulating capital). Depending on the different terms of purchase of its constituent parts, one portion of the money may sooner, another later, be converted from money into materials of production, but finally it is wholly consumed that way. Another portion of the money realised by the sale of the commodity is held in the form of a money-supply, in order to be gradually expended in the payment of the labour-power incorporated in the process of production. This part constitutes the variable circulating capital. Nevertheless the entire replacement of either portion always originates from the turnover of capital, from its conversion into a product, from a product into a commodity, from a commodity into money. This is the reason why, in the preceding chapter, the turnover of the circulating capital, constant and variable, was treated jointly and separately without paying any regard to the fixed capital.
In the question which we shall now take up, we must go a step farther and proceed with the variable portion of the circulating capital as though it along constituted the circulating capital. In other words, we leave out of consideration the constant circulating capital which is turned over together with it.
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 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 surplus-value, it is absolutely correct to make this average calculation, according to which the value of the annual product is divided by the value of the advanced capital and not by the value of that portion of this capital which is employed constantly in one working period (thus, in the present case not by 400 but by 500, not by capital I but by capital I plus capital II). We shall see later that, from another point of view, the calculation is not quite exact, just as this average calculation generally is not quite exact. That is to say, it serves well enough for the practical purposes of the capitalist, but it does not express exactly or properly all the real circumstances of the turnover.
We have hitherto ignored one part of the value of the commodity-capital, namely the surplus-value contained in it, which was produced during the process of production and incorporated in the product. To this we have now to direct our attention.
Suppose the variable capital of £100 invested weekly produces a surplus-value of 100%, or £100, then the variable capital of £500 invested over a 5-week turnover period produces £500 of surplus-value, i.e., one half of the working day consists of surplus-labour.
If £500 of variable capital produce a surplus-value of £500, then £5,000 produce ten times £500, or £5,000 in surplus-value. But the advanced variable capital amounts to £500. The ratio of the total surplus-value produced during one year to the sum of value of the advanced variable capital is what we call the annual rate of surplus-value. In the case at hand it is 5,000 to 500 or 1,000%. If we analyse this rate more closely, we find that it is equal to the rate of surplus-value produced by the advanced variable capital during one period of turnover, multiplied by the number of turnovers of the variable capital (which coincides with the number of turnovers of the entire circulating capital).
The variable capital advanced in the case before us for one period of turnover is £500. The surplus-value produced during this period is likewise £500. The rate of surplus-value for one period of turnover is therefore 500s/500v or 100%. This 100%, multiplied by 10, the number of turnovers in one year, makes 5,000s/500v, or 1,000%.
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 advanced during this period, of £500 in the present case, multiplied by the rate of surplus-value, in the present case therefore 500 times 100/100, or 500 times 1, or £500. If the advanced variable capital were £1,500, then with the same rate of the surplus-value the amount of surplus-value would be 1,500 times 100/100, or £1,500.
We shall apply the term capital A to the variable capital of £500, which is turned over ten times per year, producing an annual surplus-value of £5,000 for which, therefore, the yearly rate of surplus-value is 1,000%.
Now let us assume that another variable capital, B, of £5,000, is advanced for one whole year (i.e., here for 50 weeks), so that it is turned over only once a year. We assume furthermore that at the end of the year the product is paid for on the same day that it is finished, so that the money-capital, into which it is converted, returns on the same day. The circulation period is then zero, the period of turnover equals the working period, namely, one year. As in the preceding case there is to be found in the labour-process each week a variable capital of £100, or of £5,000 in 50 weeks. Let the rate of surplus-value be the same, or 100%, i.e., let one half of the working-day of the same length consist of surplus-labour. If we consider 5 weeks, the invested variable capital is £500, the rate of surplus-value 100% and therefore the amount of surplus-value produced in 5 weeks £500. The quantity of labour-power here exploited, and the intensity of its exploitation, are assumed to be exactly the same as those of capital A.
Each week the invested variable capital of £100 produces a surplus-value of £100, hence in 50 weeks the invested capital of 50 × 100 = £5,000 produces a surplus-value of £5,000. The amount of surplus-value produced annually is the same as in the previous case, £5,000, but the yearly rate of surplus-value is entirely different. It is equal to the surplus-value produced in one year divided by the advanced variable capital: 5,000s/5,000v, or 100%, while in the case of capital A it was 1,000%.
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 divided into necessary labour and surplus-labour. The amount of variable capital employed in the course of the year is £5,000 in either case; it sets the same amount of labour in motion, and extracts the same amount of surplus-value, £5,000, from the labour-power set in motion by these two equal capitals. Nevertheless there is a difference of 900% in the annual rate of surplus-value of the two capitals A and B.
This phenomenon creates the impression, at all events, that the rate of surplus-value depends not only on the quantity and intensity of exploitation of the labour-power set in motion by the variable capital, but besides on inexplicable influences arising from the process of circulation. And it has indeed been so interpreted, and has — if not in this its pure form, then at least in its more complicated and disguised form, that of the annual rate of profit — completely routed the Ricardian school since the beginning of the twenties.
The strangeness of this phenomenon disappears at once when we place capitals A and B in exactly the same conditions, not only seemingly but actually. These equal conditions exist only when the variable capital B in its entire volume is expended for the payment of labour-power in the same period of time as capital A.
In that case the £5,000 of capital B are invested for 5 weeks, £1,000 per week makes an investment of £50,000 per year. The surplus-value is then likewise £50,000, according to our premises. The turned-over capital of £50,000 divided by the advanced capital of £5,000 makes the number of turnovers 10. The rate of surplus-value, 5,000s/5,000v, or 100%, multiplied by the number of turnovers, 10, makes the annual rate of surplus-value 50,000s/5,000v, or 10/1, or 1,000%. Now the annual rate of surplus-value are alike for A and B, namely 1,000%, but the amounts of the surplus-value are £50,000 in the case of B, and £5,000 in the case of A. The amounts of the surplus-value produced are now in the same proportion to one another as the advanced capital-values B and A, to wit: 5,000:500 = 10:1. But capital B has set in motion ten times as much labour-power as capital A within the same time.
Only the capital actually employed in the labour-power 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. [See Karl Marx, Capital, Ch. XI. — Ed.]
The labour-process itself is measured by time. If the length 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 10 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-week 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 the advanced and the employed variable capital affect the production of surplus-value — the rate of surplus-value being given — only to the extent, and only by reason of the fact that they differentiate the quantity of variable capital which can be really employed in a stated period of time, for instance in one week, 5 weeks, etc. The advanced variable capital functions as variable capital only to the extent and only during the time that it is actually employed, and not during the time in which it remains in stock, is advanced, without being employed. But all the circumstances which differentiate the relation between the advanced and the employed variable capital come down to the difference of the periods of turnover (determined by the difference of either the working period, or the circulation period, or both). The law of production of surplus-value states that equal quantities of functioning variable capital produce equal quantities of surplus-value if the rate of surplus-value is the same. If then, equal quantities of variable capital are employed by the capitals A and B in equal periods of time with equal rates of surplus-value, they must generate equal quantities of surplus-value in equal periods of time, no matter how different the ratio of this variable capital employed during a definite period of time to the variable capital advanced during the same time, and no matter therefore how different the ratio of the quantities of surplus-value produced, not to the employed but to the advanced variable capital in general. The difference of this ratio, far from contradicting the laws of the production of surplus-value that have been demonstrated, rather corroborates them and is one of their inevitable consequences.
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 of 1/10, or 10%. Hence it is 10% for capital B and 100% for capital A, i.e., ten-fold. If it were said that this difference in the rate of surplus-value for equal capitals, which have set in motion equal quantities of labour equally divided at that into paid and unpaid labour, is contrary to the laws of the production of surplus-value, the answer would be simple and prompted by a mere glance at the actual relations: In the case of A, the actual rate of surplus-value is expressed, i.e., the relation of a surplus-value produced in 5 weeks by a variable capital of £500, to the variable capital of £500. In the case of B on the other hand the calculation is of a kind which has nothing to do either with the production of surplus-value or with the determination of its corresponding rate of surplus-value. For the £500 of surplus-value produced by a variable capital of £500 of variable capital advanced during their production, but with reference to a capital of £5,000, nine-tenths of which, or £4,500, have nothing whatever to do with the production of this surplus-value of £500, but are on the contrary intended to function gradually in the course of the following 45 weeks, so that they do not exist at all so far as the production of the first 5 weeks is concerned, which alone is at issue in this instance. Hence in this case the difference in the rates of surplus-value of A and B presents no problem at all.
Let us now compare the annual rates of surplus-value for capitals B and A. For capital B it is 500s/500v = 100%; for capital A it is 5,000s/500v = 1,000%. But the ratio of the rates of surplus-value is the same as before. There we had
(Rate of Surplus-Value of Capital B) / (Rate of Surplus-Value of Capital A)
= 10% / 100%
Now we have
(Annual Rate of Surplus-Value of Capital B) / (Annual Rate of Surplus-Value of Capital A)
= 100% / 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 known to us and of the rate of surplus-value corresponding to this production. During the year 5,000v have been advanced and productively consumed, and they have produced 5,000s. The rate of surplus-value therefore equals the above fraction, 5,000s/5,000v = 100%. The annual rate agrees with the actual rate of surplus-value. In this case it is therefore not capital B but capital A which presents the anomaly that has to be explained.
We have here the rate of surplus-value 5,000s/500v = 1,000%. But while in the first case 500s, the product of 5 weeks, was calculated for an advanced capital of £5,000, nine-tenths of which were not employed by its production, we have now 5,000s calculated for 500v, i.e., for only one-tenth of the variable capital actually employed in the production of 5,000s; for the 5,000s are the product of a variable capital of £5,000 productively consumed during 50 weeks, not that of a capital of £500 consumed in one single period of 5 weeks. In the first case the surplus-value produced in 5 weeks had been calculated for a capital advanced for 50 weeks, a capital ten times as large as the one consumed during the 5 weeks. Now the surplus-value produced in 50 weeks is calculated for a capital advanced for 5 weeks, a capital ten times smaller than the one consumed in 50 weeks.
Capital A, of £500, is never advanced for more than 5 weeks. At the end of this time it returns and can renew the same process in the course of the year ten times, as it makes ten turnovers. Two conclusions follow from this:
Firstly: The capital advanced in the case of A is only five times larger than that portion of capital which is constantly employed in the productive process of one week. On the other hand capital B which is turned over only once in 50 weeks and must therefore be advanced for 50 weeks, is fifty times larger than that one of its portions which can constantly be employed for one week. The turnover therefore modifies the relation between the capital advanced during the year for the process of production and the capital constantly employable for a definite period of production, say, a week. Here we have, then, the first case, in which the surplus-value of 5 weeks is not calculated for the capital employed during these 5 weeks, but for a capital ten times larger, employed for 50 weeks.
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 successively re-invested. The employed capital is here equal to the capital advanced for 5 weeks, multiplied by the number of periods of turnover per year. The capital employed during the year is 500 times 10, or £5,000. The capital advanced during the year is 5,000/10, or £500. Indeed, although the £500 are always re-employed, the sum advanced every 5 weeks never exceeds these same £500. On the other hand in case of capital B only £500 are employed during 5 weeks and advanced for these 5 weeks. But as the period of turnover in this case is 50 weeks, the capital employed in one year is equal to the capital advanced for 50 weeks and not to that advanced for every 5 weeks. The annually produced quantity of surplus-value, given the rate of surplus-value, is however commensurate with the capital employed during the year, not with the capital advanced during the year. Hence it is not larger for this capital of £5,000, which is turned over once a year, than it is for the capital of £500, which is turned over ten times a year. And it is so big only because the capital turned over once a year is itself ten times larger than the capital turned over ten times a year.
The variable capital turned over during one year — hence the portion of the annual product, or of the annual expenditure equal to that portion — is the variable capital actually employed, productively consumed, during that year. It follows therefore that if the variable capital A turned over annually and the variable capital B turned over annually are equal and the employed under equal conditions of self-expansion, so that the rate of surplus-value is the same for both of them, then the quantity of surplus-value produced annually must likewise be the same for both of them. Hence the rate of surplus-value calculated for a year must also be the same, since the amounts of capital employed are the same, so far as the rate is expressed by (quantity of surplus-value produced annually) / (variable capital turned over annually). Or, expressed generally: Whatever the relative magnitude of the turned-over variable capitals, the rate of the surplus-value produced by them in the course of the year is determined by the rate of surplus-value at which the respective capitals have worked in average periods (say, the average of a week or day).
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 see further what is expressed by the ratio
(Capital turned over annually) / (capital advanced)
(taking into account, as we have said before, only the variable capital). The division shows the number of turnovers made by the capital advanced in one year.
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 turnover is 10/1 years; hence 500 times 10/1, or 5,000. In the case of B, 5,000 times 1/1, 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 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 (£5,000) as A to set in motion the same quantity of variable capital and hence — the rate of surplus-value being given — of labour (paid and unpaid), and thus to produce also the same quantity of surplus-value during the year. The real rate of surplus-value expresses nothing but the ratio of the variable capital employed during a definite period to the surplus-value produced in the same time; or the quantity of unpaid labour set in motion by the variable capital employed during this time. It has absolutely nothing to do with that portion of the variable capital which is advanced during the time in which it is not employed. Hence it has likewise nothing to do with the ratio between that portion of capital which is advanced during a definite period of time and that portion which is employed during the same period of time — a ratio that is modified and differentiated for different capitals by the turnover period.
It follows rather from what has been set forth above that the annual rate of surplus-value coincides only in one single case with the real rate of surplus-value which expresses the degree of exploitation of labour; namely in the case when the advanced capital is turned over only once a year and the capital advanced is thus equal to the capital turned over in the course of the year, when therefore the ratio of the quantity of the surplus-value produced during the year to the capital employed during the year in this production coincides and is identical with the ratio of the quantity of surplus-value produced during the year to the capital advanced during the year.
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 × variable capital advanced × n) / (variable capital advanced)
For instance, in the case of capital B = 100 × 5,000 × 1 / 5,000 , or 100%.
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'vn/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 turnover 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.
S' = 100% × 5,500 × 10/11 / 5,500 = 100 × 10/11 = 1000/11 = 90 10/11%. 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%.
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 not 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) / (variable capital employed in one turnover period)
must be multiplied by the number of turnover periods, or of the periods of reproduction of the advanced variable capital, by the number of periods in which it renews its circuit.
We have already seen (Buch I, Kap. IV [English edition: Part II. — Ed.]) (The Transformation of Money into Capital), and furthermore (Buch I, Kap. XXI [English edition: Ch. XXIII. — Ed.]) (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 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 therefore 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 which produced it, we may substitute s/v for the value of s' in s'n, and get the other formula S' = sn/v.
But by its ten-fold turnover and thus the ten-fold renewal of its advance, the capital of £500 performs the function of a ten times larger capital, of a capital of £5,000, just as 500 shillings which circulate ten times per year perform the same function as 5,000 shillings which circulate only once.