Effect of Turnover Time on Magnitude of Advanced Capital Chap. 2.15.2 by Karl Marx Lyrics
II. The Working Period Greater than the Period of Circulation
The working and turnover periods of capitals I and II cross one another instead of relieving one another. Simultaneously some capital is set free. This was not so in the previously considered case.
But this does not alter the fact that, as before, 1) the number of working periods of the total capital advanced is equal to the sum of the value of the annual product of both advanced portions of capital divided by the total capital advanced, and 2) the number of turnovers made by the total capital is equal to the sum of the two amounts turned over divided by the sum of the two advanced capitals. Here too we must consider both portions of capital as if they performed turnover movements entirely independent of each other.
Thus, we assume once more, that £100 are to be advanced weekly to the labour-process. Let the working period last 6 weeks, requiring therefore every time an advance of £600 (capital I). Let the time of circulation be 3 weeks, so that the period of turnover is 9 weeks, as before. Let capital II of £300 step in during the three-week circulation period of capital I. Considering both capitals as independent of each other, we find the schedule of the annual turnover to be as follows:
Table II
CAPITAL I, £600
Periods of Turnover Working Periods Advance Periods of Circulation
I.1st-9th week 1st-6th week £600 7th-9th week
II. 10th-18th " 10th-15th " £600 16th-18th"
III. 19th-27th " 19th-24th " £600 25th-27th "
IV. 28th-36th " 28th-33rd " £600 34th-36th "
V. 37th-45th " 37th-42nd " £600 43rd-45th "
VI. 46th-[54th] 46th-51st " £600 [52nd-54th] "
ADDITIONAL CAPITAL II, £300
Periods of Turnover Working Periods Advance Periods of Circulation
I. 7th-15th week 7th-9th week £300 10th-15th week
II. 16th-24th " 16th-18th " £300 19th-24th "
III. 25th-33rd " 25th-27th " £300 28th-33rd "
IV. 34th-42nd " 34th-36th " £300 37th-42nd "
V. 43rd-51st " 43rd-45th " £300 46th-51st "
The process of production continues uninterruptedly the whole year round on the same scale. The two capitals I and II remain entirely separate. But in order to represent them as separate, we had to tear apart their real intersections and intertwinings, and thus also to change the number of turnovers. For according to the above table the amounts turned over would be:
by capital I, 5⅔ times 600, or £3,400 and
by capital II, 5 times 300, or £1,500
——————————————————
Hence by the total capital 5 4/9 times 900, or £4,900.
But this is not correct, for, as we shall see, the actual periods of production and circulation do not absolutely coincide with those of the above schedule, in which it was mainly a question of presenting capitals I and II as independent of each other.
In reality, capital II has no working and circulating periods separate and distinct from those of capital I. The working period is 6 weeks, the circulation period 3 weeks. Since capital II amounts to only £300, it can suffice only for a part of the working period. This is indeed the case. At the end of the 6th week a product valued at £600 passes into circulation and returns in money-form at the close of the 9th week. Then, at the opening of the 7th week, capital II begins its activity, and covers the requirements of the next working period, the 7th to 9th week. But according to our assumption the working period is only half up at the end of the 9th week. Hence capital I of £600 having just returned, at the beginning of the 10th week, once more enters into operation and with its £300 supplies the advances needed for the 10th to 12th week. This disposes of the second working period. A product value of £600 is in circulation and will return at the close of the 15th week. At the same time, £300, the amount of the original capital II, are set free and are able to function in the first half of the following working period, that is to say, in the 13th to 15th week. After the lapse of these weeks the £600 return; £300 of them suffice for the remainder of the working period, and £300 remain for the following working period.
The thing therefore works as follows:
First period of turnover: 1st-9th week.
1st working period: 1st-6th week. Capital I, £600, performs its function.
1st period of circulation: 7th-9th week. End of 9th week, £600 return.
Second period of turnover: 7th-15th week.
2nd working period: 7th-12th week.
First half: 7th-9th week. Capital II, £300, performs its function.
End of 9th week, £600 return in money-form (capital I).
Second half: 10th-12th week. £300 of capital I perform their function. The other £300 of capital I remain freed.
2nd period of circulation: 13th-15th week.
End of 15th week, £600 (half taken from capital I, half from capital II) return in the form of money.
Third period of turnover; 13-21st week.
3rd working period: 13th-18th week.
First half: 13th-15th week. The freed £300 perform their function. End of 15th week, £600 return in money-form.
Second half: 16th-18th week, £300 of the returned £600 function, the other £300 again remain freed.
3rd period of circulation: 19th-21st week at the close of which £600 again return in money-form. In these £600 capital I and capital II are now indistinguishably fused.
And so there are eight full turnover periods of a capital of £600 (I: 1st-9th week; II: 7th-15th week; III: 13th-21st; IV: 19th-27th; V: 25th-33rd; VI: 31st-39th; VII: 37th-45th; VIII: 43rd-51st week) to the end of the 51st week. But as the 49th-51st weeks fall within the eighth period of circulation, the £300 of freed capital must step in and keep production going. Thus the turnover at the end of the year is as follows: £600 have completed their circuit eight times, making £4,800. In addition we have the product of the last 3 weeks (49th-51st), which, however, has completed only one-third of its circuit of 9 weeks, so that in the sum turned over it counts for only one-third of its amount, £100. If, then, the annual product of 51 weeks is £5,100, the capital turned over is only 4,800 plus 100, or £4,900. The total capital advanced, £900, has therefore been turned over 5 4/9 times, a trifle more than in the first case.
In the present example we assumed a case in which the working time was ⅔ and the circulation time ⅓ of the period of turnover, i.e., the working time was a simple multiple of the circulation time. The question now is whether capital is likewise set free, in the way shown above, when this assumption is not made.
Let us assume a working time of 5 weeks, a circulation time of 4 weeks, and a capital advance of £100 per week.
First period of turnover: 1st-9th week.
1st working period: 1st-5th week. Capital I, or £500, performs its function.
1st circulation period: 6th-9th week. End of 9th week, £500 return in money-form.
Second period of turnover: 6th-14th week.
2nd working period: 6th-10th week.
First section: 6th-9th week. Capital II, of £400, performs its function. End of 9th week, capital I of £500 returns in money-form.
Second section: 10th week. £100 of the returned £500 perform their function. The remaining £400 are set free for the following working period.
2nd circulation period: 11th-14th week. End of 14th week. £500 return in money-form.
Up to the end of the 14th week (11th-14th), the £400 set free above perform their function; £100 of the £500 then returned fill the requirements of the third working period (11th-15th week) so that £400 are once more released for the fourth working period. The same thing is repeated in every working period; at its beginning £40 are ready at hand, sufficing for the first 4 weeks. End of the 4th week, £500 return in money-form, only £100 of which are needed for the last week, while the other £400 remain free for the next working period.
Let us further assume a working period of 7 weeks, with a capital I of £700; a circulation period of 2 weeks, with a capital II of £200.
In that case the first period of turnover lasts from the 1st to the 9th week; its first working period from the 1st to the 7th week, with an advance of £700, its first circulation period from the 8th to the 9th week. End of the 9th week, £700 flow back in money-form.
The second period of turnover, from the 8th to the 16th week, contains the second working period of the 8th to the 14th week. The requirements of the 8th and 9th weeks of this period are covered by capital II. End of the 9th week, the above £700 return. Up to the close of this working period (10th-14th week), £500 of this sum are used up; £200 remain free for the next working period. The second circulation period lasts from the 15th to the 16th week. End of the 16th week £700 return once more. From now on, the same thing is repeated in every working period. The need for capital during the first two weeks is covered by the £200 set free at the close of the preceding working period; at the close of the second week £700 return; but only 5 weeks remain of the working period, so that it can consume only £500; therefore £200 always remain free for the next working period.
We find, then, that in the given case, where the working period has been assumed to be greater than the circulation period, a money-capital will at all events have been set free at the close of each working period, which is of the same magnitude as capital II advanced for the circulation period. In our three illustrations capital II was £300 in the first, £400 in the second, and £200 in third. Accordingly, the capital set free at the close of each working period was £300, £400 and £200 respectively.
The working and turnover periods of capitals I and II cross one another instead of relieving one another. Simultaneously some capital is set free. This was not so in the previously considered case.
But this does not alter the fact that, as before, 1) the number of working periods of the total capital advanced is equal to the sum of the value of the annual product of both advanced portions of capital divided by the total capital advanced, and 2) the number of turnovers made by the total capital is equal to the sum of the two amounts turned over divided by the sum of the two advanced capitals. Here too we must consider both portions of capital as if they performed turnover movements entirely independent of each other.
Thus, we assume once more, that £100 are to be advanced weekly to the labour-process. Let the working period last 6 weeks, requiring therefore every time an advance of £600 (capital I). Let the time of circulation be 3 weeks, so that the period of turnover is 9 weeks, as before. Let capital II of £300 step in during the three-week circulation period of capital I. Considering both capitals as independent of each other, we find the schedule of the annual turnover to be as follows:
Table II
CAPITAL I, £600
Periods of Turnover Working Periods Advance Periods of Circulation
I.1st-9th week 1st-6th week £600 7th-9th week
II. 10th-18th " 10th-15th " £600 16th-18th"
III. 19th-27th " 19th-24th " £600 25th-27th "
IV. 28th-36th " 28th-33rd " £600 34th-36th "
V. 37th-45th " 37th-42nd " £600 43rd-45th "
VI. 46th-[54th] 46th-51st " £600 [52nd-54th] "
ADDITIONAL CAPITAL II, £300
Periods of Turnover Working Periods Advance Periods of Circulation
I. 7th-15th week 7th-9th week £300 10th-15th week
II. 16th-24th " 16th-18th " £300 19th-24th "
III. 25th-33rd " 25th-27th " £300 28th-33rd "
IV. 34th-42nd " 34th-36th " £300 37th-42nd "
V. 43rd-51st " 43rd-45th " £300 46th-51st "
The process of production continues uninterruptedly the whole year round on the same scale. The two capitals I and II remain entirely separate. But in order to represent them as separate, we had to tear apart their real intersections and intertwinings, and thus also to change the number of turnovers. For according to the above table the amounts turned over would be:
by capital I, 5⅔ times 600, or £3,400 and
by capital II, 5 times 300, or £1,500
——————————————————
Hence by the total capital 5 4/9 times 900, or £4,900.
But this is not correct, for, as we shall see, the actual periods of production and circulation do not absolutely coincide with those of the above schedule, in which it was mainly a question of presenting capitals I and II as independent of each other.
In reality, capital II has no working and circulating periods separate and distinct from those of capital I. The working period is 6 weeks, the circulation period 3 weeks. Since capital II amounts to only £300, it can suffice only for a part of the working period. This is indeed the case. At the end of the 6th week a product valued at £600 passes into circulation and returns in money-form at the close of the 9th week. Then, at the opening of the 7th week, capital II begins its activity, and covers the requirements of the next working period, the 7th to 9th week. But according to our assumption the working period is only half up at the end of the 9th week. Hence capital I of £600 having just returned, at the beginning of the 10th week, once more enters into operation and with its £300 supplies the advances needed for the 10th to 12th week. This disposes of the second working period. A product value of £600 is in circulation and will return at the close of the 15th week. At the same time, £300, the amount of the original capital II, are set free and are able to function in the first half of the following working period, that is to say, in the 13th to 15th week. After the lapse of these weeks the £600 return; £300 of them suffice for the remainder of the working period, and £300 remain for the following working period.
The thing therefore works as follows:
First period of turnover: 1st-9th week.
1st working period: 1st-6th week. Capital I, £600, performs its function.
1st period of circulation: 7th-9th week. End of 9th week, £600 return.
Second period of turnover: 7th-15th week.
2nd working period: 7th-12th week.
First half: 7th-9th week. Capital II, £300, performs its function.
End of 9th week, £600 return in money-form (capital I).
Second half: 10th-12th week. £300 of capital I perform their function. The other £300 of capital I remain freed.
2nd period of circulation: 13th-15th week.
End of 15th week, £600 (half taken from capital I, half from capital II) return in the form of money.
Third period of turnover; 13-21st week.
3rd working period: 13th-18th week.
First half: 13th-15th week. The freed £300 perform their function. End of 15th week, £600 return in money-form.
Second half: 16th-18th week, £300 of the returned £600 function, the other £300 again remain freed.
3rd period of circulation: 19th-21st week at the close of which £600 again return in money-form. In these £600 capital I and capital II are now indistinguishably fused.
And so there are eight full turnover periods of a capital of £600 (I: 1st-9th week; II: 7th-15th week; III: 13th-21st; IV: 19th-27th; V: 25th-33rd; VI: 31st-39th; VII: 37th-45th; VIII: 43rd-51st week) to the end of the 51st week. But as the 49th-51st weeks fall within the eighth period of circulation, the £300 of freed capital must step in and keep production going. Thus the turnover at the end of the year is as follows: £600 have completed their circuit eight times, making £4,800. In addition we have the product of the last 3 weeks (49th-51st), which, however, has completed only one-third of its circuit of 9 weeks, so that in the sum turned over it counts for only one-third of its amount, £100. If, then, the annual product of 51 weeks is £5,100, the capital turned over is only 4,800 plus 100, or £4,900. The total capital advanced, £900, has therefore been turned over 5 4/9 times, a trifle more than in the first case.
In the present example we assumed a case in which the working time was ⅔ and the circulation time ⅓ of the period of turnover, i.e., the working time was a simple multiple of the circulation time. The question now is whether capital is likewise set free, in the way shown above, when this assumption is not made.
Let us assume a working time of 5 weeks, a circulation time of 4 weeks, and a capital advance of £100 per week.
First period of turnover: 1st-9th week.
1st working period: 1st-5th week. Capital I, or £500, performs its function.
1st circulation period: 6th-9th week. End of 9th week, £500 return in money-form.
Second period of turnover: 6th-14th week.
2nd working period: 6th-10th week.
First section: 6th-9th week. Capital II, of £400, performs its function. End of 9th week, capital I of £500 returns in money-form.
Second section: 10th week. £100 of the returned £500 perform their function. The remaining £400 are set free for the following working period.
2nd circulation period: 11th-14th week. End of 14th week. £500 return in money-form.
Up to the end of the 14th week (11th-14th), the £400 set free above perform their function; £100 of the £500 then returned fill the requirements of the third working period (11th-15th week) so that £400 are once more released for the fourth working period. The same thing is repeated in every working period; at its beginning £40 are ready at hand, sufficing for the first 4 weeks. End of the 4th week, £500 return in money-form, only £100 of which are needed for the last week, while the other £400 remain free for the next working period.
Let us further assume a working period of 7 weeks, with a capital I of £700; a circulation period of 2 weeks, with a capital II of £200.
In that case the first period of turnover lasts from the 1st to the 9th week; its first working period from the 1st to the 7th week, with an advance of £700, its first circulation period from the 8th to the 9th week. End of the 9th week, £700 flow back in money-form.
The second period of turnover, from the 8th to the 16th week, contains the second working period of the 8th to the 14th week. The requirements of the 8th and 9th weeks of this period are covered by capital II. End of the 9th week, the above £700 return. Up to the close of this working period (10th-14th week), £500 of this sum are used up; £200 remain free for the next working period. The second circulation period lasts from the 15th to the 16th week. End of the 16th week £700 return once more. From now on, the same thing is repeated in every working period. The need for capital during the first two weeks is covered by the £200 set free at the close of the preceding working period; at the close of the second week £700 return; but only 5 weeks remain of the working period, so that it can consume only £500; therefore £200 always remain free for the next working period.
We find, then, that in the given case, where the working period has been assumed to be greater than the circulation period, a money-capital will at all events have been set free at the close of each working period, which is of the same magnitude as capital II advanced for the circulation period. In our three illustrations capital II was £300 in the first, £400 in the second, and £200 in third. Accordingly, the capital set free at the close of each working period was £300, £400 and £200 respectively.