The effect of turnover on the production of surplus-value, and so also of profit, has already been discussed in Volume 2. It can be summed up briefly like this: because turnover takes time, not all of a capital can be employed in production at once. Part of it is constantly lying idle — as money capital, as stocks of raw material sitting in store, as finished but still unsold commodity capital, or as debts owed to the capitalist that aren't yet due. The capital actually at work producing and appropriating surplus-value is constantly cut down by this idle part, and the surplus-value produced and appropriated is reduced in the very same proportion.
The shorter the turnover time, the smaller this idle part of the capital becomes compared with the whole — and so, other things being equal, the greater the surplus-value appropriated.
It has already been shown in detail in Volume 2 how shortening the turnover time — or either of its two parts, the production time and the circulation time — increases the mass of surplus-value produced. But since the rate of profit only expresses the ratio of the mass of surplus-value produced to the total capital engaged in producing it, it's obvious that any such shortening raises the rate of profit as well. What was worked out in Part Two of Volume 2 with respect to surplus-value holds equally for profit and the rate of profit, and there's no need to repeat it here. We'll just pick out a few of the main points.
The main means of shortening production time is raising the productive power of labour — what's usually called the progress of industry. If this doesn't also bring about a significant increase in the total capital outlay — say, through installing expensive machinery — and so a fall in the rate of profit reckoned on the whole capital, then that rate must rise. And this is certainly true of many of the most recent advances in metallurgy and the chemical industry.
The newly discovered methods of making iron and steel — Bessemer's, Siemens's, Gilchrist-Thomas's, and others — cut processes that used to take a very long time down to a minimum, and at relatively low cost. Making alizarin, the madder dye, out of coal tar produces in a few weeks, using the plant already in place for coal-tar dyes, the very same result that used to take years: madder needed a year just to grow, and then the roots still had to mature for several more years before being turned into dye.
The main means of shortening circulation time is improved communications. And here the last fifty years have brought a revolution comparable only to the industrial revolution of the last half of the previous century. On land the macadamized road has been pushed into the background by the railway; at sea, the slow and irregular sailing ship by the fast and regular steamship line; and telegraph wires now span the whole globe. The Suez Canal has really opened East Asia and Australia up to steamship traffic. The circulation time for a shipment of goods to East Asia, still at least twelve months in 1847 (as already noted in Volume 2), can now be brought down to roughly as many weeks.
The two great trouble spots behind the crises of 1825-1857, America and India, have been brought 70-90 per cent closer to the industrial countries of Europe by this revolution in transport, and have thereby lost much of their power to set off a crisis. The turnover time of world trade as a whole has been shortened to the same degree, and the same capital engaged in it can now do more than two or three times as much business. That this hasn't been without effect on the rate of profit goes without saying.
To show the effect of turnover of the total capital on the rate of profit in a pure form, we have to take the two capitals being compared as equal in every other respect. Besides the rate of surplus-value and the working day, let their percentage composition in particular also be equal.
Let's take a capital A of composition 80c + 20v = 100 C, which turns over twice a year at a rate of surplus-value of 100 per cent. Then the annual product is:
160c + 40v + 40s. But to work out the rate of profit, we don't reckon this 40s against the turned-over capital-value of 200 — we reckon it against the 100 that was advanced, which gives us p' = 40 per cent.
Let's compare this with a capital B = 160c + 40v = 200 C, which turns over at the same rate of surplus-value of 100 per cent, but only once a year. Then the annual product is, as above:
160c + 40v + 40s. But this time the 40s has to be reckoned against a capital advanced of 200, which gives a rate of profit of only 20 per cent — just half the rate for A.
So this is what follows: for capitals of equal percentage composition, at an equal rate of surplus-value and an equal working day, the profit rates of two capitals stand in inverse proportion to their turnover times.
If the composition, or the rate of surplus-value, or the working day, or the wage differs between the two cases being compared, then further differences in the rate of profit will indeed arise from that too — but these are independent of turnover, and so are none of our concern here. They have already been dealt with in Chapter 3.
The direct effect of a shortened turnover time on the production of surplus-value, and hence of profit, lies in the increased effectiveness this gives to the variable part of the capital — which is worked out in Volume 2, Chapter 16, on the turnover of the variable capital. It was shown there that a variable capital of 500, turning over ten times a year, appropriates in that time just as much surplus-value as a variable capital of 5,000 which, at the same rate of surplus-value and the same wage, turns over only once a year.
Let's take a capital I, made up of 10,000 in fixed capital, whose annual depreciation comes to 10 per cent = 1,000, plus 500 in circulating constant capital and 500 in variable capital. At a rate of surplus-value of 100 per cent, let the variable capital turn over ten times a year. For simplicity, in all the examples that follow we'll assume the circulating constant capital turns over in the same time as the variable capital, which in practice is usually more or less the case anyway. Then the product of one such turnover period will be:
And the product for the whole year, from all ten such turnovers:
Now let's take a capital II: fixed capital 9,000, its annual depreciation 1,000, circulating constant capital 1,000, variable capital 1,000, rate of surplus-value 100 per cent, number of annual turnovers of the variable capital: 5. The product of each turnover period of the variable capital will then be:
And the total product for the year, at five turnovers:
Let's further take a capital III, containing no fixed capital at all, but instead 6,000 in circulating constant capital and 5,000 in variable capital. At a rate of surplus-value of 100 per cent, let it turn over once a year. The total product for the year is then:
So in all three cases we have the same annual mass of surplus-value, = 5,000, and since the total capital is likewise the same in all three cases, namely = 11,000, we get the same rate of profit of 45 5/11 per cent.
If, on the other hand, the variable part of capital I above turns over only 5 times a year instead of 10, things look different. The product of one turnover is then:
Or, the annual product:
The rate of profit has fallen by half, because the turnover time has been doubled.
The mass of surplus-value appropriated over the course of the year is thus equal to the mass of surplus-value appropriated in one turnover period of the variable capital, multiplied by the number of such turnovers in the year. Let's call the surplus-value or profit appropriated per year S, the surplus-value appropriated in one turnover period s, and the number of annual turnovers of the variable capital n. Then S = sn, and the annual rate of surplus-value is S' = s'n, as already shown in Volume 2, Chapter 16.
The formula for the rate of profit, p' = s'v/C = s'v/(c+v), obviously only holds good if the v in the numerator is the same v as the v in the denominator. In the denominator, v is the whole part of the total capital that functions, on average, as variable capital laid out on wages. The v in the numerator, though, is at first fixed only by this: it is the wage outlay that has produced and appropriated a certain quantity of surplus-value = s, and s divided by that v is the rate of surplus-value s'. Only by this route does the equation p' = s/(c+v) turn into the other one, p' = s'v/(c+v). The v in the numerator is then more precisely pinned down as having to equal the v in the denominator — that is, the whole variable part of the capital C.
In other words, the equation p' = s/C can only be turned, without error, into p' = s'v/(c+v) if s means the surplus-value produced in one turnover period of the variable capital. If s covers only part of that surplus-value, then s = s'v still holds, but this v is smaller than the v in C = c+v, because less than the whole variable capital has been laid out in wages. But if s covers more than the surplus-value of a single turnover of v, then part of that v — or even the whole of it — functions twice: first in the first turnover, then in the second, or a further one. The v that produces the surplus-value, and that is the sum of all wages paid, is then larger than the v in c+v, and the calculation goes wrong.
For the formula for the annual rate of profit to come out exactly right, we have to put the annual rate of surplus-value in place of the simple rate of surplus-value — that is, put S', or s'n, in place of s'. In other words, we have to multiply s', the rate of surplus-value — or, what comes to the same thing, the variable part of the capital v contained in C — by n, the number of turnovers of that variable capital in the year. This gives us p' = s'n v/C, which is the formula for working out the annual rate of profit.
But how large the variable capital in a business actually is, is something the capitalist himself usually doesn't know. We saw in Chapter 8 of Volume 2, and will see further on, that the only distinction within his capital that forces itself on the capitalist as essential is the distinction between fixed and circulating capital. From the till that holds the part of his circulating capital that's in money form, so far as it isn't sitting in the bank, he draws the money for wages, and from that same till the money for raw and ancillary materials, crediting both to one and the same cash account.
And even if he did keep a separate account of wages paid, at the end of the year this would show only the whole year's wage bill — that is, v paid out over and over, n times — and not the variable capital v itself. To work that out, he'd have to make a separate calculation, and we want to give an example of one here.
For this we take the cotton-spinning mill of 10,000 mule spindles already described in Volume 1, and assume that the figures given for one week of April 1871 held good for the whole year. The fixed capital tied up in machinery was £10,000. The circulating capital wasn't given; we'll assume it was £2,500 — a fairly high figure, but justified by the assumption we always have to make here, that there are no credit operations, that is, no permanent or temporary use of someone else's capital.
By value, the week's product was made up of £20 for depreciation of machinery, £358 advanced as circulating constant capital (rent £6, cotton £342, coal, gas and oil £10), £52 in variable capital laid out on wages, and £80 surplus-value — that is:
The weekly advance of circulating capital was thus 358c + 52v = 410, with a percentage composition of 87.3c + 12.7v. Worked out for the whole circulating capital of £2,500, this gives £2,182 constant and £318 variable capital. Since the total outlay on wages for the year was 52 times £52, that is £2,704, it follows that the variable capital of £318 turned over almost exactly 8½ times in the year. The rate of surplus-value was 80/52 = 153 11/13 per cent.
From these figures we work out the rate of profit by putting the values into the formula p' = s'n v/C: s' = 153 11/13, n = 8½, v = 318, C = 12,500; so:
We can check this by using the simple formula p' = s/C. The total surplus-value or profit for the year comes to £80 times 52 = £4,160; dividing this by the total capital of £12,500 gives 33.28 per cent, almost the same figure as above — an abnormally high rate of profit, explained only by conditions that happened at that moment to be extremely favourable (very cheap cotton prices alongside very high yarn prices), and one that certainly can't have held for the whole year in reality.
In the formula p' = s'n v/C, s'n is, as already said, what Volume 2 called the annual rate of surplus-value. In the case above it comes to 153 11/13 per cent times 8½, or, worked out exactly, 1,307 9/13 per cent. So if a certain worthy citizen threw up his hands over the monstrosity of an annual rate of surplus-value of 1,000 per cent set out in an example in Volume 2, he may perhaps be reassured by this fact, drawn straight from the living practice of Manchester, of an annual rate of surplus-value of over 1,300 per cent. In times of the highest prosperity — which, admittedly, we haven't seen for a long while now — such a rate is by no means a rarity.
By the way, this gives us an example of the actual composition of capital within modern large-scale industry. The total capital splits into £12,182 constant and £318 variable capital, £12,500 together. Or, as a percentage: 97½c + 2½v = 100 C. Only a fortieth of the whole serves to cover wages — but it does so by coming round more than eight times over in the year.
Since hardly any capitalist thinks to make this kind of calculation about his own business, statistics stay almost completely silent on the ratio of the constant part of the total social capital to the variable part. Only the American census provides what's possible under today's conditions: the total wages paid and profits made in each branch of business. However questionable this data may be, resting as it does only on the industrialists' own unchecked statements, it's still extremely valuable — the only thing we have on the subject. In Europe we're far too squeamish to expect our big industrialists to make disclosures of that kind. — F.E.
The effect of turnover on the production of surplus-value, and so also of profit, has already been discussed in Volume 2. It can be summed up briefly like this: because turnover takes time, not all of a capital can be employed in production at once. Part of it is constantly lying idle — as money capital, as stocks of raw material sitting in store, as finished but still unsold commodity capital, or as debts owed to the capitalist that aren't yet due. The capital actually at work producing and appropriating surplus-value is constantly cut down by this idle part, and the surplus-value produced and appropriated is reduced in the very same proportion.
The shorter the turnover time, the smaller this idle part of the capital becomes compared with the whole — and so, other things being equal, the greater the surplus-value appropriated.
It has already been shown in detail in Volume 2 how shortening the turnover time — or either of its two parts, the production time and the circulation time — increases the mass of surplus-value produced. But since the rate of profit only expresses the ratio of the mass of surplus-value produced to the total capital engaged in producing it, it's obvious that any such shortening raises the rate of profit as well. What was worked out in Part Two of Volume 2 with respect to surplus-value holds equally for profit and the rate of profit, and there's no need to repeat it here. We'll just pick out a few of the main points.
The main means of shortening production time is raising the productive power of labour — what's usually called the progress of industry. If this doesn't also bring about a significant increase in the total capital outlay — say, through installing expensive machinery — and so a fall in the rate of profit reckoned on the whole capital, then that rate must rise. And this is certainly true of many of the most recent advances in metallurgy and the chemical industry.
The newly discovered methods of making iron and steel — Bessemer's, Siemens's, Gilchrist-Thomas's, and others — cut processes that used to take a very long time down to a minimum, and at relatively low cost. Making alizarin, the madder dye, out of coal tar produces in a few weeks, using the plant already in place for coal-tar dyes, the very same result that used to take years: madder needed a year just to grow, and then the roots still had to mature for several more years before being turned into dye.
The main means of shortening circulation time is improved communications. And here the last fifty years have brought a revolution comparable only to the industrial revolution of the last half of the previous century. On land the macadamized road has been pushed into the background by the railway; at sea, the slow and irregular sailing ship by the fast and regular steamship line; and telegraph wires now span the whole globe. The Suez Canal has really opened East Asia and Australia up to steamship traffic. The circulation time for a shipment of goods to East Asia, still at least twelve months in 1847 (as already noted in Volume 2), can now be brought down to roughly as many weeks.
The two great trouble spots behind the crises of 1825-1857, America and India, have been brought 70-90 per cent closer to the industrial countries of Europe by this revolution in transport, and have thereby lost much of their power to set off a crisis. The turnover time of world trade as a whole has been shortened to the same degree, and the same capital engaged in it can now do more than two or three times as much business. That this hasn't been without effect on the rate of profit goes without saying.
To show the effect of turnover of the total capital on the rate of profit in a pure form, we have to take the two capitals being compared as equal in every other respect. Besides the rate of surplus-value and the working day, let their percentage composition in particular also be equal.
Let's take a capital A of composition 80c + 20v = 100 C, which turns over twice a year at a rate of surplus-value of 100 per cent. Then the annual product is:
160c + 40v + 40s. But to work out the rate of profit, we don't reckon this 40s against the turned-over capital-value of 200 — we reckon it against the 100 that was advanced, which gives us p' = 40 per cent.
Let's compare this with a capital B = 160c + 40v = 200 C, which turns over at the same rate of surplus-value of 100 per cent, but only once a year. Then the annual product is, as above:
160c + 40v + 40s. But this time the 40s has to be reckoned against a capital advanced of 200, which gives a rate of profit of only 20 per cent — just half the rate for A.
So this is what follows: for capitals of equal percentage composition, at an equal rate of surplus-value and an equal working day, the profit rates of two capitals stand in inverse proportion to their turnover times.
If the composition, or the rate of surplus-value, or the working day, or the wage differs between the two cases being compared, then further differences in the rate of profit will indeed arise from that too — but these are independent of turnover, and so are none of our concern here. They have already been dealt with in Chapter 3.
The direct effect of a shortened turnover time on the production of surplus-value, and hence of profit, lies in the increased effectiveness this gives to the variable part of the capital — which is worked out in Volume 2, Chapter 16, on the turnover of the variable capital. It was shown there that a variable capital of 500, turning over ten times a year, appropriates in that time just as much surplus-value as a variable capital of 5,000 which, at the same rate of surplus-value and the same wage, turns over only once a year.
Let's take a capital I, made up of 10,000 in fixed capital, whose annual depreciation comes to 10 per cent = 1,000, plus 500 in circulating constant capital and 500 in variable capital. At a rate of surplus-value of 100 per cent, let the variable capital turn over ten times a year. For simplicity, in all the examples that follow we'll assume the circulating constant capital turns over in the same time as the variable capital, which in practice is usually more or less the case anyway. Then the product of one such turnover period will be:
And the product for the whole year, from all ten such turnovers:
Now let's take a capital II: fixed capital 9,000, its annual depreciation 1,000, circulating constant capital 1,000, variable capital 1,000, rate of surplus-value 100 per cent, number of annual turnovers of the variable capital: 5. The product of each turnover period of the variable capital will then be:
And the total product for the year, at five turnovers:
Let's further take a capital III, containing no fixed capital at all, but instead 6,000 in circulating constant capital and 5,000 in variable capital. At a rate of surplus-value of 100 per cent, let it turn over once a year. The total product for the year is then:
So in all three cases we have the same annual mass of surplus-value, = 5,000, and since the total capital is likewise the same in all three cases, namely = 11,000, we get the same rate of profit of 45 5/11 per cent.
If, on the other hand, the variable part of capital I above turns over only 5 times a year instead of 10, things look different. The product of one turnover is then:
Or, the annual product:
The rate of profit has fallen by half, because the turnover time has been doubled.
The mass of surplus-value appropriated over the course of the year is thus equal to the mass of surplus-value appropriated in one turnover period of the variable capital, multiplied by the number of such turnovers in the year. Let's call the surplus-value or profit appropriated per year S, the surplus-value appropriated in one turnover period s, and the number of annual turnovers of the variable capital n. Then S = sn, and the annual rate of surplus-value is S' = s'n, as already shown in Volume 2, Chapter 16.
The formula for the rate of profit, p' = s'v/C = s'v/(c+v), obviously only holds good if the v in the numerator is the same v as the v in the denominator. In the denominator, v is the whole part of the total capital that functions, on average, as variable capital laid out on wages. The v in the numerator, though, is at first fixed only by this: it is the wage outlay that has produced and appropriated a certain quantity of surplus-value = s, and s divided by that v is the rate of surplus-value s'. Only by this route does the equation p' = s/(c+v) turn into the other one, p' = s'v/(c+v). The v in the numerator is then more precisely pinned down as having to equal the v in the denominator — that is, the whole variable part of the capital C.
In other words, the equation p' = s/C can only be turned, without error, into p' = s'v/(c+v) if s means the surplus-value produced in one turnover period of the variable capital. If s covers only part of that surplus-value, then s = s'v still holds, but this v is smaller than the v in C = c+v, because less than the whole variable capital has been laid out in wages. But if s covers more than the surplus-value of a single turnover of v, then part of that v — or even the whole of it — functions twice: first in the first turnover, then in the second, or a further one. The v that produces the surplus-value, and that is the sum of all wages paid, is then larger than the v in c+v, and the calculation goes wrong.
For the formula for the annual rate of profit to come out exactly right, we have to put the annual rate of surplus-value in place of the simple rate of surplus-value — that is, put S', or s'n, in place of s'. In other words, we have to multiply s', the rate of surplus-value — or, what comes to the same thing, the variable part of the capital v contained in C — by n, the number of turnovers of that variable capital in the year. This gives us p' = s'n v/C, which is the formula for working out the annual rate of profit.
But how large the variable capital in a business actually is, is something the capitalist himself usually doesn't know. We saw in Chapter 8 of Volume 2, and will see further on, that the only distinction within his capital that forces itself on the capitalist as essential is the distinction between fixed and circulating capital. From the till that holds the part of his circulating capital that's in money form, so far as it isn't sitting in the bank, he draws the money for wages, and from that same till the money for raw and ancillary materials, crediting both to one and the same cash account.
And even if he did keep a separate account of wages paid, at the end of the year this would show only the whole year's wage bill — that is, v paid out over and over, n times — and not the variable capital v itself. To work that out, he'd have to make a separate calculation, and we want to give an example of one here.
For this we take the cotton-spinning mill of 10,000 mule spindles already described in Volume 1, and assume that the figures given for one week of April 1871 held good for the whole year. The fixed capital tied up in machinery was £10,000. The circulating capital wasn't given; we'll assume it was £2,500 — a fairly high figure, but justified by the assumption we always have to make here, that there are no credit operations, that is, no permanent or temporary use of someone else's capital.
By value, the week's product was made up of £20 for depreciation of machinery, £358 advanced as circulating constant capital (rent £6, cotton £342, coal, gas and oil £10), £52 in variable capital laid out on wages, and £80 surplus-value — that is:
The weekly advance of circulating capital was thus 358c + 52v = 410, with a percentage composition of 87.3c + 12.7v. Worked out for the whole circulating capital of £2,500, this gives £2,182 constant and £318 variable capital. Since the total outlay on wages for the year was 52 times £52, that is £2,704, it follows that the variable capital of £318 turned over almost exactly 8½ times in the year. The rate of surplus-value was 80/52 = 153 11/13 per cent.
From these figures we work out the rate of profit by putting the values into the formula p' = s'n v/C: s' = 153 11/13, n = 8½, v = 318, C = 12,500; so:
We can check this by using the simple formula p' = s/C. The total surplus-value or profit for the year comes to £80 times 52 = £4,160; dividing this by the total capital of £12,500 gives 33.28 per cent, almost the same figure as above — an abnormally high rate of profit, explained only by conditions that happened at that moment to be extremely favourable (very cheap cotton prices alongside very high yarn prices), and one that certainly can't have held for the whole year in reality.
In the formula p' = s'n v/C, s'n is, as already said, what Volume 2 called the annual rate of surplus-value. In the case above it comes to 153 11/13 per cent times 8½, or, worked out exactly, 1,307 9/13 per cent. So if a certain worthy citizen threw up his hands over the monstrosity of an annual rate of surplus-value of 1,000 per cent set out in an example in Volume 2, he may perhaps be reassured by this fact, drawn straight from the living practice of Manchester, of an annual rate of surplus-value of over 1,300 per cent. In times of the highest prosperity — which, admittedly, we haven't seen for a long while now — such a rate is by no means a rarity.
By the way, this gives us an example of the actual composition of capital within modern large-scale industry. The total capital splits into £12,182 constant and £318 variable capital, £12,500 together. Or, as a percentage: 97½c + 2½v = 100 C. Only a fortieth of the whole serves to cover wages — but it does so by coming round more than eight times over in the year.
Since hardly any capitalist thinks to make this kind of calculation about his own business, statistics stay almost completely silent on the ratio of the constant part of the total social capital to the variable part. Only the American census provides what's possible under today's conditions: the total wages paid and profits made in each branch of business. However questionable this data may be, resting as it does only on the industrialists' own unchecked statements, it's still extremely valuable — the only thing we have on the subject. In Europe we're far too squeamish to expect our big industrialists to make disclosures of that kind. — F.E.