The Effect

Turnover time contains circulation time and production time.

1. The time capital takes to perform $C-M$ and $M’-C’$ is time during which it does not valorise itself, but only changes its form of value. To keep production going during this time additional expenditures are required which lie idle, until they are needed. Roughly: as long as part 1 of capital is in the production sphere, part 2 only circulations and vice versa.

2. For production we have that if it takes, say, 5 weeks to complete a product then 5 weeks of capital must be advanced. Hence, capital for 4 weeks of production lies idle in the first week, it does not valorise itself. Here we have: the longer production time, the more capital must be advanced which only lies idle.

In summary: the short the turnover, the more effective capital is in producing surplus-value, since less capital lies idle or is busy merely changing form.

On to the profit rate:

163:2 We explained in detail in the second volume how a reduction in turnover time or in one of its two component sections, production time and circulation time, raises the mass of surplus-value produced. But since the rate of profit simply expresses the ratio of the mas of surplus-value produced to the total capital engaged producing it, it is evident that a reduction of this kind raises the rate of profit as well. The points made in Part Two of the second volume with respect to surplus-value apply equally here to profit and the rate of profit, and do not need to be repeated.

The question here is mass of surplus-value in relation to what. The mass of surplus-value does not change in a year, because capital turns over more than once. The same mass $v$ is put into motion. If the rate of surplus-value is the same, this implies the same mass of surplus-value. However, if capital turns over faster, then a smaller capital puts into motion the same $v$ and hence produces the same surplus-value. Put differently: it produces more surplus-value per advance in $v$ and what increases is the annual rate of surplus-value: $S’$.

Since the rate of profit is related to a some time span anyway — typically a year — what was developed for the annual rate of profit also applies to the rate of profit. A smaller capital puts the same mass of $v$ into motion if it turns over faster and therewith — everything else being equal — the ratio $S/(v+c)$ increases because $S/v$ increases.

However, there is more to be considered for the profit rate but which Engels in Chapter 4 does not deal with. Faster turnover also means faster turnover of circulating constant capital $c$. This means that the ratio $S/(v+c)$ also increases because $c$ shrinks relatively (this does not apply to fixed capital). To consider the extreme cases:

1. Only circulating capital: the ratio increases most because all $c$ shrinks;

2. Only fixed capital: then only the shrinking of $v$ has an effect.

An example. Assume the year has 50 weeks, all capital is circulating (fixed capital is treated later):

$v = 200$, $c = 200$, $\frac{s}{v} = 100\%$, turnover: $2 \mbox{wks}$, $S = 25·200 = 5,000$, $\frac{S}{v} = 25$, $S/(v+c) = 12 1/2$
$v = 100$, $c = 100$, $\frac{s}{v} = 100\%$, turnover: $1 \mbox{wks}$, $S = 50·100 = 5,000$, $\frac{S}{v} = 50$, $S/(v+c) = 25$

In this example, $S’$ and $p’$ scaled by the same factor two. This holds if,

1. the value composition $C=v+c$ or the relation $v/C$ and

2. the rate of surplus-value $s/v$

are fixed. Then we have:

$p’/S’ = \frac{S/(c+v)}{S/v} = \frac{v}{c + v}$

which means that under these conditions $p’$ and $S’$ grow and shrink by the same ratios.

If the two factors — value composition and rate of surplus-value — that determine the profit rate according to Chapter 3 are fixed then an increased turnover increases the profit rate. Hence, we have found another factor which affects the profit rate.

167:2 In order that the formula for the annual rate of profit may be completely correct, we must replace the simple rate of surplus-value with the annual rate, $S’$ or $n·s’$ in place of $s’$. In other words, we must multiply $s’$, the rate of surplus-value – or else multiply the $v$, the variable capital $v$ contained in $C$ — by $n$, the number of turnovers that this variable capital makes in a year, and we then obtain $p’ = s’n\frac{v}{C}$, the formula for calculation the annual rate of profit.

When we transition from the annual rate of surplus-value to the rate of profit, then we have to use $p’ = s’n\frac{v}{C}$, where $n$ is the number of turnovers.

1. The rate of surplus-value is valid for every day, because it expresses the general rate of exploitation of applied $v$.

2. The annual rate of surplus-value expresses how effective the advance in $v$ puts this labour-power into motion to exploit it.

3. The profit rate is the efficiency of capital to valorise itself. Its reference point is also the advance — this is why we use $S’$ and not $s’$ - but the complete advance $C=v+c$, not only $v$.

Hence, the category annual rate of profit is somewhat odd: a profit rate is related to a time span anyway and expressed the efficiency of capital to valorise itself. The transition from the rate of surplus-value to the annual rate of surplus-value marks a conceptual distinction, the annual rate of profit is merely the rate of profit related to a year (which should be the norm, anyway).

Techniques for shortening turnover time

Shorting turnover time is hence a means for capital to increase the profit rate — its criterion for efficiency. Capital can attempt to shorten production time and circulation time.

163:3 The main means whereby production time is reduced is an increase in the productivity of labour, which is commonly known as industrial progress. If this does not also involve a major increase in the total capital investment, due to the installation of expensive machinery etc., and therefore a fall in the rate of profit as reckoned on the total capital, then this profit rate must rise.

Turnover time can be shortened by shortening production time, i.e. by increasing the productivity of labour (more use-values per time). This has the effect discussed above on the annual rate of surplus-value and on the profit rate.

Circulation time can also be shortened by technical progress:

164:1 The main means of cutting circulation time has been improved communications. […] It is evident that this cannot but have had its effect on the profit rate.

Excursus: Effects of cutting turnover time on other factors of the profit rate

In the discussion of the techniques used to speed up turnover the following assumption is made explicitly:

163:3 If this does not also involve a major increase in the total capital investment, due to the installation of expensive machinery etc., and therefore a fall in the rate of profit is reckoned on the total capital.

This assumption is justified because here the effect of turnover on the profit rate ought to be studied in its pure form. However, the techniques of cutting turnover time do have their effect on $s/v$ and $v/C$, i.e. the other factors which determine the profit rate. Gains in productivity and new communication technologies cost: the first is an additional expenditure in $c$ the second is a reduction of $S$. The improved turnover time then must compensate these factors as well:

165:2 The result is therefore that for capitals of the same percentage composition, with the same rate of surplus-value and the same working day, the profit rates of two capitals vary inversely as their turnover time. If either the composition or the rate of surplus-value or the working day or the wage of labour is not the same in the two cases to be compared, further differences in the rate of profit are also brought about, but these are independent of the turnover, and do not concern us here.

Fixed and circulating capital##

The question which effect — if any — fixed capital has on the profit rate. Consider the following three examples:

• Capital I consists of $10,000c$ fixed capital, wear and tear 10\% per year, hence $1,000c$; $500c$ circulating constant capital and $500v$ variable capital. This capital turns over 10 times and has a rate of surplus-value of $100\%$. Hence, it produces $5,000m$ surplus-value:

  $10,000c + 500c + 500v = 11,000C → p’ = 5,000m/11,000C \approx 45\%.$

• Capital II consists of only $9,000c$ fixed capital, wear and tear stays $1,000c$, which is more than $10\%$. It also consists of $1,000c$ circulating constant capital and $1000v$ variable capital. This capital turns over $5$ times in a year and has a rate of surplus-value of $100\%$. This capital also produces $5,000m$ surplus-value and we have:

  $9,000c + 1000c + 1000v = 11,000C → p’ = 5,000m/11,000C \approx 45\%.$

• Capital III consists only of circulating capital, but a lot of it: $6,000c + 5,000v$. It turns over only once per year and $m/v$ still is $100\%$. We have:

  $6,000c + 5,000c = 11,000C → p’ = 5,000m/11,000C \approx 45\%.$

In all three cases we have the same rate of profit. The moral of this story is that when we are considering $S/C$ then $S$ and $C$ are of interest. For both it is completely irrelevant how capital splits into fixed and circulating constant capital. However, as discussed above, if turnover speed is increased, this might lead to a faster turnover of circulating $c$ which means that less $c$ (and hence $C$) overall needs to be advanced.

166:3 In all three cases, therefore, we have the same annual mass of surplus-value $=5,000$, and since the total capital is the same in all these cases, i.e. $11,000$, we have the same profit rate of $45\frac{5}{11}$ per cent.

Another example to drive the point home:

• Capital IV consists only of circulating capital: $10,000c + 1,000v$. It turns over $5$ times per year (just as Capital II). We then have:

  $10,000c + 1,000v = 11,000C → 5,000m/11,000C \approx 45\%.$

The expenditure on $v$, the rate of surplus-value $s/v$ and the number of turnovers $n$ determine $S=n\frac{s}{v}$. The expenditure on $v$ and $c$ determine $C$. The distribution of fixed and circulating capital has exactly no effect.

Expressed using surplus-value $S$:

166:3 If in the case of the above capital I there took place not ten but only five turnovers of its variable portion, the matter would be different. The product of one turnover would then be: $200c$ (depreciation) $+ 500c + 500e + 500s = 1,700;$ or the annual product:

$1,000c$ (depreciation) $+ 2,500c + 2,500v + 2,500s = 8,500;$

$C = 11,000, s = 2,500, p’ = 2,500/11,000 = 22 8/11$ per cent.

The profit rate has now fallen by half, as the turnover time has doubled.

In this example $S$ shrunk, because turnover slowed down, but $C$ remained the same. Hence, the rate of profit decreased (everything being equal).

Calculating the (annual) rate of surplus-value

Engels wants to calculate how to get to the rate of surplus-value from the rate of profit. This is insofar useful as it highlights that expenditures in $v$ are not the same as the advance for $v$. On the other hand, he uses several keywords and phrases (“abnormally high”, “enormous size of the annual rate of surplus-value of 1,000” etc.) which leave the impression as if quantity of exploitation was the issue — the rate of surplus-value — and not exploitation itself.

167:2 The capitalist himself does not know in most cases how much variable capital he employs in his business. We have already seen in Chapter 8 of Volume 2, and we shall now see further, that the only distinction within his capital that impresses itself on the capitalist as fundamental is the distinction between fixed and circulating capital. From the same till that contains the part of his circulating capital that exists in his hands in the money form, in so far as this is not placed in the bank, he fetches both money for wages and money for raw and ancillary materials, and enters both of these in the same cash account. Even if he were to keep a separate record for wages paid, this would simply indicate the total sum paid at the end of the year, i.e. $v$n, and not the variable capital $v$ itself.