## Tuesday, 26 January 2016

### The Rate of Profit

The rate of profit is a derivative of the rate of surplus value. Just as the rate of surplus value is calculated as the proportion of the surplus value to the laid out variable capital, so the rate of profit is calculated as the proportion of the surplus value to the laid out constant capital, and variable capital.

That laid out capital also includes the value of the wear and tear of the fixed capital, even though, in any one year, any individual capital may not actually lay out capital to replace its fixed capital. It must set aside this value of wear and tear, so that fixed capital can eventually be replaced, and so it represents a part of the cost of producing the profit. As Marx sets out, in Capital II, for the economy as a whole, this will tend to average out. If fixed capital has an average lifespan of ten years, in any one year, it will transfer, through wear and tear, 10% of its value to the commodities it helps produce. So, if the total fixed capital stock has a value of £1,000, it will transfer £100. But, in any one year, on average, 10% of the fixed capital stock will need to be physically replaced, which also equals £100. In other words, for the economy as a whole, though not for any individual capital, the amount of value of wear and tear recovered in the value of its output, and set aside to cover the replacement of fixed capital, will be equal to the amount of capital actually laid out to replace fixed capital.

In fact, however, as Marx sets out in Capital II, this is never likely to be exactly true. If fixed capital lasts longer than is expected, more value will be extracted from circulation in the value of wear and tear, than is thrown back into circulation for the purchase of replacement fixed capital. In that case, a disproportion between Department I and Department II arises, so that the under-consumption of fixed capital by Department II, causes an overproduction by Department I. If, fixed capital lasts for less time than expected, the opposite situation arises.

As with the rate of surplus value, this rate of profit, because it is based upon the laid out capital, as opposed to the advanced capital, is the same whether it is measured for a day, week or year. If £1000 of capital is laid out in a week, made up of £500 materials (c), plus £400 wages (v), plus £100 wear and tear (d), and the surplus value (s) is £400, then the rate of profit s/c + d + v, which is equal to 40%. If we measure the rate of profit for the year, we will find it is the same. It would then be, for a fifty week year £50,000 of capital laid out made up £25,000 materials, £20,000 wages and £5,000 wear and tear, whilst the total surplus value would be £20,000, again giving a rate of profit of 40%.

Marx makes clear that the rate of profit, is the rate of profit on the productive-capital, although later in Capital III, Chapter 18, he modifies this so as to include the capital laid out as merchant capital, in the calculation, which merely reflects the fact that the portion of industrial capital forming the commodity-capital, and money-capital, during its circulation phase, has been transformed into independent capitals. The starting point for Marx then in calculating the rate of profit is the circuit of this productive-capital. That is all the more clear in Marx's analysis of the process of social reproduction, in which Marx follows on the model set out by the Physiocrats in the Tableau Economique.

For Marx, as with the Physiocrats, that circuit of productive-capital begins with the stock of physical capital in the possession of the capitalist/s. No production can occur unless there already exists a quantity of physical commodities, which comprise the constant and variable capital, which is to be advanced in the process of production. Before workers can be set to work, the capitalist must have factories, machines, and materials, for example. These do not simply appear out of thin air, but are themselves the product of previous years' production. Capitalism itself could never have commenced unless, in the thousands of years preceding it, societies had produced a stock of various products, and commodities, which could then form this physical capital stock.

In the same way, there must exist a physical stock of means of subsistence required both by workers and capitalists, as well as landlords, and money-lenders, who must live by consuming such commodities, whilst production is taking place to replace them. Marx sets out the circuit of productive capital then in the following expanded form.

This indicates that a physical mass of commodities exist, in the shape of fixed and circulating constant capital, as well as of variable capital. Its important to understand the variable capital in the terms Marx describes in his analysis of social reproduction, following on from the Physiocrats. In other words, not as a sum of money wages, but as a mass of commodities required for the workers' reproduction. The value of both the constant and variable capital, here, are expressed in money terms, only, as Marx sets out, because it is impossible to undertake any rational calculation without doing so. But, money here only acts as unit of account for the purpose of undertaking such calculation, and should not be confused with the money prices paid for the commodities bought that comprise the constant and variable capital.

The capital laid out here, is the capital consumed in the production process, and reproduced by that same process. As Marx sets out later, it is the physical use values that are consumed by this process, which must be physically reproduced by the reproduction process, on a like for like basis, so that social reproduction can occur, on at least the same scale, and for that reason, what is determinant for their value, the surplus value produced, and thereby the rate of profit, is the current labour-time required for their reproduction, not the labour-time required for their production at some point in the past.

“This entire portion of constant capital consumed in production must be replaced in kind. Assuming all other circumstances, particularly the productive power of labour, to remain unchanged, this portion requires the same amount of labour for its replacement as before, i.e., it must be replaced by an equivalent value. If not, then reproduction itself cannot take place on the former scale.”

(Capital III, Chapter 49, p 835)

and later.

“In so far as reproduction obtains on the same scale, every consumed element of constant capital must be replaced in kind by a new specimen of the same kind, if not in quantity and form, then at least in effectiveness.”

(Capital III, Chapter 49, p 849)

In other words, if we take the total social capital, the use values that comprise the consumed constant and variable capital, and which were produced in previous periods, must be physically replaced out of current production. If current production does not physically reproduce the machines and other fixed capital that has been worn out, in its own production, then those machines will not be available to assist in the processing of material, so less material will be processed, and less labour will be employed, so social reproduction will contract. If the materials consumed in production are not physically replaced, they will not be available to take part in the reproduction process, so again fewer workers will be employed, and social reproduction will contract. If the food and other necessities required for their subsistence are not reproduced out of current production, there will be insufficient to sustain the current workforce, which will then contract.

If we assume constant levels of productivity, then Marx's expanded formula for the circuit of productive-capital, above, shows this process. C' is the social product, created by the current production process. It divides into C, the physical use values, consumed in its own production. The money equivalent, or value of this product is given by M, which then also represents the value of the use values, which are thrown into the next cycle of production, so that the circuit here is C – M – C, or P... C – M – C... P.

This can also apply to an individual productive-capital. It starts with a quantity of physical capital, which is thrown into the production process. Of its output, a certain proportion, equal to C, is required to reproduce, the use values consumed in its production. This proportion of its total output is sold, and provided it is sold at its value, results in its money equivalent, M. This money equivalent, then buys the commodities, means of production and labour-power, required to replace those consumed in the current production.

In both cases, a proportion of the total product, over and above C, represents a surplus product, c, and this is available to either be consumed by non-producers (capitalists, landlords, the state) or else to be accumulated. It is the surplus physical product that enables firms to employ the additional machines, to process additional material, and to provide the means of subsistence for additional workers, which comprise this surplus physical product. This can be seen if we consider the situation in relation to a farmer who produces corn, which here represents all of the constant and variable capital.

The farmer begins the period with 500 kg of corn. Of this 100 kg is required as seed (c), whilst 400 kg is required to be paid to his workers as wages (v). As a consequence of production, 600 kg of corn are produced. This means that the 100 kg of seed is replaced, and the 400 kg, paid as wages to workers, and required to feed the workers in the next period is also replaced. This means that a surplus product of 100 kg of corn is produced. This can be consumed by the farmer, so there is simple reproduction. The rate of surplus value here is equal to 25%, the ratio of the surplus product to the variable capital, or necessary product. The rate of profit is 20%, the ratio of the surplus product to the constant and variable capital.

Suppose the workers work for 1,000 hours to produce this output. In Marx's terms as set out in Capital I, this 1,000 hours can be broken up and viewed in different ways. If it is considered as a single social working day, then, firstly, a part of this day comprises necessary labour, undertaken solely to reproduce the consumed labour-power. It takes the form of a necessary product, produced during that time, which comprises the commodities required to reproduce that labour-power. Secondly, the remainder of this social working day represents surplus labour, and the product of this portion of the day represents a surplus product.

That means 1,000 of new value is produced. In that case, the value of c = 1/5 of 1,000 = 200. The total value of current production is then equal to 1200, which is the value of the constant capital consumed, plus the new value created by labour, which itself divides into 800 v + 200 s. The value of a kg of corn is equal to 2 hours. So we have,

c 200 + v 800 + s 200 = 1200. s' = 25%, p' = 20%.

If workers continue to work for 1,000 hours, this continues to be the new value they create, but this new value will divide differently between v and s, dependent upon the level of productivity. In all events, in order for social reproduction to continue, on at least the same scale, the workers will need to be paid 400 kg of corn, to ensure their reproduction. What proportion this 400 kg represents of the total product, and the surplus product, and so also of the total labour-time, and surplus labour-time, depends upon the level of productivity. If productivity rises, more corn is produced in a given time, so less time is required to produce the corn required to replace both the constant and variable capital, and vice versa. This means both that a greater mass of surplus product and surplus value is created, and that it represents a greater proportion to the value of the capital laid out for its production.

If productivity rises, so that output is equal to 800 kg, 100 kg is still required to replace seed, and 400 kg replaces (v). In that case, (s) rises to 300 kg. Now the rate of surplus value, s', has risen to 75%, and the rate of profit has risen to 60%. If we measure this in terms of values, then 100 kg of seed was used, and was converted into 800 kg of output. The 1000 hours of labour, created 700 kg of output, so that the current value of a kg of corn falls from 2 hours to 1.43 hours. The current value of the seed consumed in production, therefore, falls from 200 hours to 143 hours.

So, we have,

c 143 + v 571.43 + s 428.57 = 1143. s' = 75%, p' = 60%.

This demonstrates Marx’s other point about the contradictory nature of the commodity as both use value and value. If this were a society, its total wealth, represented by the quantity of use values produced, has risen by 33.3%, because previously 600 kg. was produced, and now that has risen to 800 kg. However, the total value of this new, higher level of output is lower, at 1143, as opposed to 1200, because the labour-time required to produce it has fallen.

Suppose workers continue to work 1,000 hours, creating 1,000 of new value. If productivity now falls so that only 500 kg of corn is produced, then 100 kg is still required to reproduce the seed, and 400 kg to replace the variable capital. That means that there is no surplus product, and no surplus value. All of current production must go simply to reproduce the capital consumed in current production. The 1,000 of new value is equal to 400 kg of output, giving a value per kg of 2.5 hours. Now, the 100 kg of (c) is equal to a value of 250, the 400 kg of (v) to a value of 1000. The total output of 500 kg has a value of 1250 hours. So, we have,

c = 250 + v 1000 + s 0 = 1250.

This reflects the situation described by Marx and Engels that class society is only possible when social productivity has reached a level whereby the producers are able to produce sufficient not only to replace the means of production, but also their own means of consumption, with an additional surplus product over and above that level. Because, under capitalism, this social surplus takes the form of surplus value, this means that they must be able to firstly reproduce the value of the consumed means of production, in the value of the final output, and must create sufficient new value, so as to not only reproduce the value of their labour-power, but to produce a surplus value in excess of it.

Of course, every capitalist engages in production on the assumption that this will be the case, but it cannot be guaranteed. The workers they employ will always create new value equal to the labour-time they expend, (provided it is socially necessary labour) but there is no reason that this new value will always exceed the value of the labour-power used in production, as the above demonstrates. If total output had fallen to 400 kg for instance, 100 kg would still be required to reproduce seed, but now there is insufficient production to reproduce the consumption requirements of the workers – 400 kg are required, but only 300 kg are available.

In that case, to continue production on the same scale, the capitalist would have to add to their capital to make up the difference. Instead of a surplus value, the capital would have produced a loss. Now, 1000 hours expended produced an additional 300 kg, giving a value per kg of 3.33 hours. So, now we would have,

c 333 + v 1333 + s – 333 = 1333.

In other words, rather than extracting a surplus value, and being able to accumulate capital, the capitalist must add an additional 100 kg of corn, or 333 hours of additional value, just to continue production on the same scale. This situation could occur in agriculture due to a crop failure, for example. Suppose, such a crop failure resulted not just in output failing to cover the requirement to reproduce the variable capital, but also failed even to reproduce all of the constant capital, so that output falls to just 50 kg. In order to ensure that reproduction could continue on at least the same scale, the capitalist would then have to add an additional 450 kg of corn as additional capital.

The value of a kg of corn would now rise to 20 hours. We would have,

c 2000 + v 8000 – s 9000 = 1,000.

The workers would have continued to produce 1,000 of new value, as before, because they performed 1,000 hours of socially necessary labour-time, but the crop failure causes such a collapse of productivity that the value of a kg of corn soars to 20 hours. The workers were paid 400 kg of corn, as wages, and this now has a value of 8,000 hours, the amount of labour-time now required to replace it.  They must continue to be paid the 400 kg of corn required for their subsistence, if production is to continue on the same scale. So, the capitalist suffers a loss of 7000 hours, in terms of the new value created by labour, as opposed to the value of labour-power consumed in its production. In addition, they must now also add a further 2000 hours of capital to replace the consumed constant capital, leaving them with a loss of 9000 hours.

This is the difference between Marx’s method of calculating the rate of profit on the basis of the current value of the laid out capital, as opposed to calculating it on the basis of the historic prices paid for the consumed capital. Marx's method shows the real relation on the basis of the potential to accumulate capital, or indeed, as described above, for capital to contract, as a sharp fall in productivity causes a much larger proportion of the total social product to be required simply to replace the consumed capital.

This can be seen clearly by examining again Marx's expanded formula for the circuit of productive-capital.

Suppose 100 kilos of cotton are consumed in the production of yarn, the realised value of the yarn must contain, an equivalent amount of value to the current reproduction cost of 100 kilos of cotton. Suppose the 100 kilos of cotton required 10 hours of labour to produce, equal to £10. This £10 is transferred to the value of the yarn, provided productivity remains constant. If the yarn also comprises £5 of variable-capital, and £5 of surplus value, it will sell for £20.

If productivity rises, so that the cotton can now be produced in just 5 hours, its value falls to just £5. It is then this value, not the £10 originally paid, which is transferred to the yarn, which now sells for £15. This £15, however, is still capable of reproducing the capital in kind, because only £5, or 5 hours of labour-time are now required to physically reproduce the 100 kilos of cotton.

“If the price of raw material, for instance of cotton, rises, then the price of cotton goods — both semi-finished goods like yarn and finished goods like cotton fabrics — manufactured while cotton was cheaper, rises also. So does the value of the unprocessed cotton held in stock, and of the cotton in the process of manufacture. The latter because it comes to represent more labour-time in retrospect and thus adds more than its original value to the product which it enters, and more than the capitalist paid for it...

The reverse takes place when the price of raw material falls. Other circumstances remaining the same, this increases the rate of profit.”

(Capital III, Chapter 6)

The same applies to Marx’s comment about “effectiveness” quoted above from Chapter 49 (p 849). If a producer replaces a machine costing £100, that is capable of producing 1000 units per day, with another machine costing £100 but which produces 2000 units per day, this is the same thing as if productivity had risen, so that the old machine now only required half the labour-time to produce, or had fallen in value to £50. It is the basis of what Marx calls “moral depreciation”.

But, in all these cases, the purpose is to reproduce the physical capital on at least the same scale – simple reproduction – and, in reality, on an expanded scale.

“In the reproduction process of capital, the money-form is but transient – a mere point of transit.”

(Capital III, Chapter 24)

The term M, in fact, only refers to the money equivalent of the current value of the capital, which must be reproduced. As Marx makes clear, it is only money as unit of account, required in order to make rational calculations. The historic cost of the consumed cotton may have been £10 (because that reflected the previous amount of labour-time required for its production), but that is irrelevant to its current value, and the value it transfers to the yarn, as well as to the portion of the yarn (and similarly of social-labour-time) required to reproduce the cotton. That is apparent in Marx's analysis in Capital II, where he separates out the portion of the end product, of the commodity-capital, C', into C and c. C is the physical portion of the commodity-capital required to physically reproduce the commodities (that comprise the constant capital and labour-power) consumed in its production, whilst c, is the portion of the commodity-capital in excess of that. It is represented as its money equivalents, by M and m.

The fact that £10 was the actual historic price paid for the 100 kilos of cotton, therefore, becomes irrelevant, because the circuit here is based on the actual value of the commodities that take part in the production and subsequent circulation process.

P is equal to £10, which comprises £5 value of cotton and £5 for labour-power (£5 constant capital, £5 variable capital) . As a result of the production process, £5 of surplus-value is created by labour, which now forms part of the value of the commodity-capital, C' £15. It has a money equivalent of £15, which is realised on sale, M' £15.

Assuming simple reproduction, £10 of this £15 then goes to reproduce the £5 value of cotton, and £5 value of labour-power, M £10. These commodities, then form the firm's productive-capital once more, C £10, and this value once again enters the production process… P £10. If the output consisted of 90 kilos of yarn, then it would break down into 60 kilos (C), required to reproduce the cotton and labour-power consumed in its production, and 30 kilos (c) which constitutes a surplus product. The money equivalent of these would be £10 M plus £5 m.

The importance of this can be seen when considering not the M, but the m, the money equivalent of the surplus value. At its original price of £10 for 100 kilos of cotton, £5 would have bought 50 kilos of cotton, but it now buys 100 kilos. In other words, the rate of profit, the ratio of the surplus to the actual capital value required for its production, has risen, and it is for this reason that Marx bases his calculation for the rate of profit on the current reproduction cost of the capital, and not upon the historic prices paid for it.  It is this rate of profit Marx says he is referring to when discussing the Law of The Tendency for the Rate of Profit to Fall.

"{Incidentally, when speaking of the law of the falling rate of profit in the course of the development of capitalist production, we mean by profit, the total sum of surplus-value which is seized in the first place by the industrial capitalist, [irrespective of] how he may have to share this later with the money-lending capitalist (in the form of interest) and the landlord (in the form of rent). Thus here the rate of profit is equal to surplus-value divided by the capital outlay."

(Theories of Surplus Value, Chapter 16)

In terms of the total social capital, this rate of profit is equal to the profit margin, p/k, where p is the amount of profit, and k is the cost of production (c + v). In the same way that the rate of surplus value differs from the annual rate of surplus-value, as a consequence of the rate of turnover of the circulating capital, so too the rate of profit differs from the annual rate of profit. The more the rate of turnover of the total social capital increases, the more the annual rate of profit will tend to rise, whilst the rate of profit will tend to fall.

The average or general rate of profit is the annual rate of profit, not the rate of profit, and in Capital III, Marx even refers to it as the annual general rate of profit. For individual capitals whose rate of turnover is higher than the average, their annual rate of profit will tend to be higher than the average and vice versa, whilst their rate of profit, or profit margin will be lower than the average, for the same reason. I've described that elsewhere.

The average rate of profit is based upon the annual rate of profit of the total social capital, i.e. on the surplus value produced in a year, measured against the capital advanced during one turnover period. This determines the amount of profit to be added to the cost of production for each sphere, and thereby determines its price of production. This then determines the profit margin in that sphere, which necessarily differs from the average annual rate of profit.

“Take, for example, a capital of 500, of which 100 is fixed capital, and let 10% of this wear out during one turnover of the circulating capital of 400. Let the average profit for the period of turnover be 10%. In that case the cost-price of the product created during this turnover will be 10c for wear plus 400 (c + v) circulating capital = 410, and its price of production will be 410 cost-price plus (10% profit on 500) 50 = 460.”

(Capital III, Chapter 9)

This is clearly different than a price of production calculated as k + kp', which would be, 410 + (410 x 10%) = 41, giving a price of production of 451.

This is also important for the study of development economics, as Ken Tarbuck set out in his analysis of Bukharin's “Economics of the Transition Period”. An economy whose production is geared towards production where the rate of turnover of capital is higher than the global average will tend to have a higher annual general rate of profit, whilst its rate of profit will tend to be lower. Its lower profit margins will mean that its output is more globally competitive than other economies with a lower rate of turnover of capital.