Part Seven:—The Rate Of Profit

The first eight chapters of Volume 3 develop the implications of the theories outlined in Volumes 1 and 2. Friedrich Engels wrote this volume from notes that Marx had left before he died. However, it is certainly the case that he was far more than a mere editor. He wrote one important chapter in its entirety without the benefit of any notes left by Marx.

As I have indicated earlier Engels had a better grasp of Maths than Marx. In the early chapters of Volume 3 he enlisted the help of a Cambridge mathematician, Samuel Moore, to derive formulas from the theories developed in the first two volumes.

Changes in the Components of Value

The volume begins with a discussion of the components of a commodity's value: constant capital, variable capital and surplus value. The example that is used is of a commodity with a value of 600. This value consists of 400 constant capital, 100 variable capital and 100 surplus value. If the value of the constant capital increases by 200 the value of the commodity will also increase by 200 from 600 to 800.

The components of the commodity's value have now changed to 600c, 100v and 100s. An increase in the value of the constant capital is caused by a decline in the productivity of the industry which produces that item of constant capital. For instance, if the constant capital was wheat, the value of that product might increase if there was unfavourable weather in wheat producing areas resulting in more labour having been expended to produce a given quantity of that product. So the value of wheat will increase, but also those commodities which contain wheat, such as flour and bread, will increase in value.

However, a change in the value of variable capital will have no effect on the value of the commodity produced. This is because variable capital only represents what the capitalist pays for the commodity "labour power". While labour power is a cost to the capitalist its value, unlike the value of constant capital, is not transferred to the commodity produced. The costs of labour power or the costs of the means of subsistence required to keep the worker in a fit condition to work and reproduce a family are irrelevant in determining the value of the product that he produces. They are only relevant in determining the capitalist's profits. It is only through the use of labour power that value is added to a commodity.

A change in the value of variable capital or labour power will only affect the proportions of value allocated between the capitalists and the worker.

So, what is the effect of a change in the value of variable capital on a commodity with a value of 800, consisting of constant capital of 600 and variable capital and surplus of 100 each? If the variable capital is reduced from 100 to 80, the surplus value is increased to 120. Therefore the total value remains at 800 consisting of 600 in constant capital, 80 in variable capital and 120 in surplus value.

As indicated in Volume 1 a change in the value of variable capital can be caused by changes in the productivity of industries in which subsistence commodities are manufactured.

Rate of Profit and Surplus Value

In chapter 3 there is an analysis of the relationship between the rate of surplus value and the rate of profit.

The rate of surplus value is defined as surplus value divided by variable capital or s/v. Given the fact that all value is created by the worker, the rate of surplus value is equal to that proportion of the value created by the worker which is appropriated by the capitalist divided by that proportion held on to by the worker. Marx also called the rate of surplus value "the rate of exploitation".

The rate of profit is defined as surplus value divided by the sum of constant and variable capital or = s/(c + v). This could be defined as the return on the capitalist's costs.

The above formula indicates that other things being equal the greater the surplus value (s) the greater will be the rate of profit. On the other hand, if surplus value is held constant the greater the constant capital plus the variable capital figures, the less will be the rate of profit.

If we multiply the numerator and the denominator by "v" we are left with the following formula for the rate of profit:

(s/v).(v/(c + v))

Notice that the first part of the formula (s/v) is equal to the rate of surplus value. The second part of the formula (v/(c + v)) is equal to that proportion of total capital which is accounted for by variable capital or living labour. Marx referred to this as "the value composition of capital".

So the above formula indicates that the rate of profit is equal to the rate of surplus value multiplied by the value composition of capital. From this the following deductions can be made:

1) If the rate of surplus value is held constant, the percentage change in the value composition of capital will result in the same percentage change in the rate of profit.

2) If the value composition of capital remains constant, a change in the rate of surplus value will result in the same percentage change in the rate of profit.

The point of recasting the rate of profit in the above way is that Marx noticed two countervailing trends in the rate of profit as capitalism develops. On the one hand the proportion of living labour or variable capital in relation to total capital had a tendency to decline. This resulted in a declining rate of profit. On the other hand the countervailing tendency was for the rate of surplus value to increase, which would lead to an increase in the rate of profit.

Other deductions that can be made from the above formula are:

1) The rate of profit will rise or fall at a quicker rate than changes in the rate of surplus value if the value composition of capital changes in the same direction.

This is possible, but unlikely. It is more likely that the value composition of capital will move in the opposite direction to the rate of surplus value. The rate of surplus value usually increases as a result of increases in productivity, which usually involves a reduction in the value composition of capital (especially a greater use of constant capital). However, it is possible that a dramatic increase in productivity in the industries that produce the constant capital could reduce the value composition of capital despite a reduction in the value of variable capital.

2) The rate of profit rises or falls at a slower rate than the rate of surplus value if the value composition of capital changes in the opposite direction but at a slower rate.

This is quite probable. For instance, in an industry which does not increase its productivity, the rate of surplus value might rise as a result of an increase in the productivity of those industries which produce the means of subsistence of the workers.

To give an example, assume that in a given quantity of a product the surplus value is 50, the variable capital is 50 and the constant capital is 150. The rate of surplus value will be then equal to 100%. The value composition of capital will equal 25% (50/(150 + 50)) The rate of profit will therefore also equal 25%.

Now, if the variable capital drops by 20% to 40 the surplus value will increase to 60. The rate of surplus value will now equal 150% (60/40). The value composition of capital will drop to approximately 21% (40/(150 + 40)). The rate of profit will therefore increase to about 32% (150% by 21%). The increase in the rate of profit is about 28% (7/25) despite a 50% increase in the rate of surplus value.

3) The rate of profit rises or falls in the opposite direction to the rate of surplus value if the value composition of capital changes inversely at a faster rate.

This scenario is by no means unlikely. For example, it is quite probable that an increase in the rate of surplus value will result in a greater decline in the value composition of capital, which in turn will result in a decline in the rate of profit.

This is because an increase in the rate of surplus value is often associated with an increase in the productivity of labour. Such an increase usually involves each unit of labour using more inputs in a given time to produce more outputs. In other words the value of constant capital increases as a proportion of the total capital.

Let us return to some of the same figures used in part 2 above. But we will also assume that the constant capital element changes from 150 to 360. In this case the value composition of capital will be reduced to 10% (40/(360 + 40)). The rate of profit will decline from 25% to 15% (150% by 10%) despite an increase in the rate of surplus value of 50%.

4) The rate of profit will remain constant if the rate of surplus value changes and the value composition of capital changes inversely and in the same proportion.

This is a compromise between parts 2 and 3. Using the same figures as in part 2 above, if the constant capital increases from 150 to 200, the value composition of capital will be reduced to 16.67%. By multiplying the increased rate of surplus value (150%) by the reduced value composition of capital (16.67%) you arrive at the same rate of profit figure (25%) as you started with.

This is because the rate of surplus value figure has increased by 150% and the value composition figure has been reduced by 1/150%.

Rate of Profit Revisited

In the above calculations the unstated assumption is that the number of turnovers of capital in a year is one. The other unstated assumption is that the fixed capital is zero. As I have indicated in previous instalments Marx was quite weak on the topics of turnover of capital and fixed capital. Chapter 4, which was completely written by Engels sets out to look at the effects of more than one turnover of capital and of fixed capital not equal to zero.

Engels starts this important chapter by giving very straightforward examples of two capitals with different turnovers. Capital A is composed of 80c + 20v = 100. It has two turnovers a year and a rate of surplus value equal to 100%. Its total product for the year is obtained by multiplying by 2 (the number of turnovers). So this amounts to 160c + 40v + 40s = 240. Engels then makes the point that the rate of profit is not equal to 40 divided by the capital of the annual product (i.e. 160c + 40v = 200). The rate of profit should be calculated on the advanced capital of 100 (80 + 20). This is because after one turnover of capital the capitalist receives his money back. So his maximum capital outlay at any one time is 100, which is reached at the point of time just before he receives his money for his product. Therefore the rate of profit is equal to 40%.

The other example he gives is of capital composed of 160c + 40v + 40s = 240. But unlike the previous example the turnover of this capital is one. This means that it has to have a capital outlay of 200. Therefore, the rate of profit on this capital is indeed 40/200 equalling 20%.

After giving these examples, Engels introduces examples of capital, which include fixed Capital. As I have indicated in the previous instalment, Marx tended to ignore this important element of production.
In the first example he gives, "Capital 1" consists of 10,000 in fixed capital with an annual depreciation of 10% or 1,000 per annum. The circulating constant capital is 500 and the variable capital is 500. The variable and constant capital turnover 10 times a year and the surplus value is equal to 100% of the variable capital.

Engels says that the product of one turnover is:

100c (depreciation) + 500c + 500v + 500s = 1,600

This is correct. He then sayss that the product of one entire year, with ten turnovers is:

1,000c (depreciation) + 5,000c + 5,000v + 5,000s = 16,000

Again, this is correct. He then says without explanation the following:

C = 11,000, s = 5,000 therefore the rate of profit = 5,000/11,000 or 45.5%.

Most people reading this would assume that the C = 11,000 is obtained by adding the 1000c, 5000c and 5000v figures of total annual output. In fact it is a pure "coincidence" that these figures happen to add up to 11,000. The "C" or capital outlay figure is, actually, obtained by adding the fixed capital figure (10,000) to the capital outlay figure of one turnover (i.e. 500c + 500v). In general the figures will not be the same.

In his second example he gives, the sum of the depreciation, constant capital and variable capital of annual output and again they "just happen" to equal the capital outlay.

The third example has only one turnover in capital and no fixed capital.

It is almost as if Engels is trying to imply that the flaws in Marx's analysis regarding turnover of capital and fixed capital are of no account. Following these examples there is a longwinded analysis of variable capital and then he finishes the chapter by giving a final example.

In this example, the figures are presented in a slightly different way and Engels is much more explicit in how he arrives at the calculation of the rate of profit. The fixed capital figure is equal to 10,000. He then gives the circulating capital figure, which he says is 2,500. The value of the weekly product is:

20c (depreciation) + 358c + 52v + 80s = 510

He then reasons that the weekly capital outlay is 410 (358 + 52). The depreciation element (20c) is not a cash cost and therefore is not part of the capital outlay.

The 358 in constant capital represents 87.3% of the total weekly capital outlay (410) and the variable capital of 52 represents the remaining 12.7%. Given that we know that the entire circulating capital outlay is 2,500, the proportion of this accounted for by constant capital is 2,182 (87.3% of 2,500) and 318 in variable capital.

Engels then calculates that the total annual expenditure of variable capital is 2,704. Since the variable capital proportion of the circulating capital outlay is 318, the number of times the capital turns over in a year is 8.5 times or 2,704 divided by 318. The rate of surplus value is 153.8% or 80 divided by 52. Finally the capital outlay figure is arrived at by adding the fixed capital figure to the circulating capital figure.

We now have all the elements of the rate of profit calculation which is equal to:

(s/v).n.v/C

Where "s/v" is the rate of surplus value, "n" is the number of turnovers of capital in a year, "v" is the variable capital component in one turnover and "C" is the capital outlay required in a year. This differs from the previous formula of Marx by including "n" or the number of turnovers in a year. Also, the "C" element represents the capital outlay rather than the sum of constant capital and variable capital contained in the value of the commodity.

Putting the figures in the formula we obtain the following:

153.8% x 8.5 x 318/(12,500) = 33.3%

But this formula is a rather longwinded way of arriving at the rate of profit. Presumably, Engels uses it to illustrate the relationship between the rate of surplus value and the rate of profit. As Engels himself indicates, a more straightforward method of arriving at the rate of profit is by calculating the annual profit which is 4,160 and dividing it by the capital outlay (12,500) giving the same answer of 33.3%.

Interestingly, unlike in the first three examples of the chapter, Engels does not calculate the components of the total product in the year. This can be done very easily by multiplying the components of the total weekly product by 52 weeks to arrive at the following annual figures:

1,040c (depreciation) + 18,616c + 2,704v + 4,160s = 26,520

The total constant capital contained in the total product is equal to 19,656. When this is added to the variable capital of 2,704 a figure of 22,360 is arrived at for the c + v part of Marx's formula. Obviously, this does not equal the capital outlay figure which Engels arrived at in his calculations for this example. The fact that the annual capital outlay figure equalled the c + v figure for the annual product in the first two examples that Engels gave in chapter 4 was a pure "coincidence". The only time the c + v figure always equals the capital outlay figure is when there is no fixed capital and the number of turnovers of capital in a year is equal to one.

Engels understood far better than Marx, that capitalists are interested in not how much capital is contained in the value of a product, but how much capital is tied up in production to generate a given level of profit. For example, a very small percentage, if indeed any, of the value of a factory building is transferred to the value of the products produced within the factory. Arguably the factory does not depreciate in value at all. But the value of the factory building might represent a huge capital commitment on behalf of the capitalist. In calculating his rate of profit from operating the factory he might well decide that he would obtain a greater return on his capital by closing the factory, selling it to a property developer and putting the money in the bank!

Return on Capital Employed

Engels calculation is very similar to the "return on capital employed" calculation which is well known to modern accountants. However, Engels as he acknowledges, assumed that there were no credit transactions. A modern businessman would take account of the capital he has tied up in debtors or money that is owed to him by customers. The money he owes to creditors helps him finance his business and is deducted from his capital outlay. In some businesses the difference between the debtors figure in the balance sheet and the creditors figure may not be that large. In this instance, one figure offsets the other.

Engels's calculation of the outlay on circulating capital is not that dissimilar to the outlay that a businessman would calculate that he has made on "work in progress" stock. However, Engels assumed that the full amount of capital necessary to produce one cycle of production is tied up at all times. For example if it takes four weeks to produce a product with a capital outlay of 10,000 Engels would say that the capital outlay is 10,000. But it is possible that this capital is not spent at the beginning of the production cycle. The expenditure could be spread equally throughout the period. So, after week one 2,500 is spent and after week two the amount is 5,000. It is only at the end of week four that the full 10,000 has been spent. Using this logic the average capital outlay on work in progress is half the total of 10,000, which is equal to 5,000.

To some extent this is pedantic. Even if the capitalist does not need the 10,000 immediately he will need to have short term access to this amount. This might be reflected by cash in the current or "short term" assets section of his balance sheet. Such cash is unlikely to earn much interest because it is needed on a short term basis.

Another minor criticism is that while Engels has rightly excluded depreciation from the capital outlay figure because it is not an extra cash cost and fixed capital is already included in the capital outlay figure, there is an argument that it should be added back to the profit figure. This argument is similar to the one about "work in progress" above. However, it is stronger because it may take many years for a machine to be replaced. The capitalist will therefore be able to use the value represented by the depreciation of the machine for other purposes. He may not even have to consider spending money on a new machine until the old machine is near to the end of its useful life.

It is now quite common to see in the financial statements of companies a figure for "EBITDA". This is known as Earnings (or Profits) Before Interest, Tax, Depreciation and Amortisation. It is felt that this gives a better understanding of the operations of a company and is more meaningful as the numerator in the "Return on Capital Employed" calculation than the "profits" figure.

Stocks and Flows

A slightly more serious criticism is that Engels did not consider the effects of stocks of finished goods or raw materials on the capital outlay. Marx and Engels were aware that not all finished goods were sold immediately and that raw materials which were bought by the capitalists were not immediately used in production. Their analysis in Volume 2 indicates that they understood that this represented a problem for capitalists, but they were unable to incorporate this in their calculations of capital outlay and rate of profit.

The problem with their analysis is that they did not appear to understand the difference between "stocks" and "flows" as applied to a business.

These concepts are often explained by an analogy. Water "flows" into a basin from a tap. The water going into the basin is an "inflow". The amount of water in the basin is a "stock". If the basin has a hole in it there will be an "outflow" of water. If the "outflow" exceeds the "inflow" the stock of water in the basin will diminish. On the other hand if the "inflow" exceeds the "outflow" the "stock" in the basin will rise.

In a business, expenditure on purchases of raw materials represents a "flow". The resulting build up of raw materials represents a "stock". The "stock" of raw materials is reduced by their transfer to the "flow" of production. The "flow" of production increases the "stock" of finished goods and the "flow" of sales reduces the stock of finished goods.

In Volume 2 Marx indicated that the time between the completion of the finished goods and the purchase of new raw materials to begin a new production cycle was the "Circulation time". This period included:

a) The length of time the goods were in the warehouse waiting to be sold.
b) The time it took to transfer the goods to the market place.
c) The time it took the customer to pay (if credit was offered).
d) The time it took to buy the raw materials to start a new cycle.
e) The time it took for the raw materials to be transferred to production.

He calls the time taken to produce the goods the "Production time".

Marx was aware that the longer the "Production Time" and "Circulation Time" the lower the number of turnovers of capital. Engels was aware that "Production time" was more important than "Circulation time" in this calculation because production could continue and overlap "Circulation time" (see part 5 of this series).

However there was no analysis of the capital outlay which is required during the "Production time" and "Circulation time". The longer the "Production time", the greater will be the stock of "work in progress". The longer it takes to sell the product, the greater will be the build up of "finished goods" stock. A requirement to guarantee continuity in production might necessitate large stocks of "raw materials". All of these stocks are part of the capital outlay or "working capital" requirements of a business.

If we assume credit transactions, the longer it takes customers to pay for the goods the greater will be the "debtors" figure in the balance sheet. If the business receives credit the "creditors" figure can be deducted from the debtors figure in calculating capital outlay.

Conclusion

While there are limitations in the analysis of Engels in relation to capital outlay, he was able to grasp the essential point, which is that it represents capital that is tied up in the production of commodities. In a subsequent instalment we will examine the important role that profit divided by capital outlay or the "rate of profit" has in the functioning of the capitalist system.

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