3) s' and v constant, c and therefore C variable.
The formula, p' = s' v/C, cannot apply here because C and p' are no longer constant. It must be p1' = s' v/C'. The relation of p1' to p' then reduces down to p1':p' = C:C'. in other words, the rate of profit varies in inverse proportion to the change in the total capital.
“Should we, for example, have three capitals, or three different conditions of the same capital:
I. 80c + 20v + 20s; C = 100, s' = 100%, p' = 20%;
II. 100c + 20v + 20s; C = 120, s' = 100%, p' = 16⅔%;
III. 60C + 20v + 20s; C = 80, s' = 100%, p' = 25%.
Then we obtain the proportions:
20% : 16⅔% = 120 : 100 and 20% : 25% = 80 : 100.” (p 59-60)
Because the variable capital is held constant, any change in C has to come about as a result of a change in c. If c fell to zero, so that only variable capital was employed, (which can't happen) then the rate of profit would be equal to the rate of surplus value. So, that forms the maximum limit. Any rise in c, therefore, results in a lower rate of profit.
This, of course, is a fundamental element in the falling rate of profit. As any capital expands, then, as shown in Volume I, the tendency will be for the constant capital to expand relative to the variable capital. That is because what today would be called economies of scale, mean that the advantages of the division of labour, and co-operative power of labour, raise its productivity, so a given amount processes more material in a given amount of time. Moreover, as machine industry develops, so the tendency is for newer machines to be more productive, and thereby to replace increasing amounts of labour-power, whilst the volume of material (circulating constant capital) processed, rises significantly.
So, the conclusion from this, derived from the above formula, is that the rate of profit must fall. But, of course, as we will see later, Marx provides a whole series of countervailing tendencies, that necessarily also flow from this process, which will mollify if not nullify this tendency. More importantly, this tendency at best can only apply to the increasing size of an individual capital. As new businesses are being started all the time, in new industries, with capital drawn from old areas of production, all of these new industries can, and usually will, have low organic compositions of capital, and high rates of profit.
In addition, this tendency applies to the “Rate of Profit” as defined above (s/C), which is the same as p/k or profit over cost price. Later Marx identifies other definitions of the “Rate of Profit”, which take into consideration the change in the rate of turnover (Annual Rate of Profit), brought about by the same changes in productivity that cause the organic composition of capital to rise. Consequently, there is no reason why a law, which operates in respect of an individual capital should have any specific importance for the economy as a whole, other than it will tend to go through phases when few new businesses are being created (Falling Rate of Profit), and other periods when lots of new businesses are being created (Rising Rate of Profit), as well as periods when the rate of turnover is rising more quickly, and the Annual Rate of Profit will rise along with it, and others periods when the rate of turnover is rising more slowly.
“The alteration of c may be due either to a mere change in the value of the material elements of constant capital, or to a change in the technical composition of the total capital, that is, a change in the productivity of labour in the given branch of industry.” (p 60)
Which, of course, means, in either case, that the condition of constant productivity is breached. If the value of the constant capital has fallen that must be because productivity has risen, so less labour-time is required for its production.
“In the latter case, the productivity of social labour mounting due to the development of modern industry and large-scale agriculture would bring about a transition (in the above illustration) in the sequence from III to I and from I to II.” (p 60)
But, in that case, this rise in the productivity of social labour inevitably means that the rate of surplus value, s', rises, which breaches the requirements of this example. As Marx set out in Volume I, if this is a single capital, this does not simply mean an increase in relative surplus value, as the higher productivity reduces the value of labour-power. Any individual capital that benefited from such higher levels of productivity would obtain higher levels of surplus value, because it would be as if its labour were complex labour, i.e. treated as a multiple of the same labour employed by other capitals. But, unlike where complex labour is employed, the firm would enjoy a higher rate of surplus value, because the labour-power itself would not have any different value than that employed by other capitals.
“A quantity of labour which is paid with 20 and produces a value of 40 would first utilise means of labour to a value of 60; if productivity mounted and the value remained the same, the used up means of labour would rise first to 80, and then to 100.” (p 60)
But, of course, if productivity mounted in general, rather than just in relation to this particular type of labour, the value of the constant capital would not remain the same. In fact, if the productivity of this particular labour increased, its difficult to see how this comes about other than via the introduction of new, more productive fixed capital, machines etc. That means moral depreciation of fixed capital occurs.
“An inversion of this sequence would imply a decrease in productivity. The same quantity of labour would put a smaller quantity of means of production into motion and the operation would be curtailed, as may occur in agriculture, mining, etc.” (p 60)
But, more likely is that as a mine becomes less productive, greater quantities of constant capital are required to compensate. Digging coal from greater depths may require no more miners, but may require the introduction of steam engines for pumping out water etc.
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