“The total labour power of society […] is embodied in the sum total of the values”
Marx – the Capital Book I : I.1
“The reproduction of a mass of labour power, which must incessantly re-incorporate itself with capital for that capital’s self-expansion; which cannot get free from capital, and whose enslavement to capital is only concealed by the variety of individual capitalists to whom it sells itself, this reproduction of labour power forms, in fact, an essential of the reproduction of capital itself. Accumulation of capital is, therefore, increase of the proletariat.”
(enphasis added) K. Marx – the Capital Book I: XXV.I
But:
“Now we have seen that it is a law of capitalist production that its development is attended by a relative decrease of variable in relation to constant capital, and consequently to the total capital set in motion. This is just another way of saying that owing to the distinctive methods of production developing in the capitalist system the same number of labourers, i.e., the same quantity of labour-power set in motion by a variable capital of a given value, operate, work up and productively consume in the same time span an ever-increasing quantity of means of labour, machinery and fixed capital of all sorts, raw and auxiliary materials — and consequently a constant capital of an ever-increasing value.”
MIA: K. Marx – the Capital – Book III (13)
Chapter 13 of Book III of Capital contradicts chapters 1 and 25 of Book I of Capital, which define the value on the one hand, and the value composition of Capital on the other hand. The quantitative increase in “means of labour, machinery and fixed capital of all sorts, raw and auxiliary materials”, non-human material resources, has nothing to do with the value of capital, which depends exclusively on the quantity of labor, human resources, which is incorporated therein. A quantitative increase in the material incorporated in capital can be determined by the increase in productivity without an increase in labor, and therefore without an increase in value. As stated in Book I: “Accumulation of capital is, therefore, increase of the proletariat”.
(Addendum 2021-09-08: Reread, one hundred times reread the definitions of the technical, value and organic composition of capital in chapter 25 of book I of Capital, and don’t trust the English translation.)
There is therefore no economic tendency of the rate of profit to fall, according to Book I of Capital.
The contradiction between Book I and Book III of Capital is explained by the fact that Books II and III are a compilation of the drafts of Marx by Engels, while Book I is a completed work.
Thus, Book III of Capital employs an older conception of value than Book I. In Book I, capital is measured in quantity of labor, while in Book III, Capital is still represented in the form of an accumulation of material things. It goes without saying that these measures are totally different, and cannot be combined in the same calculation as if they had the same unit.
There are, and there will be, however, two distinct declines in the rate of profit of capital, one measured in quantities of labor, the other measured in material quantities, but for reasons different from those described in chapter 13 of book III of the Capital.
There is currently a decline in the rate of profit measured in quantity of work, due to the slowdown in world population growth, and therefore ultimately in the part of the population that creates value.
There will soon be a drop in the rate of profit measured in material quantities, due to the depletion of natural resources and the destruction of the environment by capitalism. This material “rate of profit” could turn negative. The accumulation of material capital could turn negative for other reasons: economic crisis, catastrophic management of an epidemic or world war.
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The Capital is not a bible. Marxists must not have the fetishism of the tendency of the rate of profit to fall.
Book I is a completed treatise on economics, with precise definitions and a precise use of measure and units. It has been the subject of several revisions and translations carried out and verified by Marx himself, so that the latest editions, particularly German and French, must be considered as the final version of Book I.
Books II and III are drafts compiled with maximum rigor by Engels. They enlighten us on the evolution of Marx’s thought, and inform us about many elements that should have been included in the Capital. But they are incomplete and often contradictory with Book I. When a contradiction is raised, it must be understood and clarified.
All economic reasoning must be tested in the data of econometrics. Speculative reasoning without econometric confrontation is worthless because it is non-materialist.
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Particular attention must be paid to measurement and units. The measure is the magnitude of a property of an object: for example its length or its mass. A unit is a standard whose multiplication and fraction give the measure, for example the meter or the kilogram.
Some units are concrete, others abstract. The concrete hour of work is, for example, a concrete unit of measurement, but it has the defect of being heterogeneous: an hour of concrete work is never quite identical to another hour of concrete work, and completely different in different economic sectors.
The abstract work year is an abstract unit of measurement, but it is homogeneous: the work year of an abstract worker is always equal to another year of work by an abstract worker. This is a simple average from the total sum of a year of work for all concrete workers.
Be careful, however, to the measurement of value in the quantity of labor, because the quantity of labor necessary for the production of a certain quantity of goods is not the same according to the place and the moment. The working year of an average worker must therefore always be defined according to the place (for example: “World”), and the moment (for example: “2019”).