The basis of Marx's law is this. A period of intensive accumulation is initiated, because existing supplies of labour-power have started to be used up, causing wages to rise, and the rate of surplus value to fall, which causes a squeeze on profits. This squeeze on profits is the Smithian explanation of the Law of a falling rate of profit. In fact, the intensive accumulation is a response to it, and it is the intensive accumulation, which provides the basis for Marx's Law of the Tendency for the Rate of Profit to Fall. This period of intensive accumulation sees newer labour-saving machines introduced, to replace the existing machines. Each of these newer machines, thereby replaces several of the older machines. This is also the basis for not only the proportion of labour in total output falling, but also the proportion attributable to fixed capital falling, in total output. As Marx says, in Capital III, Chapter 15,
“While the circulating part of constant capital, such as raw materials, etc., continually increases its mass in proportion to the productivity of labour, this is not the case with fixed capital, such as buildings, machinery, and lighting and heating facilities, etc. Although in absolute terms a machine becomes dearer with the growth of its bodily mass, it becomes relatively cheaper. If five labourers produce ten times as much of a commodity as before, this does not increase the outlay for fixed capital ten-fold; although the value of this part of constant capital increases with the development of the productiveness, it does not by any means increase in the same proportion. We have frequently pointed out the difference in the ratio of constant to variable capital as expressed in the fall of the rate of profit, and the difference in the same ratio as expressed in relation to the individual commodity and its price with the development of the productivity of labour.”
In this context, the proportion of total value accounted for by fixed capital falls for two reasons. Firstly, the rise in productivity reduces the value of the machine itself, as a consequence of moral depreciation. Either greater productivity enables the machine itself to be produced with less labour, or else a new more productive machine is introduced, which requires only the same amount of labour to produce. Secondly, the more advanced machine produces a much larger volume of output, so that its value is spread across this larger quantity, and thereby diminished, whilst the amount of material processed by the machine and the labour increases.
Suppose a current machine costs £1,000, and lasts for a year. In a factory, ten of these machines are employed, and ten workers operate them. The workers are each paid £1,000 in wages, and the rate of surplus value is 100%. They process 10,000 kilos of yarn each, with a value of £6,000 into 10,000 metres of cloth. For the factory's output, we then have:-
Machines £10,000
Materials £60,000
Wages £10,000
Surplus Value £10,000.
The rate of profit is 1/8 = 12.5%. The price per metre is £90,000/100,000 = £0.90. The proportion of fixed capital of total output is 1/9 = 11.1%, or £0.10 per metre. Materials account for 6/9 of total output value = 66.6%, or £0.60 per metre. Wages accounts for 11.1% of total output value, or £0.10 per metre, and the same for profit.
Now, assume that a new machine is introduced that costs £1,000, but processes 50% more yarn. Now we have,
Machines £10,000
Materials £90,000
Wages £10,000
Surplus Value £10,000
Total output rises to 150,000 metres. The value per metre falls to 120/150 = £0.80. The proportion of fixed capital in total output value falls to 1/12 = 8.33%, or £0.067 per metre. The proportion of wages in total output value, and of surplus value in total output value similarly falls to 8.33%, or £0.67 per metre. However, the proportion of total output value accounted for by materials rises to 90/120 = 75%, or £0.60 per metre. The rate of profit falls to 10/110 = 9.09%.
This is the basis of Marx's Law of the Tendency for the Rate of Profit to Fall. In Chapter 14 of Capital III, Marx sets out a number of countervailing forces that operate against this law. If the rise in social productivity reduces the value of materials, for example, this will reduce the value of the circulating constant capital, and thereby raise the rate of profit. For example, suppose the value of yarn fell from £0.60 per kilo to £0.50 per kilo. We would then have,
Machines £10,000
Materials £75,000
Wages £10,000
Surplus Value £10,000
The rate of profit would then be 10/95 = 10.53%. But, the value of yarn would have to fall by more than 50%, before the result was that the rate of profit rose.
Similarly, the rise in social productivity reduces the value of labour-power, and thereby raises the rate of surplus value, which acts to raise the rate of profit. Suppose, wages fell to £8,000, so that profit rises to £12,000. Using this last example, the rate of profit would then be 12/93 = 12.90%.
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