The rate of profit, as Marx has demonstrated, can fall for various reasons. It can fall because the value of the commodities that comprise constant capital rises, because, for example, less fertile land has to be cultivated, or mines operated. A greater proportion of available social labour-time, of current production, must go simply to reproduce, in kind, the consumed means of production. As described in Capital III, it could be just that the market price of those means of production rises, because the supply cannot be increased to meet the demand. The effect is the same as if the value of the constant capital had risen. Or, it could be that the rate of profit falls because the rate of surplus value falls. That could be because the value of labour-power rises, or just because wages rise, as the demand for labour-power exceeds the supply.
All of these are potential, and actual causes of a fall in the rate of profit. Each has been used, prior to Marx, as an explanation for the tendency for the rate of profit to fall. But, Marx shows that none of them are the cause of that tendency. They all cause the rate of profit to fall during specific periods, but capital always responds to those causes, so as to reverse the cause. New technological developments reduce the value of the fixed capital stock, via moral depreciation; that also causes higher social productivity, which alongside the development of new lands, mines etc., causes the value of materials to fall; it also brings about labour-saving technologies that creates a relative surplus population, which causes wages to fall, and the rate of surplus value to rise, and so on.
Marx has shown that the real basis of that tendency is not any of these short term causes of a falling rate of profit, that all essentially amount to a fall in productivity, and fall in the rate of surplus value, but is the opposite. It, in fact, arises from the measures that capital introduces to overcome these causes of short-term falls in the rate of profit. Rather than being caused by falling productivity, and a fall in the rate of surplus value, it arises from rising social productivity, and a rising rate of surplus value, along with an increase in the mass of surplus value.
“[The rate of] profit falls not because the worker is exploited less, but because altogether less labour is employed in relation to the capital employed.” (p 302)
It is this which means that more material is processed by a given quantity of labour, so that the organic composition of capital rises, and it is this which creates the long term tendency for the rate of profit to fall.
“It comes to the same thing if I say that one worker is employed for a capital outlay of 50 in the one case, and one worker for a capital outlay of 100 in the other, that therefore only half the number of workers is employed by a capital of 50; in other words, if I say that in one case there is one worker for 50 capital and only half a worker for 50 capital in the other, or if I say that in one case 50 capital is used by one worker and in the other case 50 x 2 capital is used by one worker.
This latter formula is the one used by Hodgskin and others.” (p 303)
Because Hodgskin uses this latter formula, however, it necessarily leads to the logical fallacy I described earlier. By concentrating on the individual worker, with the amount of capital backing them accumulating on a compound basis, it is obvious that not only are there limits to how much absolute surplus value can be produced, but there are limits to how much relative surplus value can be produced too. For any one worker, there are only 24 hours in a day, and not all of them can comprise surplus value. However, as I described earlier, this does not apply to the collective labourer, and the social working-day. The social working day can be expanded not only by extending the individual working day, but also by increasing the number of workers simultaneously employed. Moreover, as I've pointed out elsewhere, although there are only 24 hours, maximum, of concrete labour in a day, for any worker, that is not the case for abstract labour.
If the labour of a surgeon is complex labour, which produces say 10 times as much value in a day as that of an unskilled labourer, then, for the surgeon, there are the equivalent of 240 hours in a day, so that, even if their necessary labour comprises 60 hours, and they actually only work for 10 hours (100 hours simple), they would produce a surplus value of 40 hours per day. So, a society that is increasingly able to produce its basic needs, with a declining proportion of the available workforce, can increase the proportion of the workforce that comprises this higher value, complex labour, and for whom the previous limits of the working-day do not apply.
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