Marx quotes Mill's statement that,
““The only expression of the law of profits … is, that they depend on the cost of production of wages” (loc. cit., pp. 104-05).” (p 228)
This is a basic Ricardian proposition, equating the rate of profit with the rate of surplus value. But, it is only true where the only capital advanced is that laid out in wages. Only if any materials or other means of production, that enter the production process, are not the product of labour would that be the case. But, as Marx previously demonstrated, with Adam Smith's example of the Scottish pebble collectors, virtually nowhere in capitalist production does such a condition apply. There are plenty of materials provided free by nature, which, thereby, also contribute to social wealth, (use value) but in every case, constant capital is required to transform them into products/commodities. Fish need to be caught, which requires nets etc., as well as the labour of the fishermen. Minerals are provided free by nature, but require mining equipment, as well as labour to extract them from the ground. What is true about these free gifts of nature, and makes them different to the raw materials used in manufacture, is that, because the former have no value, the increase in productivity that developing technology brings, does not result in a rise in the proportion of raw material value in output that exists in the latter, and is the mechanism for the law of the tendency for the rate of profit to fall.
This is significant, for reasons I have set out elsewhere. Suppose that industry would prefer to use coal rather than wood to generate energy. However, the price of coal makes such use unprofitable. Assume that with existing technology, it would require 1,000 workers, working a 10 hour day, each paid £10 in wages, to dig 100 tons of coal. The price per ton, assuming a 100% rate of surplus value, is £200, and, at this price there is no demand, so no capital is employed, and no workers are employed. The £10,000 profit, is then only theoretical. But, if a new technology is developed, which enables the 1,000 workers to produce 100,000 tons, this situation changes. If the new technology costs £50,000, and lasts for 10 years, so that it amounts to a cost of production of £5,000 p.a. (wear and tear) the cost of production is £5,000 + £10,000 = £15,000. If the rate of surplus value remains 100%, so that the profit is £10,000, the price of the coal is now only £25 per ton. At this price, there is an adequate demand for the coal, and so the capital is advanced, the workers are employed, and the £10,000 of profit is no longer theoretical, but real, and available to accumulate additional capital.
The rate of profit here is 10/15 = 66.66%, and the annual rate of profit is 10/60 = 16.66%. That is less than the theoretical 100% rate of profit that existed prior to the development of the new technology, but has the advantage of being real rather than theoretical. The rate of profit is equal to the ratio of the surplus value, s, to the total capital advanced, C, assuming the advanced capital turns over once during the year, i.e. s/C. Put another way, it is equal to the profit p as a proportion of the cost of production (c + v), or k, so p/k, which is also the formula for the profit margin.
“This ratio is determined not only by the size of S [and all the factors which determine the production cost of wages enter into the determination of S] but also by the size of C. But C, the total value of the capital advanced, consists of the constant capital, c, and the variable capital, v (laid out in wages). The rate of profit is therefore S : (v+c)=S:C.” (p 229)
But, S is not only determined by the rate of surplus value. It also depends upon the number of labourers simultaneously exploited. The rate of surplus value is always equal to the relation of unpaid labour to paid labour, in a working-day. If a working-day is 12 hours, and 2 hours constitute surplus labour, then the rate of surplus value is 2:10 = 20%. However, that does not determine what the mass of surplus value is, because that depends on the number of workers employed. If 10 workers are employed then 10 x 2 hours = 20 hours of surplus value, whereas if 100 workers are employed 100 x 2 = 200 hours of surplus value is produced.
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