In Capital III, Marx explains it, in terms of a piece of string, cut into three parts, being the equivalent of constant capital, wages and profits. Marx's theory, in contrast to the cost of production theory, says that the value of the commodity (length of string) is determined by the labour-time required for its production. In essence this divides into two components, the constant capital, and the current labour. If the commodity is yarn, its value might be 10 hours for cotton, used as raw material, and 20 hours of labour to process it into yarn, so the value of the yarn is equal to 30 hours.
If the value of cotton rises to 12 hours, then this is, indeed, now a component of the labour required for the production of yarn, so its value rises to 32 hours. If the yarn producer had bought cotton the before the rise in its value, they would still sell yarn at a value equal to 32 hours, giving the illusion of having made an additional 2 hours profit, and higher rate of profit. This is what confuses those that operate on the basis of historic prices, and a cost of production theory, such as Ramsay or the TSSI. Marx explains it in respect of Ramsay in Theories of Surplus Value, Chapter 22, and in general in Capital III, Chapters 6 and 47.
In fact, as soon as we adopt Marx's method, and see production as continuous, rather than divided into discrete time periods, the illusion is shattered. The yarn producer must replace the consumed cotton, and the price they must, now, pay to do so, is equal to 12 hours, not 10. So, immediately, the additional 2 hours of what appeared as profit, but was only capital gain, is used up, just to replace the consumed cotton. This is one difference between forming the value of the commodity, based on its components, as against looking at how the value of the commodity must be resolved into those components, so as to reproduce it. If the current labour required to process the cotton into yarn divided into 12 hours wages and 8 hours profit, then, previously the rate of profit (s/(c + v)), was 8/(10 + 12) = 8/22. But, now, it is 8/24, because a larger proportion of the value resolves into the fund required to replace the consumed constant capital (cotton).
The importance of the rate of profit is as a measure of the extent to which capital has expanded, and can be accumulated. Because the value of cotton has risen, and the rate of profit fallen, the extent to which capital can be accumulated has fallen. Less additional cotton can be bought, and so less additional labour can be employed to process it into yarn. In term of the analogy of the string, we now have to compare a piece of string of 30 centimetres with one of 32 centimetres. In the former cotton comprised 10/30, wages 12/30, and profit 8/30. But, now, c = 12/32, wages 12/32, and profit 8/32. The relative proportion of c has risen, and that of wages and profit fallen. This is a rise in the value composition of capital.
Now, suppose that instead of the value of cotton rising, the value of labour-power rises. That is the value of the food, etc. the worker requires rises, from 12 hours to 15 hours. The value of the yarn does not rise from 30 hours to 33 hours, as a result. The value of cotton remains 10 hours, and 20 hours of labour is required to process it into yarn, so that the value remains 30 hours. However, of this 30 hours (30 centimetres of string) 10 is resolved into the reproduction of constant capital (cotton), 15 is resolved into the reproduction of labour-power, and only 5 is, now, resolved, into profit, so that the amount and rate of profit falls. This is a consequence of a fall in the rate of surplus value.
A cost of production theory of value would, rather, conclude that the value of the commodity rises to 33 hours, being comprised of 10,15 and 8, and its this which forms the basis of cost-push theories of inflation. In practice, as I have set out, elsewhere, central banks, in order to protect profits from a wage squeeze, increase liquidity – in an economic uptrend, additional liquidity arises, also, automatically, from increased commercial credit between companies – which devalues the standard of prices, so that firms can, indeed, raise money prices, even though values have not risen. But, this simply creates a price-wage spiral, because, now, the money prices of wage goods rise, meaning that, if real wages are not to fall – and in times of high demand for labour, they will tend not to – money wages must rise, and so on. In conditions of tight labour markets, money wages will always rise to ensure that real wages do not fall, even if there are lags and leads between the rise in prices, and money wages.
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