Marx is here preparing the ground for the later critique of Ricardo's false theory of the law of a falling rate of profit.
“The method of production remains the same. There is a change in the ratio of constant to variable capital, while their relative volume [in physical units] remains the same (so that each of them forms the same proportion of the total capital as before). This change in their ratio is caused by a change in the value of the commodities which enter into constant or variable capital.” (p 381)
In other words, the technical composition of capital remains the same, but the value composition changes. As Marx says, in Capital III, Chapter 6, it doesn't matter here whether this change is reflecting an actual change in the values of these commodities, or whether it is merely a question of a change in prices. For example, during the US Civil War, cotton supplies to Britain were cut off, sending the price of cotton much higher, which thereby raised the value composition of capital in textile production. The same arises where the demand for an input rises faster than the supply can rise to meet it.
Similarly, if the price of an input such as raw material, in the case cited by Ricardo, rises as a result of a tax, this raises the value composition of the capital, which acts to reduce the rate of profit.
Marx sets out four scenarios covering this situation of a rise in the value composition of capital.
“[1.] The value of the constant capital remains the same while that of the variable capital rises or falls. This would always affect the surplus-value, and thereby the rate of profit.
[2.] The value of the variable capital remains the same while that of the constant rises or falls. Then the rate of profit would fall in the first case and rise in the second.
[3.] If both fall simultaneously, but in different proportions, then the one has always risen or fallen as compared with the other.” (p 381)
In the fourth scenario, the value of the constant and variable capital changes equally.
In the first scenario, where the value of constant capital remains the same, but the variable capital changes, the rate of profit changes because the surplus value changes. If the variable capital rises, but the rate of surplus value remains the same or rises, implying more labour is employed, the mass of surplus value must rise. If the variable capital rises, because the value of labour-power/wages rise, the rate of surplus value falls, and so the mass of surplus value must fall, and so the rate of profit.
The second scenario is self-explanatory. If c rises then c + v rises, whilst s remains constant, so s/(c+v) falls.
The third scenario is again self-explanatory.
In the fourth scenario,
“If both rise, then the rate of profit falls, not because the constant capital rises but because the variable capital rises and accordingly the surplus-value falls (for only the value [of the variable capital] rises, although it sets in motion the same number of workers as before, or perhaps even a smaller number).” (p 381)
Its not clear why Marx says this. Its clear that a rise in the value of v, whether because the value of labour-power rises, or because wages rise, implies a fall in the rate of surplus value, and thereby the rate of profit. However, the rise in the value of c also causes the rate of profit to fall, as set out in scenario 2. Marx should have said that the rate of profit here rises or falls not only, because of the change in the value of constant capital, but also because of the change in the value of the variable-capital.
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