The Falling Rate of Profit by Joseph Gillman. Dennis Dobson 1958. 25s.

the tendency to a falling rate of profit is one of the main buttresses of Marx’s theoretical structure. Marx develops the theory in chapter 13 of vol. III of Capital, basing it on certain relations between the constituents of the social product. The latter is made up of c+v+s, where c = constant capital reproduced, v = variable capital (the wage fund) reproduced, and s = surplus value (the source of all profit, interest, rent and payment of unproductive workers). Then we have three socially significant ratios derived from these quantities. (a) The rate of surplus value, representing the degree of exploitation of labour throughout the economy:

Equation showing that C equals S, with both over V.
(b) The average rate of profit, which is the form in which the fact of exploitation presents itself to the capitalist and which constitutes the incentive to continue in action as a capitalist:
Equation stating that the rate of profit equals the surplus value divided by the sum of constant capital plus variable capital.
(c) The organic composition of capital, or the ratio of past-labour-embodies-in-means-of-production to living labour: k = c./v relation:
Equation stating that the rate of profit equals the surplus value divided by the sum of constant capital plus variable capital, which also equals the result of variable capital divided by constant capital plus 1, which also equals the degree of exploitation of labour divided by the organic composition of capital plus 1

This relation, since it involves only ratios of the quantities c, v and s, has the advantage that it is independent of the units (whether socially necessary labour-time or money-units of varying value) in which they are measured.