Chapter 18: Different Formulae for the Rate of Surplus-value

Outline of Marx’s Analysis


In this chapter Marx, pauses a moment before the section on wages, to juxtapose his own formulations to those of classical political economy and to critique the latter in ways that foreshadow the critiques he will make in the next three chapters.

By always comparing surplus value (or product) to the total value (or product), classical political economists portrayed the relationship between workers and capitalists in ways that 1) hid the existence of exploitation and 2) created an illusion that labor was getting its fair share. The existence of exploitation was hidden by making it appear that each factor of production, i.e., labor and capital, is rewarded according to its contribution to production. So, surplus value, s, appears to equal capital’s contribution and s/(s + v), its share, while by implication, variable capital, v, appears to equal labor’s contribution and v/(v+s), its share. Within a few decades after Capital was published, neoclassical economists, having substituted utility for labor value, would use the same trick but with fancier mathematics.

Mathematical concepts such as production functions, e.g., Q = f(K, L), permitted the use of calculus to derive marginal products for K (dQ/dK) and L (dQ/dL) and with a few more assumptions, conclude that wages = market value of dQ/dL and profits = the market value of dQ/dK. In the development of this theory of production, the labor theory of value of the classical political economists was set aside, so the only “value” left was money price determined by markets. Yet the conclusion was essentially the same, both the old formulae and the new ones hid exploitation by reducing the antagonistic social relations of production to engineering-like technical relations among things.(1)

For Marx, by formulating the value of labor as one part of the working day, the classical political economic formulation understated what was for him the essential issue: how much of workers’ time toiling produced the means of consumption they needed (or their value/money equivalent) and how much of their work time produced the means of production (or their value/money equivalent) capital needed. Clearly, both formulations of the rate of surplus-value, the classical one, s/(v+s), and his own, s/v, are possible measures of capital’s share of the total new value created. He preferred s/v because it provided a more direct representation of the division of workers’ days. When he notes how s/(v+s) is a “mode of presentation which arises, by the way, out of the capitalist mode of production itself” (2) and promises to return to the point later on, odds have it that he was thinking about the parallel between s/(v+s) and s/(c+v), the rate of profit. He did return to juxtapose the rate of profit to the rate of exploitation in material included in Volume III of Capital where he presents the rate of profit as expressing capital’s preoccupation with the rate of return on its investment (c+v) and the rate of exploitation as expressing the degree to which workers are being exploited, i.e., forced to produce products and value for someone else.(3)

Commenting on the “popular expression” that juxtaposes unpaid to paid labor, instead of surplus to necessary labor, Marx affirms the reasonableness of that way of talking about exploitation in money terms. By pretending to buy labor, rather than labor-power, capitalists argue that all labor is paid for. But as workers grasp intuitively and Marx’s analysis in Chapter 6 demonstrated, although fluctuations in supply and demand can push wages above, or drive them below the value of labor-power, on the average workers are only paid wages equivalent to the amount of work that produces the value of their labor-power and capitalists arrogate to themselves the fruits of all excess labor beyond that—with no compensation to those performing it. He concludes, “Capital, therefore, is not only command over labour, as Adam Smith thought. It is essentially the command over unpaid labor. All surplus-value . . . is in substance the materialization of unpaid labor time.” (4) But what is the importance of this command over unpaid labor time? We have seen how Marx’s focus is on one, and only one, use of surplus-value, or unpaid labor time: investment, i.e., employing it to impose more work in the future!


1 It would not be until the 1960s, when economists at Cambridge University in England, building on the work of Piero Sraffa (1898&ndash1983), attacked these formulations and forced neoclassical economists to admit that they were built on logical flaws, e.g., they pretend to derive the price of capital but to do so they must assume the price of capital in order to aggregate heterogeneous capital to come up with "K". See G. C. Harcourt, Some Cambridge Controversies in the Theory of Capital, Cambridge: Cambridge University Press, 1972.

2 Capital, Vol. I, p. 670.

3 Capital, Vol. III, Part One, Chapter 3: "The Relationship between Rate of Profit and Rate of Surplus-Value".

4 Capital, Vol. I, p. 672.