Das Kapital Ch. 18: The Math That Hides

Summary

Marx starts with one fraction written three ways. The rate of surplus-value is surplus-value over variable capital, which is the same as surplus labour over necessary labour. Classical economists prefer other formulae. They divide surplus labour by the whole working day, or surplus-value by the whole value the day creates. Take a twelve-hour day with six paid hours and six unpaid. Marx's ratio gives one hundred per cent. The economists' ratio gives fifty.

The wrong base produces a false law. If surplus labour is only a part of the day, it must always be smaller than the day, so the rate could never reach one hundred per cent. For the surplus to swallow the whole day, necessary labour would have to sink to nothing, and then the surplus would vanish with it. Marx answers with a figure from L. de Lavergne. An English farm labourer, he says, gets a quarter of the product and the farmer three quarters. Surplus labour stands to necessary labour as three to one, a rate of three hundred per cent.

Why does the false version stick? Writing wages and surplus as fractions of the value created makes the day look like a joint product, split between labourer and capitalist by what each put in. What drops out of sight is the real deal: variable capital is swapped for living labour-power, and the labourer is shut out of the product. Read correctly, the formula of unpaid over paid labour says the same thing. The capitalist pays the value of the labour-power and gets its use over two periods. In the first the worker makes the equivalent of his pay. In the second he makes value that costs the capitalist nothing. So capital is not only command over labour, as Adam Smith said. It is command over unpaid labour, whatever shape the surplus later takes as profit, interest or rent.

In this chapter:Terms Characters Key Quotes Modern Story

Why This Matters

Checking the Denominator

A percentage can be true and still tell you almost nothing, because everything depends on what it is a percentage of. Marx takes a twelve-hour day of six paid hours and six unpaid ones, where the honest ratio of surplus to paid labour gives one hundred per cent and the usual ratio of surplus to the whole day gives fifty.

Before you accept any fairness figure at work, ask what the number is divided by, then redo the sum with the paid part as the base.

This chapter

Inside the Mind: The fraction that conceals

A harmless-looking percentage can hide the split, because the form 'conceals the very transaction that characterizes capital', and surplus never reaches 100% if you measure it against the whole day. The psyche is a mind that trusts the fraction, because the fraction will not print the unpaid part.

Continue this thoughtThe Stub That Pays the Unpaid

Coming Up in Chapter 19

Next, Marx looks at the wage itself. On the surface it appears as the price of labour, so much money for so much work. Then he asks a plain question: what is the value of a twelve-hour working day? The answer, twelve hours, runs in a circle. And the labour a worker is supposed to sell does not yet exist.

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Chapter 18

The Math That Hides Exploitation

VARIOUS FORMULAE FOR THE RATE OF SURPLUS-VALUE Economic Manuscripts: Capital Vol. I - Chapter Eighteen Karl Marx. Capital Volume One Chapter Eighteen: Various Formula for the Rate of Surplus-Value We have seen that the rate of surplus-value is represented by the following formulae: I.Surplus-value(s)=Surplus-value=Surplus-labour Variable CapitalvValue of labour-powerNecessary labour The two first of these formulae represent, as a ratio of values, that which, in the third, is represented as a ratio of the times during which those values are produced. These formulae, supplementary the one to the other, are rigorously definite and correct. We therefore find them substantially, but not…

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The Math That Hides Exploitation

Summary

Why This Matters