The Math That Hides Exploitation — Das Kapital

Marx dissects the formulae used to express the rate of surplus-value and shows that conventional political economy systematically understates exploitation. The correct rate compares surplus labour to necessary labour, or surplus-value to variable capital.

In a twelve-hour day with six hours of each, the rate is one hundred percent. Popular formulae instead divide surplus by the entire working day or total new value, yielding fifty percent for the same conditions.

That presentation makes exploitation look like a fair split of a joint product and falsely suggests the rate can never reach one hundred percent. Marx restores the accurate ratio and shows that English farm labourers may receive one quarter of the product while supplying three quarters of surplus labour, a three hundred percent rate. Derivative formulae also hide the core transaction: variable capital exchanged for living labour-power, with unpaid labour following inside the same day. The chapter culminates in the claim that capital is essentially command over unpaid labour, whatever form surplus later takes as profit, interest, or rent.