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The Math of Exploitation — Das Kapital

Das Kapital - The Math of Exploitation

Karl Marx

Das Kapital

The Math of Exploitation

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Study guide
By Arvin Lioanag, Founder & Editor. Reviewed against source text (editorial standards). Last updated 12 September 2026.

Summary

Marx steps back to arithmetic after the battle over hours. Holding the value of labour-power constant, he shows how the rate of surplus-value and the number of workers jointly determine the mass of surplus-value an individual capitalist can appropriate. A higher rate helps, but so does employing more labour-power at the same rate.

Capital therefore has two routes to enlarge the unpaid portion it harvests: intensify exploitation of each worker or expand the collective workforce under its command. Guild restrictions once tried to block this multiplication by limiting how many apprentices and journeymen a master could use. The chapter ends by personifying capital as a coercive relation that cares less about any single worker than about the aggregate mass it can set in motion.

Rate and mass belong together. Understanding one without the other lets bosses boast about fairness per worker while growing total extraction across the firm.

In this chapter: Terms Characters Key Quotes Modern Story

Why This Matters

Skill: Multiplying Rate by Headcount

A boss can sound reasonable about each worker while growing total profit through hiring alone. Marx links the rate of surplus-value to the mass of surplus-value produced, showing personified capital caring for the aggregate labour force under its command.

When a company brags about fair average pay, ask how many workers that average now covers and what total surplus implies.

Coming Up in Chapter 12

Marx has linked rate and mass of surplus-value. Next he introduces relative surplus-value, showing how capital can raise exploitation not only by lengthening the day but by cheapening the goods workers need to reproduce their labour-power..

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Original text
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Chapter 11

The Math of Exploitation

RATE AND MASS OF SURPLUS-VALUE Economic Manuscripts: Capital Vol. I - Chapter Eleven Karl Marx. Capital Volume One Chapter Eleven: Rate and Mass of Surplus Value In this chapter, as hitherto, the value of labour-power, and therefore the part of the working day necessary for the reproduction or maintenance of that labour-power, are supposed to be given, constant magnitudes. This premised, with the rate, the mass is at the same time given of the surplus-value that the individual labourer furnishes to the capitalist in a definite period of time. If, e.g., the necessary labour amounts to 6 hours daily, expressed…

Public-domain chapter text, formatted for reading.

Critical Thinking Exercise

10 minutes

Decode the Numbers Game

Think of a workplace metric you encounter - productivity scores, customer satisfaction ratings, efficiency targets, or performance reviews. Write down what the numbers supposedly measure, then identify what human costs or experiences those numbers might be hiding. Finally, rewrite that metric to include what it's actually asking of people.

Consider:

  • •Numbers always tell a story - but whose story gets heard?
  • •What gets measured often becomes what gets valued, regardless of real importance
  • •The more complex the formula, the easier it is to hide who's paying the real price

Journaling Prompt

Write about a time when you were reduced to a number or metric at work, school, or in healthcare. How did it feel to be measured that way? What important parts of your contribution or experience did those numbers miss?

Master this chapter. Complete your experience

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Lessons from Das Kapital

Theme-by-theme analyses that connect this book to modern life skills.

  • Analyzing Class Interests

    Read opposing pressures between workers and owners as structural, not personal, including when decent people still produce harsh outcomes.

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Deep diving the literary elements.

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