Chapter 5 — Contradictions of the General Formula
How the Law of Value is Preserved
This chapter resolves the paradox posed in Chapter 4: how can arise if commodities exchange at their values? Marx's answer is that the use-value of the commodity — not any deviation from value — creates surplus value.
5.1 The Use-Value of Labour-Power
The capitalist buys on the market at its value:
Value of = cost of necessary subsistence goods
= ">value of labour-power">necessary labour</span></span> time</span> to produce worker's means of subsistence
But the use-value of is labour itself — the activity of working. And labour, as the substance of value, creates new value.
The trick
Capitalist buys for 1 day's value
= price of means of subsistence necessary for 1 day
= enough goods to sustain the worker for 1 day
The worker, working for 1 day, creates more value than the cost of their subsistence
The worker creates 8 hours of value but is paid for 6 hours of value (">necessary labour). The of the remaining 2 hours is unpaid — this is the source of surplus value.
5.2 The Process of Producing Surplus Value
The working day
Marx draws the working day as two parts:
[==== ">value of labour-power">necessary labour</span></span> =====][== ==]
<-------- 8 hours (paid) ----><-- 2 hours (unpaid) -->
Necessary labour: the portion of the working day required to reproduce the value of labour-power.
Surplus labour: the portion of the working day that produces — labour performed beyond what is needed to pay the worker.
The rate of surplus value
to ; creates new value including surplus value (v)">labour-power; creates new value including surplus value">variable capital</span></span>, measuring the rate of exploitation">surplus value to labour-power; creates new value including surplus value">variable capital</span> — the core ratio of capitalist exploitation">rate of surplus value</span></span> (s') = s / v = / ">labour-power">necessary labour</span></span>
Example:
If ">labour-power">necessary labour</span></span> = 6 hours and = 2 hours
s' = 2/6 = 33.3%
This is the fundamental ratio of capitalism — it measures the rate at which capital exploits labour.
The magnitude of surplus value
(s) = ; creates new value including surplus value (v)">labour-power; creates new value including surplus value">variable capital</span></span> (v) × to ; creates new value including surplus value (v)">labour-power; creates new value including surplus value">variable capital</span></span>, measuring the rate of exploitation">surplus value to labour-power; creates new value including surplus value">variable capital</span> — the core ratio of capitalist exploitation">rate of surplus value</span></span> (s')
Where v = amount advanced in wages
5.3 Why the Law of Value is Not Violated
Marx addresses the objection: doesn't this mean the worker is underpaid — paid below the value of their labour?
No. The capitalist pays the full value of labour-power — the price of the means of subsistence. The worker receives equivalent value in wage goods.
The surplus comes from the use-value of labour-power. The worker, during the hours, creates value that the capitalist keeps. This is not a fraud or a theft — it is the normal functioning of the labour market under capitalism.
"The conversion of money into capital proceeds on the basis of the immanent economic laws of commodity exchange."
5.4 The Working Day
Marx does not abstract from the working day — it is historically and politically contested.
The capitalist wants to extend the working day to increase surplus value. The worker wants to shorten it.
This is a class struggle embedded in the production process itself.
Absolute vs Relative Surplus Value
There are two ways to increase surplus value:
Absolute surplus value: extend the working day while keeping ">necessary labour constant
Working day: 8h → 10h
labour-power">Necessary labour</span>: 6h (unchanged — wages constant)
labour-power">Surplus labour</span>: 2h → 4h
increases
Relative surplus value: reduce ">necessary labour by raising labour productivity, without extending the working day
Productivity rises → means of subsistence become cheaper → ">labour-power">necessary labour</span></span> falls
Working day: 10h (constant)
labour-power">Necessary labour</span>: 6h → 4h
labour-power">Surplus labour</span>: 4h → 6h
increases
Summary
| Concept | Formula |
|---|---|
| Surplus value | s = v × s' |
| Rate of surplus value | s' = s/v = surplus labour / necessary labour |
| Necessary labour | Labour needed to reproduce labour-power |
| Absolute surplus value | Extended working day |
| Relative surplus value | Raised productivity → reduced necessary labour |