Marxist exploitation theory equations

 

Below are the standard Marxian “exploitation theory” equations and what each means. Symbols: SR = sales revenue; c = constant capital; v = variable capital (wages paid); s = surplus value; L = living labor hours; λ = MELT (money per labor-hour).

1. Value (sales) identity

$$SR = c + v + s$$

Explanation: The money-value of output equals the value transferred from used-up means of production (c) plus wages (v) plus surplus value (s).

2. Surplus value from sales

$$s = SR - c - v$$

Explanation: After covering used-up capital and wages, the remainder of sales is surplus value (profit in money terms).

3. Abstraction from constant capital (textbook simplification)

$$SR = v + s \quad \Rightarrow \quad s = SR - v$$

Explanation: When c is held aside, surplus value is simply sales minus wages.

4. New value created by living labor

$$\text{New value} = v + s$$

Explanation: Workers’ living labor adds all new value; part returns as wages (v), the rest is surplus (s).

5. Rate of exploitation (rate of surplus value)

$$e \equiv \frac{s}{v}$$

Explanation: Measures how much surplus is extracted per unit of wages paid.

6. Time interpretation of exploitation

$$e = \frac{\text{surplus labor time}}{\text{necessary labor time}}$$

Explanation: Necessary labor time is the part of the day that reproduces the wage; surplus labor time produces s for capitalists.

7. Linking money and labor time (using MELT λ)

$$\text{New value (money)} = \lambda L$$

$$s = \lambda L - v$$

$$e = \frac{\lambda L - v}{v}$$

Explanation: With λ converting labor-hours into money, surplus value is the money-value created by living labor minus wages.

8. Wage-equivalent in labor time

$$\text{Necessary labor time} = \frac{v}{\lambda}, \quad \text{Surplus labor time} = L - \frac{v}{\lambda}, \quad e = \frac{L - v/\lambda}{v/\lambda}$$

Explanation: Expresses wages and surplus as portions of the working day.

9. Rate of profit (distinct from exploitation rate)

$$r \equiv \frac{s}{c + v}$$

Explanation: Profit as a share of the total advanced capital; can move differently from $e$ because $c/v$ may change.

10. Organic composition of capital (descriptive ratio)

$$\frac{c}{v}$$

Explanation: Capital intensity; in Marx, a rising $c/v$tends to press $r$ down even if $e$ rises.

Free‑market note: The equations above present Marx’s internal accounting. Laissez‑faire economists explain profit and wages via time preference, uncertainty-bearing, capital formation, entrepreneurship, and marginal productivity under voluntary exchange, challenging the causal claims Marx draws from these identities.

Learn more

• George Reisman, Capitalism: A Treatise on Economics.
• George Reisman, “Marxism/Socialism, A Sociopathic Philosophy Conceived in Gross Error and Ignorance…”.
• William J. Bernstein, The Birth of Plenty.
• Hans-Hermann Hoppe, A Theory of Socialism and Capitalism.
• Eugen von Böhm-Bawerk, Capital and Interest (critiques of exploitation theory).
• Ludwig von Mises, Human Action.
• F. A. Hayek, The Constitution of Liberty.