Simple Reproduction in an Abstract Capitalist Society

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Capitalism is characterised within the Marxist tradition as generalised commodity production; in Marx’s view, a correct understanding of the commodity encapsulates its fundamentals.

Key is the concept of labour power and surplus value. In the following extract from Michael Heinrich’s “An Introduction to the Three Volumes of Karl Marx’s Capital” (Chapter 5, The Capitalist Process of Production), the term ‘means of production’ relates to machinery and raw materials.

“With regard to the value of the newly produced commodities, the means of production and labour-power play completely different roles.

“The value of the means of production consumed in the creation of a commodity constitutes part of the value of the newly produced commodity. If means of production are completely used up in the process of production, then the value of these means of production is completely transferred to the newly produced mass of commodities.

“But if means of production such as tools or machines are not completely used up, then only a part of their value is transferred. If for example a particular machine has a life span of ten years, then one-tenth of its value is transferred to the mass of commodities produced within a year.  The portion of capital laid out in means of production will, under normal conditions, not change value during the production process, but a portion of its value will constitute a portion of the value of the commodities produced.

“Marx calls this portion of capital constant capital, or c for short.

“Things are different with labour-power. The value of labour-power is not all transferred to the commodities produced. The value newly generated by the “consumption” of labour-power, that is, by labour expenditure, is what is transferred to the value of the newly created commodities.
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“How much value the worker adds to the product of labour does not depend upon the value of labour-power, but upon the extent to which the labour expended counts as value-creating, abstract labour. The difference between the newly added value and the value of labour-power is the surplus value, or s.

“Or to put it differently, the newly added value is equal to the sum of the value of labour-power and surplus value. Marx calls the portion of capital used to pay wages variable capital, or v for short. This portion of capital changes value during the production process; the workers are paid with v, but produce new value in the amount of v + s.

“The value of a mass of commodities produced within a specific period of time (a day or even a year) can therefore be expressed as:

c + v + s

Here c indicates the value of the constant capital consumed, that is, the value of the raw materials and the proportionate share of the value of tools and machines, insofar as they are used.

“The valorisation of capital results solely from its variable component. The level of valorisation can therefore be measured by relating the surplus value to the variable capital: Marx calls the quantity s/v the rate of surplus value. It is simultaneously also the measure of the exploitation of labour-power.

“The rate of surplus value is usually given as a percentage. For example, if s = 40 and v = 40, then one does not speak of a rate of surplus value of 1, but rather of a rate of surplus value of 100 percent. If s = 20 and v = 40, than the rate of surplus value amounts to 50 percent.”

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An exercises in Marxist economics is to show how capitalism can reproduce itself. In the most basic case, we look at an idealised steady state situation, where capitalists appropriate surplus value and consume it without re-investment.

Expanded reproduction will be modelled in the next post.

The economy is divided into two departments: Department 1 is the sector which creates means of production (machines and/or raw materials); this department provides and reproduces the ‘c’ in commodity value.

Department 2 produces means of consumption:  food, shelter and all the other necessities for the survival and continuing existence of the workers and capitalists. It underpins the ‘v + s’ in commodity value.

For simple reproduction to occur, the following relation must hold*:

c2 = v1 + s1

This says that the value of the constant capital in Department 2 (means of consumption) must be equal to the variable + surplus value in Department 1.

All other levels of capital may be chosen freely to reflect the size of the economy, the amount of constant capital and labour-power employed and the degree of exploitation**. The economy will turn-over and reproduce itself provided the above relationship holds.

Here is an example spreadsheet, followed through 9 iterations. As you can see, it never changes and equivalent values (Exch) are exchanged between Department 1 and Department 2.

Link to spreadsheet

Department 1 has to buy means of consumption for its own workers and capitalists (v1 + s1) from Department 2 (it makes its own constant capital c1); Department 2 has to buy its constant capital c2 from Department 1, but can produce the necessaries of life for its own workers and capitalists (v2 + c2) itself.

Examine the first row of the spreadsheet above. Department 1 (creator of means of production) creates a value of 12 (in some units) in cycle one. This will purchase the next round of machines and raw materials in the second cycle: 3 units of value available for Department 1 and 9 for Department 2 (the creator of means of consumption).

Department 2 creates 22 units of value which supply workers and capitalists: 9 units required for Department 1 and 13 units for Department 2.

The column 'Exch' indicates the values exchanged between Departments 1 and 2. Department 1 'exports' a value of 9 to Department 2 to maintain/'depreciate' its machinery and raw materials; Department 2 'exports' a value of 9 also to keep the workers and capitalists in Department 1 in shape (5 + 4).

In a certain sense, Department 1 'exports' its surplus machine + raw material value while Department 2 'exports' its surplus necessaries of living value. The two have to match in the market place, where they share the common value of 9.

What counts is that the value created in Department 1 over and above what's needed to reproduce its own constant capital (c1 + v1 + s1 - c1 = v1 + s1) is exactly the same as the constant capital recurrently employed in Department 2 (c2). When that is the case, Department 1 finds a market for its output in Department 2 and can therefore afford to buy its necessaries of life from Department 2 (v1 + s1).

Department 2 will employ sufficient workers, at a cost of v2, to properly employ the means of production (of value c2).

The case for expanded reproduction exploits exactly the same procedure.

This proves that capitalist equilibrium (at least in this ever-so-simple model) is possible in principle; in reality capitalists make independent and non-centralised decisions so coordination cannot be as exact as in the spreadsheet. This will eventually lead us into a theory of crises.

Things get a little more complex and interesting when we consider expanded reproduction, the typical case of a capitalist economy in growth.

The subject of the next post: "Expanded Reproduction in an Abstract Capitalist Society".

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* See 'Imperialism and the Accumulation of Capital, Bukharin 1925' for more details.

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** 'Exploitation' is a pejorative word but should be here understood analytically. In any form of society which is economically growing, workers will receive less to spend than the value of their work-production. Otherwise, where is the infrastructure of civilisation to come from?

In the case of capitalism, that 'surplus value' is appropriated privately by the capitalist. In feudalism it was appropriated mainly by the aristocracy, and in slave societies it was directly, coercively owned by the slave's master.

In any society where humans work to society's benefit, there will be a social surplus product .. but it may not take the form of surplus value if labour is not commodified.

Who knows whether that will ever come about?