Expanded Reproduction in an Abstract Capitalist Society

In the previous post, 'Simple Reproduction in an Abstract Capitalist Society', we looked at a basic model of how a capitalist society engaged in generalised commodity production can reproduce itself - but without growing. If you didn't read that post, now would be a good time - we use it below.

Unlike previous modes of production which were mainly focused on the production of use values, capitalism as practiced by capitalists is motivated purely by the search for surplus value (i.e. growth in capital). The production of specific use values is a matter of indifference as long as the commodities concerned can be sold in the market, thereby releasing their monetary value.

Capitalists will not invest unless they think they can grow their capital, so a properly-functioning capitalist society is a growing one. This has posed a problem for some Marxist economists. How, they argue, can capitalism grow when the workers are paid only a portion (v out of v+s) of the value they produce, and the capitalists - although they live well - need to keep most of their capital gains for further investment?

This has been termed the 'underconsumption theory of capitalist crises' and was the subject of a historical dispute between Nikolai Bukharin and Rosa Luxemburg in the 1920s. Luxemburg thought that capitalism could only grow (via realising the value of an increasing mass of commodities) through vigorous expansion into new markets, and that this explained 'imperialism'.

Bukharin put her right.

So here is Bukharin's model in spreadsheet form - click on image to make larger..

Link to spreadsheet

As before we have Department 1, making machines and raw materials, and Department 2, making consumables to keep workers and capitalists alive for another day's toil.

We split the surplus value created by workers into three categories: that proportion consumed unproductively by the capitalists, (a); that proportion which is capital re-invested in machines, (δc); and that proportion invested in increased labour (δv).

All of the variables here measure capital value, so that δv is increased capital allocated to wages. This could be more workers to use extra machines or raw materials, or more highly-paid (more highly-skilled and productive) workers to use more sophisticated machines.

The constraint between Departments 1 and 2 to ensure that reproduction can occur is a simple generalisation of the previous case:

c2 = v1+a1 and δc2 = δv1.

This equates the constant capital in Department 2 with the payments to workers and capitalists in Department 1 through the endless cycles of capitalist reproduction of the relations of production.

The model is very, very simple. It is assumed that the capitalists don't increase their consumption iteration-on-iteration .. though they probably would. Also, the incremental growth of constant and variable capital is held constant, although it would probably be increasing geometrically. These details don't invalidate the 'in principle' character of the model.

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  Bukharin comments:

"In other words, the following grow:

• the constant capital of society, 
• the consumption of the workers, 
• the consumption of the capitalists (everything taken in values). 

"In this connexion we will not make any further analysis of the relation in which this growth of the various above-listed values proceeds. This question needs to be treated separately.

"Here we must mention, even if only briefly, the following circumstances: along with the growth of production, the market of this production grows too, the market of means of production expands, and the consumer demand grows also (since, taken in absolute terms, the capitalists' consumption grows as well as that of the workers).

"In other words, here the possibility is given of, on the one hand, an equilibrium between the various parts of the total social production and, on the other, an equilibrium between production and consumption.

"In this process the equilibrium between production and consumption is for its part conditioned by the production equilibrium, i.e. the equilibrium between the various parts of the functioning capital and its various branches.

"In the above analysis we neglect at first a series of highly important, specifically capitalist moments, e.g. money-circulation.
...
"This resulted in a series of the most serious mistakes, it resulted further in the denial of the existence of contradictions within capitalism, finally a direct apology for the capitalist system, an apology which attempts – to use a Marxist word – to ‘reason away' the crises, the over-production, the mass misery and so on.

‘It must never be forgotten, that in capitalist production what matters is not the immediate use value but the exchange value, and in particular, the expansion of the surplus value.'

Here, Bukharin is writing as a typical soviet Bolshevik, echoing Marx's extrapolations of the inevitable fate of capitalism. Reality was to turn out very differently, to the point where it is a genuine and profound question of Marxist analysis as to whether capitalism is indeed subject to structural crises (not just regular business cycles) which could catalyse a revolutionary dynamic towards a higher mode of production.

Simple Reproduction in an Abstract Capitalist Society

Link to online PDF

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.
...
“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?