Modelling total automation under capitalism (a progress report)

What actually happens to a capitalist economy as automation increases, employees are laid off and the budget for workers' wages tends to zero? It's possible to explore this in a spreadsheet using Marx's equations for expanded capitalist reproduction (which I wrote about here).

You divide the economy into Department 1, which makes machines (capital goods) and Department 2 which makes consumables (wage goods and luxuries). Then you iterate through cycles in which you try to make both Departments more capital-intensive while aggressively laying off workers.

There are some constraints: Department 1 sells Department 2 its machines; Department 2 supplies the consumption needs of workers and capitalists in Department 1. The following quantities need to stay non-negative:

1. Constant capital (machines, factories, raw materials) - c
2. Variable capital (wages) - v
3. Capitalist personal remuneration (dividends) - a
4. Overall sector profits - s  (or p, when adjusted to equalize the rate of profit between Departments).

Additionally the rate of surplus value s/v can't go through the roof. You can't have one worker alone in an enormous factory who works ten minutes to produce the value of their own wage, and then eight hours plus to provide the surplus value which pays for dividends and the next round of automation investment (s/v = ~50). They really wouldn't buy-in to that.

Click on the figures to make the spreadsheets large enough to read. You are not meant to understand what's going on - just to get an impression. More detailed stuff later.

Department 1: s/v tends to infinity while production is anaemic

The problem is this: as automation increases and the number of workers declines in Department 1, those few left have to (unrealistically) produce far more value than their wages to keep the edifice afloat.

Meanwhile the collapse in the number of workers overall leads to a chronic decrease in demand for Department 2's consumer goods. No new machines are being bought: instead there's accelerated depreciation - which destroys surplus value, hitting profits there.

Department 2: this sector begins to collapse

To reiterate: with decreasing demand for wage-goods, Department 2 finds itself losing the value invested in its machines, not buying more. Depreciation hits surplus value making Department 2 increasingly unprofitable.

So far I've been unable to find a combination of parameters which allows capitalism to eliminate all its workers. I'll keep trying ... .

More: Five questions on the last days of capitalism.

---

You ask, why use the framework of Marxist economics? Because orthodox (ie bourgeois) economics has no interest or explanation as to where profit comes from:

"Rent, wages, interest, and profit are the four factor incomes that land, labor, capital, and enterprise provide respectively."

Roughly the idea that if you put some money into 'enterprise' then by some magic it can become larger (profit). Magic is not a good analytic framework for edge cases of capitalist reproduction.

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.

---

  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.