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.

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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.