What follows is a crash course for those unfamiliar with Marx’s economic formulas.  Those of you already familiar with this nomenclature may prefer to skip over to the page explaining simple reproduction schemes here.

For any capitalist enterprise the following formula applies:

The Constant Capital (c) + the Variable Capital (v) + the Surplus Value (s) = the Total Value (w).

or, c+v+s=w.

Simply put, the capitalist invests money in an enterprise with the intention of making more money. Part of the investment is what Marx referred to as “constant” or “fixed” capital. This represents all of the things the capitalist must purchase to set up shop — machines, raw materials, buildings. etc. These items are referred to as “constant” because the value they contribute to the final product is nothing more than their own value passed through the production process. These lifeless things cannot, on their own, create greater value, this power Marx reserves for variable capital.

Variable capital is the money spent on human labor. It is referred to as “variable” because it transfers to the final product a varying amount of value. This is where the value in the phrase “value-added” is generated. Marx explained the secret behind this as being the difference between the price the employer must pay to acquire labor (the value of labor-power) and the profitability of the labor being performed (the value of labor). Imagine two employees hired at minimum wage. One is set to work running a machine which produces 10 parts per hour. Each part sells for $10. The other runs a similar machine and also makes 10 parts per hour, but the parts sell for $25 each. The investment in minimum wage labor power yields a variable return because their labors produce different values.

Since the capitalist has purchased the means of production and the labor power of these individuals, the values generated by their labor belong to him. All of the value generated above and beyond the amount invested belongs to the capitalist.  This value is termed “surplus value.” The combination of fixed capital, variable capital, and any surplus value created are the output (w) of the production process.

Marx then went on to derive some simple relationships from this equation:

The rate of surplus value (s’) is derived by dividing the surplus value by the variable capital, s’ = s/v. We can also think of this as the rate of exploitation. In the case of our two employees, the first is producing surplus value at a rate of 13.79% (100/7.25), while the other is producing surplus value at a rate of 34.48%.

The organic composition of capital (q) is simply the ratio of constant capital to total capital, q =c/(c+v).

And the rate of profit (p), a capitalist’s true concern, is found by dividing the surplus value by the total capital outlay, p = s/(c+v).

Through some algebraic manipulations Marx created from these three formulas an equation which expresses the profit rate as a function of the rate of surplus value and the organic composition of capital:

p= s’(1-q)

This final equation will prove interesting in a moment.

The economic consequences of the rise of the robots can be considered from two perspectives. Should we count their presence as variable capital, artificial workers displacing and assuming the roles formerly held by human laborers, or should they be considered as advanced machines, just another constant capital investment? We will consider both perspectives, only to discover that either way the conclusion is the same.

Let’s start with the approach that robots represent an increased constant capital outlay. If we look again at the equation for the rate of profit,  (p= s’(1-q)), we can see an interesting phenomenon without even doing any math. As the variable q, the organic composition of capital rises, the value inside the parentheses gets smaller. Multiply this by the rate of surplus value (s’) and the product is then smaller, which means the profit rate is reduced.

Some readers will recognize this as just another approach to Marx’s controversial theory of falling profits.

As more and more robots replace human workers profits go down, not up. Not for individual firms necessarily, but for the system as a whole. Ultimately, if we consider this in the abstract, and wonder what happens if (when) robots replace humans entirely we arrive at the conclusion that profits disappear entirely. (q tends to 1, and 1-1=0). Another way to see this would be to consider that since, according to Marx, the only source of surplus value is variable capital, when variable capital disappears so do profits. This is what happens if robots are considered constant capital. What happens if we count them as variable capital? After all, if they are standing in for human workers they are generating a variable amount of value, no? Can’t we just let the cost of the robot replace the wages of the worker and calculate everything else the same?

To explore this we turn to a discussion of reproduction schemes, and we see things get quite interesting indeed.