# Marx’s Capital Volume III – Chapter 3 – The Relation of the Rate of Profit and the Rate of Surplus Value

~ 800 words, ~ 4 min reading time

## Summary

If we define the rate of profit as the profit divided by the expenditure (not too far from profit margin by standard accounting, though also not quite the same), and the rate of surplus value as the amount of surplus value (that is, profit) divided by the wage bill (that is, the amount of variable capital), then we’ll find this relationship:

Rate of profit = rate of surplus value x (variable capital/total capital)

“Capital” here being the term that Marx uses for “costs” – including wages (that is variable capital), depreciation, materials, etc.

This chapter mostly focuses on different ways in which the rate of profit can change/differ. He considers a number of cases, but comes to this conclusion in the end:

(1) The rate of profit moves in the same proportion as the rate of surplus value if the share of variable capital stays constant.

(2) The rate of profit moves more than the rate of surplus value, but in the same direction, if the share of variable capital moves in the same direction as everything else.

(3) The rate of profit moves less than the rate of surplus value, but in the same direction, if the share of variable capital moves in the opposite direction, but less than, the rate of surplus value.

(4) The rate of profit moves opposite the rate of surplus value if the share of variable capital moves in the opposite direction and more than the rate of surplus value.

(5) The rate of profit stays constant if changes in the rate of surplus value are offset exactly by changes in the variable capital share.

Marx feels a need to explain #5. So, let’s look at Marx’s example (but I’ll use \$ instead of pounds). Let’s say that, originally, the capital is divided as: \$80 constant capital + \$20 variable capital + \$20 surplus value. In this case, the rate of profit is 20% (\$20/\$100), while the rate of surplus value is 100% (\$20/\$20). Then, let’s say that wages fall, so that you can produce the same stuff with just \$16 paid in wages. Then, we’d have \$80 constant + \$16 variable + \$24 surplus value. The problem is that this would mean that the rate of profit has increased 25%. For that not to happen, the constant capital has to have increased, for example, like so: \$104 constant + \$16 variable + \$24 surplus value. Now, the rate of profit is \$24/\$120 = 20%. The change from \$80 to \$104 constant capital means that either labor productivity has dropped – that is, that workers need more materials to produce the same quantity of product, or that the cost of materials has increased.

## Why It Matters

Marx’s big point from this chapter was to establish that it is possible for two capitalists to have the same rate of profit, but different rates of surplus value. The above examples shows how that can happen. Similarly, it is trivial now to show that two capitalists can have the same rate of surplus value, but different rates of profit. I’m still not 100% sure where Marx is going with this – but I suspect part of the point is to show that, since there is a tendency toward rates of profit to equalize, we’ll have capital-intensive firms (for whom the wage share is low) with relatively higher rates of surplus value. That is: an increase in capital intensity across the economy leads to greater labor exploitation. But, I’m just speculating about that at this point.

## Where Marx Goes Wrong

This chapter was mostly mathematical identities. But, I do want to point out two oddities in Marx in this regard:

(1) Marx’s use of the rate of surplus value is really strange. Why “profit divided by wage bill” is meaningful at all is unclear to me. Even if we accept that constant capital should basically be discounted, and only consider a “value added basis”, it seems that the rate of surplus value should be “profit divided by value added by labor (that is profit + wage bill)”. No idea why Marx does what he does on this.

(2) Marx’s use of “labor productivity” is also a bit non-standard to the modern reader. Where we typically think of labor productivity as the ability of labor to make a product in a period of time, Marx is thinking in terms of relative value added (compared to the value already “embodied” in the means of production) – so a lack of productivity is seen more as a worker needing more tools/materials to produce the same thing, as opposed to the modern notion where a lack of productivity is seen more as a worker needing more TIME to produce the same thing.

As is always the case, a definition can’t be “wrong” per se. It’s just more or less useful. These are similar – but could cause confusion because of the difference between modern usage and Marxian usage.