The rate of profit is r = s / (c + v). This is, in simple terms, the ratio of profits made to capital invested. If this is 100%, then for every $1 invested, $2 will be returned. Here, what I want to talk about, however, is the adjusted rate of profits, r’.
Here is a simple table showing data for two different firms, for producing a commodity that are qualitatively the same.
For these two firms, for simplicity, the rate of surplus value is kept the same, both at 100%. The capital invested is also kept the same. The organic composition of capital, however, is different. When the organic composition of capital is higher, profits are lower.
If we assume this is the same industry, it may seem a bit strange. Why would someone invest into machines if their profits become lower? In reality, their profits are not lower, but for both firms they are the same. The r = s / (c + v) equation may be misleading here, as it does not take into account the social relation between other firms.
Here, I have added three more columns. The third to the last shows us the total amount of labor that goes into producing the commodity for the firm. As we can see, the Firm A produces its commodities with less labor content. The second to the last column shows us the market price. The market price averages out from the values of all firms. The third shows us the difference between the labor content and the market price.
Notice how Firm A would be underselling the market price while Firm B would have a deficit. Firm A would have a greater amount of profits than simply the value of s. However, these profits would not come from exploitation, but simply due to the fact that within the society they are producing for, the average price is above their actual cost of production. Firm B on the other hand would have a deficit and would be forced to cut into their profits in order to stay in business. This, again, would not affect the rate of exploitation, because their lower profits do not reflect lower exploitation, but having to make up for this deficit.
Therefore, we can introduce a new term, s’, which will be the adjusted surplus value, where s’ = s + d. From this new term, we can also define the adjusted rate of profit, which would be r’ = s’ / (c + v).
As we can see, when we make this adjustment, the profits actually the same. Firm A has a higher organic composition of capital, but also a much lower production cost, which precisely makes up for it and so the profit rates here balance out.
The fully expanded form of the adjusted rate of profit would be :
r’ = (s + (p -(c + v + s))) / (c + v)
This, however, could be simplified.
r’ = (p / (c + v)) - 1
We also see here that increasing the organic composition of capital does not, on its own, allow for greater profits. In order for this to yield greater profits, the new machine must allow for the firm to reduce the capital invested necessary to produce the commodity. If we noticed in both cases, c + v is 50. In this example, the labor costs saved by introducing the machines was exactly equal to the cost of the machines themselves. Hence why there is no difference in profits.
In order for there to be an actual actual increase in profits, ∆c + ∆v < 0. Let’s look at examples of different values for this and how it relates to profits and capital invested. We will assume Firm A and Firm B are the same firm but Firm B is the firm before it adopts new machinery and Firm A is afterwards.
As we can see, if the capital invested is reduced, then the adjusted rate of profit will increase. Let us look at the second example, and assume they are two separate firms again.
Here , Firm A is now much more profitable than Firm B. Therefore, Firm A could afford to cut his prices. But by how much? At first, we might assume they could cut out the the superprofits created from selling at a price above the cost of production, that is to say, they could sell not at a price of 65 but at a price of 50. However, we can test this by setting d to 0 and see that it does not work.
The adjusted rate of profits for Firm A actually falls below the same profits for Firm B. Firm A would want to undersell Firm B, but not so much that his own firm becomes less profitable. The amount he can lower his price depends on the size of the market. In this case, there are only two firms, so Firm A’s very existence pulls the market price down quite a bit, as it will be obvious to other consumers that Firm A can produce much cheaper.
Firm A would be able to lower the price much further if there were little other firms all similar to Firm B. By having more firms similar to Firm B, Firm A’s reduction in the cost of production would be less noticeable in the market. The market price would be closer to Firm B’s market price, and therefore Firm B would not run as large of a deficit.
Here we can see by adding a third firm, the market price increases from 65 to 70. In order to calculate how low Firm A can reduce its prices in order to now go below the profits of all other firms, we can rearrange the question for r’ to get an equation for p.
p = (r’+1)(c + v)
All the values for this are already known.
p = (0.4+1)(30 + 10) = 56
Here, 56 is 6 greater than the labor time for that went into producing the commodity, so we can change d to 6 and see that the adjusted rate of profit equalizes.
At this point, Firm A would be underselling his competitors. He would be selling a commodity for a price of 56 despite Firm B and C selling it for 70. Firm B and C can only respond to this in three ways: (1) reduce pay for the workers while keeping surplus the same, thereby increasing the rate of exploitation, (2) invest in the same new machines that Firm A has in order to stay in business, or (3) go bankrupt.
If Firm B increases the rate of exploitation, this will increase their profits. Let us move 5 units from Firm B’s variable capital to his surplus.
As we can see, that increases both the rate of profit and the adjusted rate of profit. This would mean Firm B could also lower prices.
Let’s look at a different scenario. Let’s assume Firm C does indeed go bankrupt, and rather than increasing the rate of exploitation, Firm B manages to acquire the same new machinery that Firm A possesses.
In this case, something interesting happens. The adjusted rate of profits of both firms are now equal since Firm B adopted the same machines as Firm A. However, both firms are now producing at a lower profit rate. Why? Because by all firms adopting the better production process, the average cost of production itself dropped, and so the market price is now lower. There is a higher organic composition of capital, that is to say, more machines are needed in production in relation to workers, but the commodity also now sells for less.
Assuming the rate of exploitation remains the same, once other businesses adopt this same machines, profits for all businesses will end up going down. At first, adopting this new machines gives Firm A an advantage to undersell his competitors. But by doing so, unintentionally, he causes his own profits to decline.
This is another cause of the concentration of capitals. Imagine if, for example, Firm C, after going bankrupt, was purchased by Firm A, which incorporated its laborers and machines. By incorporating Firm C into Firm A, Firm A could incorporate its new machines into Firm C, raising its profitability to be the same as Firm A. Even though the rate of profit would have been unchanged, the absolute profits would increase, as there would be less capitalists to pay dividends to, yet more capital employed.
The concentration of capitals therefore offsets the falling rate of profits. Every time the falling rate of profits leads to an economic crisis in capitalist countries, it is typically resolved through an increase in the concentration of capitals.