Does Heinrich’s article clarify anything? Let’s look at this old chestnut that Heinrich chews over. (A form of this also appears in Clarke’s article.)
Take his formulation:
p = s/ (c+v) ; which he rewrites as
p = s/v /
where p stands for the rate of profit, s for surplus value, c represents constant capital and v is variable capital. (In the Clarke formulation, c is the value of the fixed and circulating capital expended in production, v is the annual wage bill and s the total annual surplus value.) But in Heinrich’s formulation, which is the more general one, c is the stock of constant capital invested in the production process. But what then is v ? Heinrich unreflectively believes that v is simply variable capital, so that s/v stands for the rate of exploitation and c/v stands for the value composition of capital (or, perhaps in his formulation, the organic composition of capital). From this the argument is made that there is no reason for s/v to grow less rapidly than c/v. Therefore there is no basis to deduce a tendency for a falling rate of profit. This does not rule out the possibility of a falling rate of profit, but – per Heinrich – this is an empirical issue, not theoretically developed tendency.
What he misses is this. The v in the numerator (s/v) cannot stand for the same thing as the v in the denominator (c/v). The v in s/v is the annual wage bill. But the annual wage bill is a flow concept, whereas the v in c/v is, for lack of a better expression, a stock variable. It is the amount of wages capitalists must have on hand at any given time to meet their obligations. The stock of variable capital is related to the annual wage bill by the number of turnovers that take place during a year. For instance if a sector of production takes one month to produce and sell its output, the capitalist only needs 1/12 of the annual wage bill on hand as a stock of variable capital. The rest is repeatedly returned as sales are realized. Any additional tie up capital would be unnecessary.
Except for the case in which there is one annual turnover, Heinrich’s math is as pointless as the conclusions that he derives from it. If on the other hand c/v is to represent the division of the capital into that invested in machinery, plant, buildings, raw materials etc compared to that invested in wages no conclusions can be drawn from this exercise, without introducing one more variable, turnover time. But turnover time varies over the course of a business cycle, decreasing when sales are brisk and lengthening when sales are sluggish and inventories begin to build up.
The main thrust of Marx’s argument is that the process of productivity enhancement (extracting relative surplus value) is tied to the process of capital accumulation. If that is the case, a far better means of expressing this relationship can be derived. It would compare the growth of surplus value extracted per worker (assuming the working year to be fixed) to the amount of constant capital that has to be invested per worker to realize that result. This can be represented by:
P = s/(v + s) /
C/(v+ s) + V/( v+ s)
Here (v + s) is the annual value product per worker, C is the stock of constant capital invested in the production process and V is the stock of variable capital invested in the production process. s/ (v+ s) is the amount of surplus value extracted per worker; C/(v+s) is the stock of constant capital invested per worker (the organic compostion of capital) and V/(v +s) is the stock of variable capital invested per worker.
Now s/ (v + s) reaches a maximum of 1 as the rate of exploitation increases to the point that v, the wage bill, approaches zero. Conversely, V/(v+s) approaches 0. (Remember V x n turnovers = v ((the stock of variable capital x the annual amount of turnovers equals the wage bill)), so as v approaches 0, so too does V.)
The upshot is this. As long as C/(v+s) increases, there must eventually come a point in which the rate of profit falls, despite any temporarily offsetting increases in the rate of exploitation. It is for that reason that Marx, in my opinion, properly considers this law a tendency.
Is this enough of an insight for a full blown theory of crises? Clearly not. And Marx’s notes on this subject indicates that he believed additional and successive approximations to the empirical reality of crises needed to be studied.
To bring together how this law operates in reality involves, in my opinion, a more robust understanding of the concept of a profit rate, as a rate in which mobilized capital expands. The problem with leaving the theory where Marx left it is that it omits the entire banking and financial (and other nonproductive) sectors of the economy. How, for instance, is the rate of profit on banking or insurance to be measured? Against the stock of capital invested in brick and mortar and computers or against the stock of fictitious capital (securities, debt instruments, derivatives, etc) that comprise additional claims on surplus value?
If we, in fact, include these forms of capital into the denominator of the rate of profit, a clear tendency for the rate of profit to fall can be seen. I tried to do this in Solidarity and in the current issue of Critique by using the so-called Shift Index. This index derived by business for business demonstrates that the rate of return on balance sheets across the American economy has been in persistent decline since the 1960s. See also Alan Freeman’s essay, The Profit Rate in the Presence of Financial Markets, that reveals similar results for the economies of the US and UK:
I think these are the directions that we need to go if we are to develop the tendency of the falling rate of profit into more complete theory of accumulation and breakdown.