On Dec 1, 2013, at 4:00 AM, Angelus Novus wrote:
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> Heinrich's critics, and his answers to his critics.
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> http://monthlyreview.org/features/exchange-with-heinrich-on-crisis-theory
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>
My reply to Heinrich's answer:
"Shane Mage follows a different strategy to maintain the LTRPF: he simply changes the formula for the profit rate. While Marx considers s/ (c+v) as profit rate, Mage argues that v becomes smaller and smaller and therefore he simply drops it. Mathematically a little bit adventurous, but let us follow his considerations. Instead of the Marxian profit rate s/(c+v) we consider now the “Mage rate of profit” s/c."
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Heinrich begins with a formula [s/c+v)] not to be found in Marx (he originally had called it "implicit") demonstrating his total indifference to the distinction between stocks and flows, between fixed and circulating capital, as if he had not bothered to read my extensive discussion of precisely this and my careful use of upper and lower case symbols to distinguish one from the other. s [=v(s')] is clearly a flow variable, but what about his "c" and his "v?" It is obviously (except to Heinrich?) meaningless to add a stock to a flow. So are they both to be taken as flows? If so we have "v" representing the flow of wages over the course of the year and "c" representing the flow of capital consumption. But the rate of profit--for Marx, for every economist, and for every capitalist--constitutes the return on investment, the ratio between the realized mass of surplus value produced during the year and the average value of the stock of social capital during that year. And that average value of the social capital is a much larger quantity than the amount of capital consumed (and thus to be replaced) during the year. So, if "c" and "s" are both flow variables Heinrich's "Marxian" profit rate s/(c+v) has nothing to do with the profit rate that in Marx's Law falls tendentially. At most it represents a debased form of the *profit margin" (percentage of sale price constituting profit, aka "return on sales") which is calculated by every business as "s/(c+v+s)" Are both, then, to be taken as stocks? We then have p'=s/C+V. But this is just as irrelevant to the Marxian rate of profit's tendency to fall because "V" (the average value of the stock of consumer-goods inventories destined for consumption by productive laborers) has nothing to do with the rate of exploitation, which is the ratio between two flows (surplus value appropriated and variable capital expended, or the unpaid and paid portions of the average working day).
Heinrich goes on to demonstrate that he misses what is essential in Marx's conception of the composition of capital:
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"As organic composition Mage does not use the fraction c/v but the fraction c/(v+s), abbreviated by Q. With s′ for the rate of surplus value s/v, Mage now can write for his profit rate s/c = s′ / Q(1+s′)
With this formula Mage wants to refute my demonstration that in Marx’s profit rate formula one finds the rate of surplus value in the numerator and the value composition in the denominator and that there is no necessity in any claim as to which one will grow faster. With his new formula Mage states triumphantly that now the rate of surplus value appears “in both the numerator and the denominator”, but constant capital appears only in the denominator. Seemingly Mage has the idea when s′ appears in numerator and denominator this compensates each other to a certain degree and therefore the effect of growing c prevails.
However, that s′ appears in the denominator is a kind of illusion. For Q = c/(v+s) we can also write Q = c / v(1+s′) (Mage himself mentions [why does he say "mentions" when I *insist* on} this expression). When we insert this last expression for Q in the “Mage profit rate” we receive
p'=s/c = s′ / [c/v(1+s′)] (1+s′)
and we can see that s′ appears not only one time in the denominator, it appears two times. And since these two instances cancel each other totally, the two terms (1+s′) in the denominator of Mage’s profit rate can simply be shortened and we receive:
s/c = s′/(c/v)"
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Which, of course, simplifies right back to where we started, s/ c=p'=s'v/c--completely removing the organic composition of capital from the equation. Which, of course, makes it impossible to determine the change in the rate of profit as organic composition rises, given the functional relationship between organic composition (Marx insisting, of course, that labor productivity is a positive function of organic composition) and the law of the falling tendency of the rate of profit as formulated by Marx. But what can you expect when you ignore economics and are content to play with a defective algebraic expression? So let's go back to the simplest formulation of the Law, p'=s'/Q(1+s')=s/C
It is essential to remember that we are here dealing *only* with the increase of *relative* surplus value. As organic composition (labor- hours embodied in fixed and circulating constant capital divided by the number of hours in a working year) increases, relative surplus value results only from an increase in labor productivity at a *faster* rate than the rate of increase in the real wage. Labor productivity is a monotonically increasing function of organic composition. But the sum of variable capital (v) and surplus value (s) per worker is a constant (the number of hours in the working year), while the stock of constant capital can and does increase without limit. So the numerator of the profit rate, "s," has as its limit the number of hours in the working year while the denominator, "C" increases without limit. As these two coordinate terms increase the ratio between them must, whatever the shape of the functional relationship between capital per worker and labor productivity, decrease steadily once a certain point has been reached. And when, in reality, was that point reached? For Marx, as an empirical matter, that point had been reached far earlier. The falling rate of profit had been recognized as a tendency of the capitalist mode of production by Adam Smith *a whole century earlier* and none of Smith's successors had thought him wrong to have done so. Marx in no way claimed to have discovered the falling rate of profit: what he claimed was that he had solved the "riddle" which had "puzzled" all the earlier economists through his formulation of the falling tendency of the rate of profit as a decisive structural feature, a crucial "economic law of motion of modern society," in his labor-value-based dynamic model of the capitalist economy.
The following, purely arithmetical example, presents an image of how the process works. The arbitrary numerical ratios of the variables were selected to portray a more-than-proportional increase in productivity as a function of capital accumulation and a starting set of quantities permitting an initial *increase* in the rater of profit:
(a ten-percent increase of capital stock per labor-year is assumed to result in a twenty-percent increase in the productivity of labor. Each period reflects such an increase in capital stock. Period one condition of capital stock per worker equal to one labor-year is assumed. The initial rate of surplus-value is assumed to be 100%. All numbers are denominated in hours of socially necessary labor time. All the increase in productivity is assumed to go to relative surplus- value, ie., real wages are assumed to be constant). Marginal efficiency equals increase of surplus value p.w. divided by increase in capital p.w.
Period Capital per worker Wages p.w. Surplus-value p.w. profit rate (%) exploitation rate (%)marginal efficiency of capital(%)
1 2000 1000 1000 50 100 104.2 2 2200 833.3 1166.7 53.3 140 83.5 3 2420 694.4 1305.6 54.0 186.9 67.7 4 2662 578.7 1421.3 53.4 245.7 47.8 5 2936.2 482.3 1517.7 51.7 314.7 35.2 6 3229.8 401.9 1598.1 49.5 397.6 27.4 7 3552.7 334.9 1665.1 46.9 497.2 20.7 8 3908.1 279.1 1720.9 44.0 616.6 15.7 9 4298.9 232.6 1767.4 41.1 759.8 11.9 10 4728.8 193.8 1806.2 38.2 932.0 9.0 11 5201.7 161.5 1838.5 35.3 1138.4 6.8 12 5721.9 134.6 1855.4 32.4 1378.5 3.2
Any choice of initial values and parameters can be made. As long as the structural relationships are those specified by Marx it is clear that the rise of relative surplus value confirms Marx's law in theory. The actual short-term changes in profit rates do of course vary substantially and can rise as well as fall. To understand how and why, see my discussion on the MR page of the counteracting and aggravating factors!
Shane Mage
This cosmos did none of gods or men make, but it always was and is and shall be: an everlasting fire, kindling in measures and going out in measures.
Herakleitos of Ephesos