On Dec 1, 2013, at 4:00 AM, Angelus Novus wrote:
Heinrich's critics, and his answers to his critics.
http://monthlyreview.org/features/exchange-with-heinrich-on-crisis-theory
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."
---------------------------------------
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:
---------------------------------------------------
"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)"
-------------------------------------------------------
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
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