I looked at Anwar's dissertation, the section of his so-called "proof"
of the LFTRP, and -- besides the portions that Mathew reproduced here
-- there's this claim (that Anwar, correctly, traces back to Marx)
playing the role of punchline of his "proof":

"[S]ince increasing labor productivity over time is expressed in a
falling L/C, the width of the profit-rate band must be continually
decreasing!" (p. 158)

However, with all due respect to Anwar and Marx, an increasing labor
productivity over time *need not* express itself in a falling L/C.
Why?  Because, C is not machines, buildings, inventories, etc. (use
values), but the *value* of machines, buildings, inventories, etc.
And higher productivity means ability to produce more machines,
buildings, etc. in same labor time.

I'm not saying that Anwar was not aware of this.  He was, but I think
that he slipped a little.  Marx himself was, of course, well aware of
this.  In ch. 25 (vol. 1, Capital), he distinguished between the
"technical" or *physical* composition of capital (the ratio of an
physical index of MP to a physical index of LP) and the *value*
composition of capital (the ratio of a value index of MP to a value
index of LP).

There's no doubt that the technical composition of capital increases
over time as labor productivity increases.  Since the physical mass of
MP tends to increase, one would be inclined to think that its value
does as well.  I mean, is there any a-priori reason to expect
productivity in the production of MP to grow faster than the
productivity in the production of everything else?  So Marx's belief
that, as a rule, the value composition increases over time is
consistent with the sensible assumption that, in the long run at
least, productivity across all branches of production tends to grow at
a similar pace. We must say, however, that this is just a sensible
expectation.  Not an established empirical fact in the history of
capitalism.

Marx was so aware of this that he made this key note:

"I call the value-composition of capital, in so far as it is
determined by its technical composition and mirrors the changes of the
latter, the organic composition of capital. Wherever I refer to the
composition of capital, without further qualification, its organic
composition is always understood." (ch. 25)

"In so far as it is determined by the technical composition," the
value composition is Marx's "organic" composition.  Clever.  Because,
in actual practice, it may or may not be determined by it.

In support of his "proof," Anwar alludes in passing to what -- since
Kuznets -- economists consider a well-established empirical "stylized
fact" in growth economics, namely that the "capital-labor" (K/L) ratio
increases with the development of an economy.  At any point in time,
richer economies have higher K/L ratios.

However, we have to be careful with this.  Although, apparently, the
K/L ratio that empirical economists estimate is (and can only be)
computed from observed value (price times quantity) data, the concept
is in fact deliberately designed to remove the influence of prices and
isolate the ratio of *physical* MP to physical LP.

So, at least as intended by most empirical economists, the K/L ratio
is supposed to be an operational measure of the *technical*
composition of capital.  So, the stylized fact that the capital-labor
ratio increases as an economy develops is only a measure (imperfect as
all empirical measures are in measuring whatever the correlative
concept intends to designate) of the *technical* composition, not of
the *value* composition.

Moreover, the fact that, at any given point in time, richer countries
have a higher average K/L ratio than poor countries is to be expected.
 Obviously, for a given existing average labor productivity in the
production of MP, countries (or industries or businesses) with bigger
physical masses of MP (K) per hour of labor or worker (L) will have
higher K/L ratios.  But this does *not* imply that, over time, the
value of a given physical mass of K will increase vis-a-vis some
measure of LP.

As far as I know, measures of the evolution of *value* composition are
not very conclusive in validating Marx's (and Anwar's) belief that
over time the value composition reflects the increase in the technical
composition of capital.

A final note: As Anwar himself notices, his "proof" refers to the
*range* of possible variation of the profit rate (under some
assumptions).   the *actual* profit rate can be anywhere within that
band.  So, even though the ceiling of the profit rate may decline as
L/C decreases (say that it does), the actual profit rate may go up or
down or stay flat depending on where within the range it is at a point
in time.

Again, I doubt this is what Grossman had in mind when he referred to
the "breakdown" of capitalism.
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