A
KEY,
NEGLECTED
PASSAGE
by Marx
on the,
critical,
Profit-Rate
Formula.
Dear Reader,
In volume three of Marx’s treatise Capital:
A Critique of Political Economy, in its part three, “The Law
of the Tendency of the Rate of Profit to Fall”, in its Chapter XIII, “THE
LAW AS SUCH”, near the end of that chapter [p. 229 in the 1967 New World edition],
resides a key paragraph whose opening sentence marks a major ‘de-abstraction’ –
a major advance in the realism and ‘thought-concreteness’ – of Marx’s model of
the rate of profit return on industrial capital invested. To our knowledge, this crucial passage
has been completely neglected in the Marxian literature on Marx’s “The Law
of the Tendency of the Rate of Profit to Fall” to-date.
That opening sentence – which opens up, for us, a new,
trans-algebraic understanding of the mechanism of the “Law
of the Tendency of the Rate of Profit to Fall” – is as follows:
“The rate of profit must be calculated by measuring the mass of produced and realized surplus-value not only in relation to the consumed portion of capital, reappearing in the commodities
[M.D.: (c + v)], but also to this part plus that portion of unconsumed but applied capital which continues to operate in production [M.D.: i.e., “fixed capital” machinery, plant and equipment, not yet depreciated by “wear and tear”; f].”
Thus, Marx’s profit-rate formula, in this latest step
towards “the surface of society”, in its deepening of the ‘thought-concreteness’
and realism; in its further ‘de-abstraction’/‘de-simplification’, in the flow
of Marx’s subtle systematic-dialectical method of presentation, becomes –
s’t /
(ft + ct + vt)
– whose terms are defined [‘=’], for annual production “cycle”/whorl number t, as follows –
s’t = net surplus-value, net of interest payments, rent payments, tax payments, etc., per Marx’s law of value, this is the economic value-added/created by the living labor component of “productive capital”, represented in value-terns by vt, for “variable capital”, i.e., the wages portion of productive capital investment, etc.;
ft = fixed capital value unconsumed but applied during annual production period t;
ct = constant capital value invested in annual production period
t;
= (cd,t + cr,t + ca,t);
vt = variable capital value [wages] invested/applied in year t;
cd,t = depreciation by “wear-and-tear” consumption of fixed capital
plant and equipment, during annual production year period t;
cr,t = raw materials capital-value invested/applied during period t;
ca,t =
auxiliary materials
capital-value invested/applied during period t.
Note: Putting
this profit-rate formula on the annual production period “cycle”/whorl [“whorl”
because capitalist production is a non-repeating iteration; not
a circle or cycle, in detail, but a ‘qualo-quantitative’, helical spiral, with
both quantitative changes/-expansions and qualitative/ontic changes/expansions
encompassed within each annual production period] basis averts problems of
combining value-“stocks” with value-“flows”.
This further ‘de-abstracted’ version of
the Marxian profit-rate formula, the formula – s’ / (f + c + v) – is a big step closer to the
capitalist “surface of society” profit-rate formula, the formula that reflects capitalist
consciousness of the profit rate, which is the “Return On
Capital Investment”, or “ROI”, ratio, R/I. This
ratio is, approximately, $R/$I » $s’/$f, or, using our
generalized currency metrological qualifier, X, is Xs’/Xf.
Per the, “fetishistic”, delusion of the capitalist mentality, this ratio
excludes, and denies that, capital investment in wages, v, is a co-cause of
the production of the net profit Returns on capital Investment,
Xs’, treating both wages, v, and wear-and-tear on fixed capital
plant and equipment, cd, as mere expenses.
This ‘de-abstracted’ component of the Marxian profit-rate formula, s’ / f, will tend to converge to the dominant component of
s’ / (f + c + v)
if both f rises nonlinearly, and f >> (c +v) as capitalist productive-force progresses.
All value components invested/applied in each year’s “productive
capital” must count equally as portions of the capital invested to produce the
year’s commodity-capital-value output.
Marx’s profit-rate ratio is a kind of “input-output ratio” or ‘capital-value amplification factor”.
It is, as s/(c + v), a gross Output over [‘/’] Input ratio: O/I.
As s’/(c + v), it is a net output over input
ratio:
(O – I)/I.
It is based upon the causal relation
between the input and the output. That
is, the capital-value invested, now (f + c +
v), measures, in value-terms, the cause
of the net-profit effect, s’,
measuring the effect relative to its cause
– measuring the profits-producing power of that input/cause;
its ‘profits-productivity’.
This value-cause includes the
value of the fixed-capital machinery/-plant and equipment “applied”
[Marx] in, to and during the time-period, t, of the value-effect’s
production, i.e., including all of the not-yet-consumed,
not-yet-“wear-and-tear”-depreciated portion of the
value of that, applied, fixed-capital
machinery/plant and equipment, because it too, ft, is part of the cause of the s’t effect.
Implicitly, the ‘de-abstractive’, ‘de-over-simplifying’ progression from –
s’t /
(ct + vt)
to
s’t / (ft + ct + vt)
– opens the way to consider the effect of what Marx
called the ongoing “moral depreciation”
of fixed capital – technological obsolescence depreciation of fixed capital, or
‘techno-depreciation’ for short – which is caused, not by
the, “wear-and-tear”, partial consumption of that fixed capital
in each production period, but by the growth of the social forces of
production, enforced when that growth is embodied in
productivity-improved plant and equipment/-machinery, and applied, in their
production, by other, competing individual capitals.
To remain competitive/viable, the individual capitals
still employing the ‘obsoleted’ fixed capital must partially or wholly scrap that
obsoleted fixed capital – the loans by which that ‘obsoleted’ fixed capital was
originally purchased usually not yet being fully paid-off
at the time of their enforced obsolescence/-scrapping – and take out new loans
to purchase the more technologically-advanced, fixed capital to replace the scrapped
fixed capital, so as to render their individual industrial capitals once again
competent/competitive.
This means that the capital-value loss on the ‘obsoleted’
fixed capital must be subtracted from both the numerator and the denominator of
the, now further enhanced, profit-rate ratio, and the old annual sum of debt
service [interest + principal] payments on the old and the new fixed-capital loans
subtracted from the numerator of this, enhanced, net-profit-rate ratio.
That more-realistic, even-more ‘thought-concrete’ profit-rate ratio thus becomes –
(s’t + Dst - DLf,t - fo,t - Lo,t)/ ((ft - fo,t + Dft) + ct + vt )
– wherein the algebraic terms above are defined [‘=’] as –
Dst = incremental relative surplus-value via new/replacement
fixed capital;
fo,t = remaining, undepreciated value of
period t obsoleted/retired
fixed capital;
Lo,t = period t
Loan debt-service still due on obsoleted/scapped fixed capital;
DLf,t = period t
new Loan
debt-service due on new/replacement fixed capital;
Dft = capital-value of new/replacement fixed capital applied during period t.
As you can see from the revised
profit-rate/ROI formula defined above, the debt-service expense for replacement
fixed capital, to replace the, e.g., scrapped – ‘techno-depreciated’ – fixed
capital, an expense which is subtracted from period gross profits, is a key
cause of the profit-rate/ROI fall.
This cause of productive-force profit-rate fall increases its dominance
as the accumulation of capital, and of social productive force, grows, as any self-financing
of fixed capital purchases, including such replacement fixed capital purchases,
becomes increasingly ‘im-practice-able’, as the cost of fixed capital units rises,
e.g., as the ratio f/(s’ + c + v ) rises.
Moreover, the formula above still
understates the impact of bank-loan replacement financing, and consequent
debt-service expenses subtraction from gross profits. This is because the techno-depreciation of
fixed capital assets is not a one-time event. Such events recur from annual production
period to next annual production period, albeit not in
every single annual production period, as industrial technological progress
continues and even accelerates.
Thus typical industrial-capital “going concerns” accumulate a growing
sequence of layers of such replacement debt-service annual net profit
reductions – growing in size with productive-force growth and with the growing scale
of world-market industry – and that continue for many years, until the, e.g.,
10-year, or 30-year or 50-year, etc., bank loans are paid-off. The typical fixed-capital-including
profit-rate formula is thus –
(s’t + Dst - DLf,t - fo,t - Sk(Lo,t,k))/ ((ft - fo,t + Dft) + ct + vt).
Note that the profit-rate formulas defined above can “aggregate”, i.e., can “scale”, preserving “similarity”, ‘quanto-qualo-fractally’, not “infinitely”, but up from “individual capital”, to “branch of industry”, to “department of industry”, to nation-state “total social capital”, and, finally, to the, “world market”, “total social capital”.
Marx himself did not
live to fully write-out these next steps, leaving the explanation for the
profit-rate fall as if a merely “algebraical mechanism”, due to the relative
fall of v – relative
to c,
albeit both increasing in absolute terms – resulting in a relative
fall of s,
without locating precisely where the resulting relative dearth
of s
registers and manifests empirically. It manifests – the growth of the social
forces of production manifests; the growth of social ‘use-value productivity’ manifests
– in losses and write-offs, subtracted
from gross profits, for the capital-value of productivity-growth-‘obsoleted’
fixed capital, which thus loses some-to-all of its original
purchase-cost value, and its use-value to capitalists, for their profit-making,
by becoming uncompetitive, due to growth of productivity/-productive-force, elsewhere in the capitalist industry to
which it belongs, as well as in general, throughout the capitalist, world-market economy.
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¡ENJOY!
Regards,
Miguel
Detonacciones,
Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];
Elected Member, F.E.D. General Council;
Participant, F.E.D. Special Council for Public Liaison;
Officer, F.E.D. Office of Public Liaison.
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