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Date: Thu, 16 May 1996 13:24:51 -0400
Message-Id: <96051613245166@acl.nyit.edu>
From: akliman@acl.nyit.edu
To: ope-l@anthrax.ecst.csuchico.edu
Subject: Moseley interpretation, Pt. I
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This is a response to the issues Fred raised in ope-l 2193, which
will in the course of things take up other issues he's raised concerning
differences in our interpretation of _Capital_. I still owe him
a couple of proper resonses to these other posts, and hope to get to
them, but, due to lack of time, this will have to do for now.
I've entitled this "Pt. I." It deals with whether there's a quantitative
difference between Fred's interpretation of Marx's value theory and the
"Sraffian" conclusions re price and value. Part II will take up whether
the TSS "results, contrary to Marx's own results, are essentially the same
results as in the Sraffian interpretation," as Fred claims.
Fred writes: "it is not true, as Andrew seems to suggest, that the
assumption of stationary prices ALWAYS leads to the same results as the
Sraffian interpretation. My interpretation ... assumes stationary
pric[e]s ... but does not lead to the same results .... according to
the Sraffian interpretation, technological change in luxury goods
industries has no effect on the rate of profit. However, according
to my interpretation, technological change in luxury goods industries
generally ... changes the aggregate composition of capital for the
economy as a whole, [so] the rate of profit also changes, contrary
to the Sraffian interpretation. Therefore ... also the prices of
production according to my interpretation will be different [from]
the rate of profit and prices of production according to the
Sraffian interpretation."
Fred is thus suggesting that his interpretation yields *quantitative
results regarding the (uniform) profit rate and (relative) prices
of production* which differ from those of the Sraffian interpretation.
And, based on this claimed *quantitative* difference, Fred concludes
that "Because the labor theory of value [as he interpret it--AJK] leads
to different conclusions regarding the rate of profit and prices of
production, the labor theory of value is not redundant, but rather
a DIFFERENT THEORY of the determination of the rate of profit and
prices of production from Sraffian theory, or linear production
theory."
I believe Fred has focused on the key issue, and posed it entirely
correctly. We should discriminate among theories according to the
differences in their *quantitative* results (although not this
alone, of course). And the (non)redundancy of "the labor theory of
value" (I'd prefer the expression "Marx's value theory") should be
settled according to whether it gives *quantitative* conclusions
that differ from and cannot be arrived at by other means (e.g.,
input/output and real wage data).
In this Part I, I wish to show that Fred's interpretation leads to
the Sraffian results and is redundant according to the above
criterion. Part II will show that the TSS interpretation leads to
different results and is nonredundant.
Let's examine the issue of luxury production that Fred poses. To
deal with this, I'll assume a 3-dept. economy, though not necessarily
simple or balanced reproduction, and not necessarily a uniform rate
of exploitation. To convert between labor-time and money magnitudes,
I'll assume each unit of labor-time is expressed as $1. But I'll deal
only with prices of production (not market prices) and thus a uniform
profit rate.
Now, what Fred seems to have in mind is the following:
TABLE 1
Dept. C V S C+V+S profit P
I 112 48 72 232 120 280
II 80 80 120 280 120 280
III 48 112 168 328 120 280
----- --- --- --- --- --- ---
total 240 240 360 840 360 840
where P is the aggregate output price of production. The figures are
money aggregates, which imply no particular physical relations, except
insofar as the physical relations are constrained by these magnitudes
and the stipulation that input and output prices are equal. All this
is to conform to Fred's interpretation. (This happens to be a balanced
growth scheme, with a uniform rate of exploitation; but it need not
be. It also excludes fixed capital, which it need not.)
Let's compare this to Table 2:
Dept. C V S C+V+S profit P
I 112 48 72 232 112 272
II 80 80 120 280 112 272
III 48 82 123 253 91 221
----- --- --- --- --- --- ---
total 240 210 315 765 315 765
Table 2's C"s are the same. The V's differ only because the luxury
Dept's (Dept. III) advance of V has fallen. The S's differ only
because Dept. III's surplus-value is correspondingly lower. (In both
tables, the rate of exploitation is 150 0n each dept.) Both Tables
compute average profits and prices of production in Marx's way, the
way I agree with, and the way Fred will agree with *if* we stipulate
that in each table, unit input and output prices are equal.
Now, comparing the tables, it certainly *looks* as if Fred is right. It
looks like we have labor-saving tech. change in Dept. III. And there is
no doubt that the value composition of capital is greater in Table 2.
And Fred is right that the rate of profit changes, and in the direction
and to the extent that Marx says, for the reasons Marx says. Table 1's
profit rate is 75%, Table 2's is 70%. With the same rate of surplus-
value and a higher composition of capital, the profit rate falls. So
all this *looks* very unSraffian. It *looks* as if technical change
in Dept. III *alone* has caused a change in the profit rate, whereas
the Sraffian interpretation says that the profit rate won't change.
But don't be misled by superficial appearances. Underlying these money
aggregates is a wholly different set of technical and real wage data.
How do I know? Because Fred has stipulated that in each table, input
and output prices are equal. Given that stipulation, we can immediately
ascertain that there has been technical change in Dept. I. How?
Using the usual input/output notation (a, b, l, X), and using lowercase
p's for unit prices, we can write--even though Fred gives us no way to
determines the unit prices, specifies no physical data:
C1/P1 = p1*a1*X1/p1*X1 = a1
so that a1 = .4 in Table 1 and a1 = .4118 in Table 2.
Similarly,
V2/P2 = p2*b2*l2*X2/p2*X2 = b2*l2
so that b2*l2 = .2857 in Table 1 and b2*l2 = .2941 in Table 2.
We can't determine the other input/output data directly. But we can
retrieve enough information to tell us that this is a Sraffa model
in Marx-ian clothing, as will be seen presently.
In any case, what we already see is that a comparison such as this does
not support Fred's claim. We do not have tech. change in Dept. III
alone, so we can't be sure whether the tech. change in Dept. III (and
there is tech. change in Dept. III unless the rise in p1 from Table 1
to Table 2 is exactly 36.5854%--I won't bore folks with the details of
the calculation) is responsible for the fall in the profit rate or not.
It could perhaps be that the tech. change in the other depts. has
produced the fall in the profit rate, with the tech change in Dept.
III having no effect at all. Of course, that seems *very* unlikely.
BUT THAT IS PRECISELY WHAT HAS HAPPENED.
How do I know?
Well, take any linear production model without fixed capital, with
three depts., and with a uniform profit rate. We need not assume
simple, or balanced, reproduction, or a uniform real wage. But we
DO stipulate that input and output prices are equal--and that is
the key. Under such a model, as Fred notes, the technical coefficients
of Dept. III (and the scale of production) are irrelevant to the
determination of the profit rate. The profit rate and relative
prices are functions solely of technical and real wage coefficents,
and of the technical and real wage coefficients of Depts I and II
(the "basic" industries) alone.
More precisely, in such a model, the rate of profit, r, is given by
(a1*b2*l2 - a2*b1*l1)(1+r)^2 - (a1 + b2*l2)(1+r) + 1 = 0 (eq. 1)
with the larger of the 2 solutions discarded.
Now, the way the rate of profit is determined in Fred's interpretation
certainly *looks* nothing like this. Aggregate C, V, S, and the
rate of profit are given by the prior analysis of capital in general
in volume I, which gives the rate of profit, which is then used
to allocate the aggregate surplus-value to the various capitals in
proportion to capital advanced. Good Marx-ian story. Yet, input
prices are postulated to be equal to output prices, and it is this,
just this, precisely this, that makes the relations of determination
in Fred's interpretation equivalent to the Sraffian relations of
determination.
Let me now show this.
First, let us write the TAUTOLOGY
C1*V2 - C2*V1 + (C1+V1)(C2+V2) C1(C2+V2) + V2(C1+V1)
------------------------------ = ---------------------
(C1+V1)(C2+V2) (C1+V1)(C2+V2)
That this is a tautology is readily confirmed by doing some simple
manipulations to the numerators. Forget that there are no "3's" in
this expression. It doesn't matter. It doesn't even matter what the
Ci and Vi signify. All that matters is that they stand for arithmetic
magnitudes. It is just a tautology.
Now, the above can be transformed into the equally tautological
C1*V2 - C2*V1 = C1 V2
------------- + 1 ----- + -----
(C1+V1)(C2+V2) C1+V1 C2+V2
OK. Now for some political economy. In the absence of fixed capital,
each Dept's aggregate price of production can be expressed as
Pi = (Ci + Vi)(1+R), where R is the uniform rate of profit. I'm using
R to distinguish it from the Sraffian r above. According to Fred,
in his interpretation, R = (sum of S)/(sum of C + sum of V)--which is
correct--and which is quantitatively different from r. Let us see.
Rewriting the expressions for Pi as (Ci + Vi) = Pi/(1+R), plug them
into the 2d tautology:
(C1*V2 - C2*V1) 1 (C1 V2)
---------------R^2 + 1 = (-- + --)R
P1*P2 P1 P2
[sorry--in the top line, the 1 sitting above the 1 in the 2d line shouldn't
be there, but I can't get rid of it]
Now, even though we don't know the magnitudes of unit prices or tech. and
real wage coefficients, we still know that the following relations hold:
Ci = p1*ai*Xi, Vi = p2*bi*li*Xi, Pi = pi*Xi, and we can substitute them
into the above (but I'll wait a moment to do so).
Finally--and this is the crux of the matter--note the implicit assumption
made in the last paragraph--the unit prices relaevant to C's and V's
have been set equal to the unit prices relevant to the P's: stationary
prices have been assumed. Now make the substitution:
p1*a1*X1*p2*b2*l2*X2 - p1*a2*X2*p2*b1*l1*X1
-------------------------------------------(1+R)^2 + 1 =
p1*X1*p2*X2
(p1*a1*X1 p2*b2*l2*X2)
(-------- + -----------)(1+R)
( p1*X1 p2*X2 )
which gives
(a1*b2*l2 - a2*b1*l1)(1+R)^2 + 1 = (a1 + b2*l2)(1+R)
OR
(a1*b2*l2 - a2*b1*l1)(1+R)^2 - (a1 + b2*l2)(1+R) + 1 = 0 (eq. 2)
Comparing eqs. 1 and 2, it is obvious that R = r.
Hence, there is no quantitative difference between Marx's profit rate
according to *Fred's* interpretation and the Sraffian profit rate.
And hence, there is no quantitative difference between the relative
prices (even though Fred never specifies how unit prices are determined,
they MUST be such as to give us an R = r, as we have just seen). And
hence, "the labor theory of value" as Fred interprets it is quantitatively
redundant--we could skip volume 1 of _Capital_, and volume 3 as well
(if price and profit calculation were all they were good for, which I
don't think is true) and work directly from the technical and real wage
data. I'm beginning to sound a lot like Ian Steedman, no? Yes, but
with a difference--I'm not referring to "Marx's theory," but to a
particular *interpretation* of Marx's theory.
Finally, if anyone cares to work out the relations from the above
tables (or any others, given a uniform profit rate, 3-depts., and
no fixed capital), the closest we can get to input/output data from
such tables (Fred thinks starting from physical data is contrary to
Marx's methodology) is:
Xi = Pi/pi , ai = (Ci/Pi)(pi/p1) , li = Li(pi/Pi) [Li = Vi + Si],
bi = Vi/(p2*Li) .
These relations presuppose that input and output prices are equal.
With any tableaux of values and prices such as the above, one can
use the aggregate numbers to obtain these input/output relations, and
plug them into eq. 1 (or eq. 2) to determine the rate of profit. It
will *always* be the same as that which you'd get by calculating
(aggregate S)/(aggregate C + aggregate V). (Don't worry that you
don't have unit prices--unit prices cancel out when you plug the
input/output data into eqs. 1 or 2.)
I'm not sure I'll be able to write Part II today. But it's my next
project.
BTW--to be clear, I am not alleging that Fred is a Sraffian. His
theoretical account of determination (some of which I agree with,
some of which I don't) is very different from Sraffianism. All I'm
saying is that there is no quantitative difference between his
(interpreatation of Marx's) relative prices of production and profit
rate and the Sraffians. And the reason for that is that Fred holds
that Marx's input and output prices are equal by definition (not
by happenstance or convergence to equilibrium).
Andrew Kliman
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Date: Thu, 16 May 1996 15:51:32 -0400
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