[OPE-L:903] Re: the "transformation problem"

akliman@acl.nyit.edu (akliman@acl.nyit.edu)
Wed, 31 Jan 1996 14:20:25 -0800

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Andrew here, replying to Duncan.

First, some background. He had written that people discuss the "transforma-
tion problem" using models of "long-run equilibrium" and no technical change,
etc. because it is the "simplest case analytically." I responded that the
reason, in my view, is rather that everyone has accepted Bortkiewicz's
"proof" of Marx's error, namely that balanced reproduction is impossible
unless prices are stationary. (Duncan does not define what he means by
"long-run equilibrium"; I commented that he seems to imply that we must
have stationary prices in long-run equilibrium, as he understands it, and
he hasn't said otherwise.) I said also that Ted McGlone and I have shown
that balanced reproduction does not require stationary prices, contrary
to what Bortkiewicz claims to prove and Sraffa strongly implies.

Now, in his latest post, Duncan expresses confusion over whether I am
saying prices are not stationary in the "real capitalist economy" or whether
I am alleging that analytical errors have been made. Fair enough; let me
be absolutely clear. My comments, and my refutation of the "transformation
problem" critiques of Marx and the Okishio theorem, DO NOT claim to disprove
anything on the ground that the models fail to conform to reality. This
is the strategem of folks like Farjoun and Machover, not Kliman or McGlone.
For instance, in refuting allegations of internal inconsistency in Marx's
account of the transformation of values into production prices, we DID
assume uniform profitability, simple reproduction, as well as no technical
change and no fixed capital. The reason was not because we think all
this corresponds to reality, but because production prices have to permit
uniform profitability and because we wished to show Marx's critics were
wrong on there own terms. Even given all these assumptions, his
aggregate equalities hold *and* the profit rate is s/(c+v).

No "disequilibrium" in the usual sense was smuggled in, in other words.
We were able to pisprove charges of internal inconsistency on Marx's part
because we interpret the "value of capital" as differing from the "value
of the means of production and subsistence" and because we did not postulate
stationary prices. The latter is a sort of "disequilibrium" assumption,
I suppose, but notice that uniform profitability and balanced reproduction
--the usual meaning of "equilibrium"--do not require stationary prices.
Again, everyone adopts stationary prices because they have accepted that
reproduction and uniform profitability DO require this postulate.

Hence, there is absolutely no internal inconsistency in Marx's own
transformation, no error, no need for others to correct or complete it.
If they conclude that the profit rate (under conditions of uniform
profitability, balanced reproduction, etc.) is not s/(c+v), that is
because their value theory (as represented by their equations) differs
from his, or at least from the interpretation that is able to make coherent
sense out of his theory.

In his latest post, Duncan also expresses his skepticism that Sraffa "made
a logical error in deriving theorems from clearly stated modeling
assumptions, and questioned whether I really meant this (or instead, maybe
I meant I thought his assumptions were unrealistic). No, again, the point
is NOT realism. Now, Sraffa does not actually *state* explicitly that
simple (or any balanced) reproduction requires a unique (and thus
stationary) set of prices--which implies a unique profit rate is profitability
is uniform--but he strongly implies it, and that's how everyone seems to
interpret him. Major Sraffians *do* explicitly state this.

So let me show that this is indeed false, via a simple example. Say Dept. I
produces 10 units of means of production each period, 5 of which go back
to itself, 5 to Dept. II. Say Dept. II produces 15 units of articles of
consumption, 4 of which always go to the workers of Dept. 1, 8 to the
workers of Dept. II, and 3 of which are consumed unproductively. This
is simple reproduction.

First, does it require a unique relative price? Assume each Dept. must
receive a price high enough so it can replace its means of production and
re-hire workers without borrowing. Calling p1 and p2 the unit prices of the
two Depts., this means that the following must be satisfied:

10*p1 >/= 5*p1 + 4*p2 (1)

15*p2 >/= 5*p1 + 8*p2 (2)

Letting P stand for the relative price p1/p2, inequality (1) implies that
P >/= 0.8, while (2) implies that P </= 1.4. Hence, simple reproduction
DOES NOT require a unique (stationary) relative price.

Second, can supplies equal demands without the relative price being unique?
Dept. I's supply to II is 5 units of means of production; its demand from II
is 4 + u1 units of articles of consumption, where u1 is the amount of Dept.
II's output consumed unproductively by Dept I.'s capitalists. (And, of
course, II's demand is I's supply, II's supply is I's demand.) So, for
equalities of supplies and demands, we must have

5*p1 = (4 + u1)*p2 (3)

which means we must have P = 0.8 + 0.2*u1. Again, since u1 can theoretically
vary from 0 to 3, P can vary from 0.8 to 1.4. So, no, equalities of supplies
and demands DO NOT require a stationary relative price.

Third, does uniform profitability require a statinary price? The uniform
profit rate equation is

10*p1(t+1) = [5*p1(t) + 4*p2(t)](1+r) (4)

15*p2(t+1) = [5*p1(t) + 8*p2(t)](1+r) (5)

where t is the time of input, t+1 the time of output. Together, (4) and
(5) require that P(t+1) = [15*P(t) + 12]/[10*P(t) + 16], which does not
require a stationary relative price, i.e, P(t+1) = P(t) is not required.
For instance, if P(t) = 1, then P(t+1) = 27/26 > 1 will be required for
uniform profitability.

All this implies as well that the "logic" of Marx's transformation is
impeccable (if one understands that value of capital and value of means
of production are different), since, again, the "self-contradiction" was
supposedly that the non-stationarity of his prices itself disrupted
reproduction and caused imbalance of expenditures and receipts.

Notice that I haven't said a word about the real world.

The "cards are on the table" now, i.e., the Bortkiewicz-Sraffa premise for
requiring stationary prices in order to have balanced reproduction and
uniform profitability has collapsed like a house of cards and is now
strewn all over the table.

Andrew Kliman