# [OPE-L:4446] Sweezy's incorrect III equation, p. 118 as cause of the transformation problem

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Sun Nov 05 2000 - 00:58:15 EST

```Here then is the old 3 equation equilibrium scheme  (the fourth
equation  defines surplus value as total value minus cost price and
then determines the sum of the individual branch profits as equal to
surplus value)

(1) c1 + v1 +s1 = c1 + c2 + c3 (C)
(2) c2 + v2 +s2 = v1 + v2 + v3 (V)
(3) c3 + v3 +s3 = s1 + s2 + s3 (SVA)
(4) (C + V + SVA) - (C + V) = s1 + s2 + s3

the set of transformation equations should then be:

(5) (1+r) c1x + v1y = Cx
(6) (1+r) c2x + v2y = Vy
(7) (1+r) c3x + v3y = r(Cx + Vy) (SVB)
(8) (Cx + Vy + SVB) - (Cx + Vy) = r(c1x + v1y) + r(c2x + v2y) + r(c3x + v3y)

The invariance condition of course is

(9) (C + V + SVA) = (Cx + Vy + SVB),

That is, the sum of original prices (call them simple prices) and the
sum of the prices of production remain equal  because they remain
determined by the same total value of the output.

At no point in carrying out the equalisation of the profit rates has
the quantity of direct and indirect labor embodied in the output
changed; since that total value  was initially resolved into the
simple prices C + V + SVA, it must also resolve without remainder
into the prices of production Cx + Vy + SVB.

We have an invariance condition, equation (9).

However, the changes in unit prices brought about by an equalisation
of the profit can lead of course to the modification of cost prices,
but since this cannot change the total value of the product, this
only means that surplus value must be modified by the exact same
amount in the opposite direct.

This of course is the meaning of the Ricardian and Marxian critique
of the Smithean adding up theory of value: a change in cost (price)
cannot change value, only surplus value (see II Rubin History of
Economic Thought).

So after the transformation and modification of cost prices,  we will have

(10) (Cx + Vy + SVB) =([(C + V) + a)] + [SVA - a]) {a can be negative
or positive}

The modification of the cost prices thus leaves the sum of the prices
of production as equal to the sum of simple prices since the same
total value determines both.

At any rate, my set of transformation equations can be solved; my
equations (invariance condition included) do not overdetermine the
system.

THE ONLY WAY TO DEFEAT MY ARGUMENT IS TO PROVE THAT EQUATION (7)

(11) (1+r) c3x + v3y = s1 + s2 + s3 (SVA)

That is, write that equation  as Sweezy writes it on p. 118 of Theory
of Capitalist Development, instead of the way I propose here based on
the correct conception of surplus value.

Sweezy argues that after the transformation,  the output of Div III
in the transformed scheme should equal the sum of surplus value in
the *unmodified scheme* (SVA)! And this has gone without comment,
much less criticism, for 60 years!

I argue that the sum of surplus value, defined as total value minus
cost price, should change as a result of the modification of cost
prices and that the output of Div III  should now be set equal to the
modified sum of surplus value (SVB), which of course determines the
sum of the respective Division profits [see equation (8)]

At the root of the difference is the definition of surplus value.

I argue that Marx resolves commodity value into its cost price + surplus value.

Thus, as just argued, a modification of the former means a
modification in the opposite direction in the latter.

Since the completed transformation exercise aims not only to
transform the outputs but to modify cost prices as well on the basis
of a transformation of the inputs, it will also modify the sum of
surplus value. Which is not to say that sum of surplus value should
not continue to determine the sum of branch profits. This so called
equality is of course preserved in my equation (8).

The point of the completed transformation should then be to determine
how modification of cost prices brought about by the transformation
of the inputs from simple prices into prices of production changes
the mass of surplus value (the whole point of the exercise is ruled
out by Sweezy's equation system!) and thus changes both the average
rate of profit and the prices of production. We can investigate
interesting changes in  relative prices as well.

As we can show that substantive changes are brought about, we can
then confirmMarx's intuition that it is possible to go wrong if the
cost prices are left unmodified in an uncompleted transformation.

I BELIEVE THAT I AM THE FIRST TO HAVE LOCATED THE ERROR IN SWEEZY'S
TRANSFORMATION EQUATIONS WHICH DUE TO THE MISCONCEPTION OF SURPLUS
VALUE BUILT THEREIN HAS LED TO THE SO CALLED TRANSFORMATION PROBLEM.

I welcome any defense of the way Sweezy wrote the equation (which was
the basis for the way Allin carried out his iteration; I have already
laid out an alternative 9 step iteration which I argue preserves the
labor theory of value).

I would like to repeat that I do not think we should solve any
problems in terms of an equilibrium vector of prices so that the
inputs and outputs have the same unit prices of production. Despite
Andrew B's one footnote, I believe that such a formalization is
antithetical to Marx's project.

But if we are going to put Marx into timeless, static equations and
thereby study the properties of an imaginary self replicating system
through algebra and iterations, then at least we should stick to
Marx's own definitions.

Yours, Rakesh
```

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