# [OPE-L:4535] Re: Sweezy's wrong III equation, p. 118.

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Fri Nov 17 2000 - 17:05:43 EST

```I sent the clarification of my argument below to a listmember in
private correspondence. I am forwarding it to the list.

Other than Andrew's serious objections, there have been two
objections to how I proceed:

1. Fred's point that I understand the total to be in value units but
the components of cost price and surplus value to be in money units.
I argue that throughout the transformation Marx has assumed that the
unit of account is the unit of labor time or that the monetary
expression of labor value is one. Which means of course that total
value has a monetary expression. In fact Sweezy begins this way, and
grants that it is a perfectly reasonable way of proceeding. Fred has
not yet responded to my reply.

2. Allin's objection that I have used a trick definition of surplus
value. Following II Rubin, I argue that Marx always begins with total
value or price (its monetary expression) as a fixed magnitude and
then resolves it into cost price and surplus value which are
inversely related. I thus argue that once we are given a fixed
magnitude of total value in advance--as we are in the transformation
exercise--any modification of cost price necessarily means an inverse
modification of surplus value.

Allin argues that surplus value is total value minus the value of the
inputs. I argue that surplus value is *unpaid* labor time so if more
or less is *paid* for the inputs than their value, less or more of
total value or price (its monetary expression) is indeed resolved
into surplus value. If one does not modify surplus value this way,
then the sum of  surplus value and cost price would no longer be
determined by total value. Cost price and surplus value would no
longer be antagonistic components of total value but rather
independently determined magnitudes.

I argue that such a result is grossly antithetical to Marx's line of
reasoning: a modification of one component is always a modification
in the opposite direction of the other component.

Allin is busy, so he has not made a substantive counter-argument;
perhaps someone else will. But I think the way which I have defined
surplus value is at the very least a reasonable interpretation of
Marx's definition of surplus value. If one sticks to this definition,
the transformation problem disappears. Which is why Allin is
convinced that this definition of surplus value must be a trick.

At any rate here is the clarification of my argument to another
member of the list:

Both the physical and value production situation is being held
constant. At no point are we changing the physical quantity of means
of production and the number of worker hours; at no point are we
changing the value of the means of production which have been
consumed and transferred to the output and the newly produced value.
Since Marx seems to take the unit of account to be the unit of labor
value or to assume that the monetary expression of labor value is
one--and Sweezy grants that this is a perfectly reasonable
assumption--this means that the sum of "simple" prices in the
unmodified scheme has to be set equal to the sum of prices of
production in a fully transformed, inputs and outputs included,
scheme.  That is, since the sum total of values are given with the
monetary expression of labor time, one has to maintain as invariant
the sum total of prices. Sweezy himself began with this (correct)
invariance condition, and only drops it because he found it too
mathematically complicated!

This leads to the well known criticism of overdetermination,
specifically that given this invariance condition, then the sum of
surplus value  (or rate of profit) can no longer also be determined
in terms of the "volume one analysis", as Meek puts Bortkiewicz's and
Sweezy's point.

Marx's unmodified tableau is presumably sticking to the volume one
analysis since the sum of surplus value is total value minus value of
the inputs. But I argue that this is not how surplus value is defined
in volume I. Surplus value has always been dM, so that if M changes
due to a modification of cost price on the basis of the
transformation of the inputs, dM must change in the opposite
direction since M'  itself cannot be changed by the mere modification
of cost price.

(1) M' - (M + a) => dM - a

Since, following Ricardo, a mere change in the compensation for paid
(direct and indirect) labor (M + a) does not add up in itself to a
change in the value or the price (its monetary expression) of the
final product (M'), it can rather only imply an inverse change in the
mass of surplus value (dM - a).  This is simply Ricardo's critique of
Smith's adding up theory of price, and the foundation stone of Marx's
theory of surplus value (see Capital 3, Vintage p995).

It thus does not follow that since Marx holds the mass of surplus
value fixed as he transforms only the outputs by a redistribution of
that fixed magnitude of surplus value in terms of a uniform profit
rate that the mass of surplus value should also be assumed to be
fixed when the transformation procedure is extended to the inputs.
Since the latter ipso facto modifies total cost price, it has to
modify  the mass of surplus value in the opposite direction if both
cost price and surplus value are to remain the resolved, inversely
related components of total value or price.

Since in Marx's tableaux total value or price (its monetary
expression) is given in advance as the primary and fixed entity
(being dependent on the quantity of indirect and direct labor needed
to produce it), any increase in one of its parts (cost price) will
invariably lead to a fall in the other (surplus value). In Marx's
theory the parts are never treated as independently determined
magnitudes but are always broken down from the total.

It has been 100 years of dogma that once the transformation is
completed by the transformation of the inputs, Marx thought that the
mass of surplus value would again have to remain constant, instead of
being modified in inverse direction to the modification of cost
price.  Marx simply could not have thought such a thing.

What the complete transformation must solve for then is not only
simply prices of production as the inputs are included in the
procedure and cost price thereby modified but also the resultant
modification of the sum of surplus value in terms of which the sum of
branch profits is determined.

The complete transformation is indeed a much more complicated
exercise than the half done one which Marx presents us.

But even if we are going to stipulate that the inputs and outputs
should be transformed into the same unit prices of production--a so
called vector of equilibrium prices--there is both a set of equations
and a method of iteration by which the complete transformation can be
carried out. I have proposed both of them for the first time.

If one proceeds as I have recommended, the mass of surplus value will
indeed change; however, it will remain entirely derived from unpaid
labor, thereby not putting a chink in the theory of exploitation.
Moreover, the modified sum of surplus value will equal the modified
sum of the respective Dept profits.

One may object that it is inconsistent to keep total value and price
invariant throughout the transformation while allowing the sum of
surplus value and the rate of profit to change. I argue that this is
indeed not inconsistent. Since total value or price is given in
advance as a fixed entity, any increase in one of its must parts must
invariably lead to a decrease in the other part. This is in fact the
only assumption consistent with Marx's theory of value.

Since the complete transformation attempts to modify cost price on
the basis of the transformation of the inputs, it must allow for an
opposite modification in surplus value.

Why?

For example suppose as a result of the transformation of the inputs
cost price increases (this is usually what happens in most examples
since Dept I and II have higher than average OCC's and thus have
their prices raised by the equalisation and since their output is the
input to the system, cost price rises). Now if one simply adds on the
old surplus value to these modified cost prices, one is no longer
beginning with the total value of the commodity and breaking it down
into its cost price and surplus value components. One is rather
beginning with cost price and surplus value as independently
determined magnitudes and arriving at price. This is grossly
antithetical to Marx's way of reasoning.

So the whole idea that the mass of surplus value should remain
invariant as the cost price is modified by a transformation of the
inputs is the fantastic invention by Bortkiewicz, Sweezy and Meek of
an invariance condition to which Marx himself would never have
subscribed. Yes, the mass of surplus value remains invariant when
Marx is transforming the outputs, but it can no loner remain
invariant when the inputs are included in the transformation
procedure. To stipulate that the mass of surplus value remain
invariant is in fact to stipulate that Marx follow an adding up
theory of price.

All the best, Rakesh

ps here are the equations again:

Here then is pretty much the old famous equilibrium scheme  (the
fourth equation however 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

On Marx's assumption, the set of transformation equations should 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),

For the reasons, above I do not assume that SVA = SVB. Far from being
derived from volume I analysis, this assumption is antithetical to it.

And here is the iteration which I propose:

_______________
The initial value table:

c	  v	  s     value
I  225.00   90.00   60.00   375.00
II  100.00  120.00   80.00   300.00
III   50.00   90.00   60.00   200.00
Tot.  375.00  300.00  200.00   875.00

Marx's first-step transformation takes the given total s
and distributes it in proportion to (c+v).  Thus:

c	  v    profit   price   pvratio
I  225.00   90.00   93.33   408.33   1.0889
II  100.00  120.00   65.19   285.19   0.9506
III   50.00   90.00   41.48   181.48   0.9074
Tot.  375.00  300.00  200.00   875.00   1.0000
___________________
Now what I am saying is simple.

1. Apply the PV ratios to the inputs.
2. Sum the new modified cost prices, the new totals in the c and v columns.
3. Subtract the total modified cost prices from the same total value of 875
4. Divide this sum of modified SURPLUS VALUE by the modified total cost prices,
given in the second step, to arrive at r
5. Multiply the branch cost prices by this new r to arrive at branch profit.
6. Add each branch profit to each branch cost price to arrive at prices of
production for each branch.
7. Determine new PV ratios on that basis.
8. Apply the PV ratios to the inputs.
9. Iterate until you arrive at equilibrium.

That is, in each new iteration, the mass of surplus value is
determined first in step 3 by substracting from total value the
(modified) sum of paid direct and indirect labor, leaving of course
the sum of unpaid labor as surplus value; then steps 4 and 5 ensure
that the mass of profits will be equal to it.

In each new iteration,the mass of surplus value has determined the
sum of branch profits. And in each new iteration the sum of surplus
value has derived entirely from unpaid labor.

Allin followed Bortkiewicz and Sweezy in modifying the cost prices
and then adding on the same old surplus value (200) so that a change
in costs alone resulted in rising prices (1000, instead of 875).

that the labor theory of value itself implies that the sum of profit
should move in inverse direction to the modification of cost price.
This is ensured in step 3.

Following Ricardo's critique of Smith, Marx argues that the value of
a product is not determined by adding up wages, profit and rent.
Rather he maintains that the size of a product's value--as determined
by the quantity of (indirect and direct) labor expended in its
production--is the *primary*, basic magnitude that then is resolved
into or breaks down into cost price and surplus value. It is
therefore obvious that once the entire magnitude (the value of the
product) is given in advance as a fixed entity (being dependent on
the quantity of labor needed to produce it), any increase in one of
its parts (cost price) will invariably lead to a fall in the other
(surplus value).

So since at no point in the completion of the transformation have we
changed the indirect and direct labor embodied in the output, the sum
of prices in the unmodified scheme (875) should remain equal to the
sum of the prices of production (as we are assuming that unit of
account is the unit of labor time or that the monetary expression of
labor time is one). Which means of course that if cost price is
modified upward, the sum of profit has to be modified downward, not
held invariant as 100 years of dogma has insisted!

all the best, RB
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