[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).

I argue that this is clear return to an adding up theory of price and 
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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