[OPE-L:4571] Re: Re: Re: Re: Re: Re: Re: transformation

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Sat Nov 25 2000 - 00:58:05 EST

re Allin's 4570:

>On Thu, 23 Nov 2000, Rakesh Narpat Bhandari wrote:
>>  You said that surplus value, defined as total value minus the value
>>  of the inputs, would not be equal to the sum of profits in the final
>>  modified scheme.
>>  I then showed that your definition of surplus value could not be
>>  Marx's for it leads to an adding up theory of price.
>This is paradoxical.  How can a definition on which surplus
>value is explicitly a residual lead to an "adding up" theory?
>Allin C.

Because you do not accept Marx's definition of surplus value as the 
residual once the cost price has been taken from total price, that is 
dM as M' minus M. You define surplus value as the residual after the 
value of the inputs has been taken from the value of the output.

As I wrote in my 4559 (just slightly amended):

Given your definition of surplus value as the value of the output 
minus the value of the inputs, surplus value and cost price cannot 
remain resolved, antagonistic components of total value but rather 
become (at least partially) independently determined magnitudes. You 
have glossed over my criticism.

Ricardo allowed for the possibility of the price of wage goods rising 
due not only to their increased value as greater outlays of labor are 
needed for agricultural produce with the increasing cultivation of 
inferior lands but also to rising ground rent payments.

Now as long as we are assuming that total value and the value of 
money remain constant,  you would allow surplus value to be 
diminished only by the rise in the value of wage goods, not the rise 
in ground rent as well.  To this only partially diminished surplus 
value you would then add on the increased cost price.

So if we stick to your definition of surplus value--total value minus 
the value of the inputs--the sum of your (only partially modified) 
surplus value and (raised) cost price  would in the classic Ricardian 
case no longer be the total price, as determined as the product of 
the value of the output and the monetary expression of labor value 
both of which we are assuming to be constant. You are led to break 
the labor theory of value here.

  If we have price determined by your sum, then a rise in cost alone 
has not lead to diminished surplus value alone but rather to 
partially higher prices. That is, your definition leads you to accept 
Smith's adding up theory of price. This is grossly antithetical to 
Marx's theory. Your definition of surplus value cannot be accepted as 
Marx's. Moreover, your textual support is weak.

However, once we accept the definition of surplus as total value or 
price minus cost price itself, it becomes obvious that any 
modification of cost price--whether it results from the rising value 
of the input wage goods or increased ground rent or the *price* 
transformation of the inputs--implies an inverse change in the mass 
of surplus value as long as we are taking the value of the output and 
the value of money to be fixed magnitudes (which is exactly what 
Sweezy inititally did before he decided it was too mathematically 
complicated a problem).

  Once we accept the challenge of transforming the inputs  in terms of 
a vector of equilibrium prices--which I am only doing for the 
purposes of argument--we have a more complicated problem at hand than 
B-S-M realized. The problem now is to have the mass of surplus value 
modified in inverse direction to the modification of cost price 
consequent upon the transormation of the inputs while at the same 
time having the sum of Dept profits determined by this (modified) 
mass of surplus value. If this can be done, then the second equality 
can be preserved. The first equality is already given by stipulation.

This also means that there is no way to reduce the set of equations 
to  three with three unknowns, as Sweezy had hoped for the purposes 
of mathematical tractability. I am happy to find however that the 
four equations which I propose are happily neither over- nor 

I will stick to the assumption of simple reproduction.

I argue that it follows from Marxian theory that once the  value and 
the price of the total output are given, it is basic theorem of 
Ricardian-Marxian 'economics" that the difference between the 
modified cost price  and the unmodified cost price  is equal to the 
difference between the sum of the unmodified surplus value and the 
modified sum of surplus value.


   I c1 + v1 + s1 = c1 + c2 + c3 or C
  II c2 + v2 + s2 = v1 + v2 + v3 or V
III.c3 + v3 + s3 = s1 + s2 + s3 or S
  IV (C+ V +S) - (C + V)  = S


    V c1x + v1y + r(c1x + v1y) = c1x + c2x + c3x or Cx
   VI c2x + v2y + r(c2x + v2y) = v1y + v2y + v3y or Vy
  VII.c3x + v3y + r(c3x + v3y) = r(c1x + v1y) + r(c2x + v2y) + r(c3x + v3y)
VIII.(C + V + S) - (Cx + Vy) = r(Cx + Cy)

Equations IV and VIII defines the sum of surplus value as total price 
which is being held invariant  minus cost price; this then the 
determines the sum of profits, which is given on the right hand side.

This set of transforamtion equations thus has the second equality 
built into them while the the so called first equality is given by 

If this set of equations can be solved, then Marx's transformation 
procedure does not break down upon inclusion of the inputs even if we 
are assuming the burden of having to solve in terms of simple 

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