[OPE-L:3918] Re: The Transformation Problem 1

From: Ajit Sinha (ajitsinha@lbsnaa.ernet.in)
Date: Sun Oct 01 2000 - 07:10:54 EDT

Alejandro, I found an earlier and a bit longer draft of my Encyclopedia entry on
the transformation problem, which I'm puting up on ope-l in three instalment.
This one is the first one. I hope this will give you some answer to your
questions, at least for the time being. About other papers, i'll get back to you.
Thanks for your interest. Cheers, ajit sinha

Transformation Problem by Ajit Sinha

One of the central theses of Marx in Capital  is  that  the  basic
macro variables of a capitalist  economy  are  determined  by  the
socio-historical  factors  rather  than  the  market  forces.  The
appearance of the dominance  of  market  forces  in  a  capitalist
economy was characterised by Marx as "commodity fetishism". Though
commodity fetishism is  an  important  aspect  of  the  capitalist
culture, Marx's attempt was to penetrate through  this  appearance
and reveal to the world the real relations of capitalism that hide
behind the market appearances. The relation of 'values' to 'prices
of production', which has come to be known as  the  transformation
problem,  was  simply  an  attempt  to  show  that  how  the  real
capitalist relation of exploitation expressed by the  concepts  of
'value' and 'surplus value' hides behind the market appearances of
'prices' and 'profits'.

A theory of prices is  essentially  related  to  the  question  of
bourgeois accounting. A competitive capitalist  system  'requires'
that the rate of profit must be equal across the  sectors  in  the
economy. The problem is to find a basis of accounting  the  profit
and the investment such that the condition of equal rate of profit
is satisfied. Marx arrived at this theoretical problem much  later
in his theory. In the first two volumes of Capital he  worked  out
an analysis of the capitalist mode of production on the basis of a
non-bourgeois accounting. He reduced every commodity to the direct
and indirect labour-time  needed  to  produce  the  commodity  and
called it the value of the commodity. Value was   treated  as  the
social substance of capitalist economy, akin to the concept of the
mass of a physical object in physics. At  the  first  stage,  Marx
assumed that commodities exchange in proportion to  their  values.
This made it possible for him to show that all the non-wage income
must be the result of the unpaid labour-time performed by the wage
labourers. However, the assumption of  commodities  exchanging  in
proportion to their values would in general violate the  condition
of capitalist competition. For as long as the organic  composition
of capital (ie. the ratio of constant to variable  capital,  where
constant capital refers to the value of machines and raw materials
that is used up in production and variable capital refers  to  the
value of the  wage  goods  consumed  by  the  workers  during  the
production  period)  are  different  in  different  sectors,   the
exchange of commodities in proportion to their values would  imply
that the rate of  profit  in  the  lower  organic  composition  of
capital sectors would be higher than the rate  of  profit  in  the
higher  organic  composition  of  capital  sectors.   This   would
instigate a migration of capital from higher occ sectors to  lower
occ sectors raising the prices of commodities produced  by  higher
occ sectors vis-a-vis the commodities produced by  the  lower  occ
sectors. Thus the exchange ratios of commodities must diverge from
 their value ratios to bring about the condition of the equal  rate
of profit across sectors. What exchange ratios would guarantee the
equal rate of profit across sectors, and how are they  related  to
value and surplus value was the problem Marx tried to solve in the
chapter IX of Capital volume three.

The core of Marx's argument was that  the  gross  output  that  is
thrown in circulation after a period of production  is  equivalent
to its total value as its substance, and this substance has  three
basic divisions: constant capital (C), variable capital  (V),  and
surplus value (S). These three  divisions  of  the  substance  are
independent of particular exchange ratios of commodities: the size
of the constant capital is determined by the prevalent technology,
the size of the variable capital(ie. the real wage basket) by  the
social and historical factors, and the size of the  surplus  value
by the length of the working day or the class  struggle.  However,
these three determinations are not uni-causal  but  interdependent
on each other. Prices or exchange ratios  of  commodities  play  a
role in redistributing the substance of surplus  value  among  the
capitalist class to ensure the condition of competition.  As  Marx
wrote: "The various different capitals here are in the position of
shareholders in a join-stock company, in which the  dividends  are
evenly distributed for each 100 units."  (Capital  III,  p.  258).
Marx's contention was  that  the  question  of  prices  is  solely
concerned with bourgeois accounting, where the issue  is  exchange
between capitalists. As far as the  exchange  between  wo/man  and
nature and capital and labour are concerned, they  are  determined
independent of the price accounting.

Marx's solution to the problem of prices and  the  equal  rate  of
profit was simple. He aggregated the total surplus value  produced
in the economy (S), and divided it by the  aggregate  of  constant
plus variable capitals (C+V). The ratio S/(C+V) [or  sum of si /sum of (ci +vi )]

was declared to be  the  'average  rate  of  profit'  (P)  of  the
system. Given P, the prices of production of any commodity i  (pi )
was simply derived by marking up the sector's  capital  investment
in terms of its value [ie. (ci +vi )] by its average  share  in  the
total profit, ie. pi   =  (ci +vi )  +  P(ci +vi ).  Marx's  method  of
calculating the average or the equal rate of profit and the prices
of production ensured that the total prices would be equal to  the
total value, and the total profits would be  equal  to  the  total
surplus value in the system [ie. Sum of pi  = sum of li , where li  = (ci +vi +si
and sum of P(ci +vi ) = sum of si ].  These  two  results  confirm  Marx's  basic

proposition that even though in a competitive  capitalist  economy
the exchange ratios of commodities differ from their value  ratios
(ie. pi /pj  is not = li /lj ), the basic division of the economy into
C, V, and S remains intact and prices seem  to  only  redistribute
the total surplus value among the  capitalist  class.  The  reader
should note that Marx's "prices of production" are  not  empirical
 'market prices' but rather the 'ideal prices' that would hold when
the rate of profits are equal in all sectors. It was considered  the
gravitational point towards which the market prices gravitated due
to  the  competitive   forces,   given   the   technological   and
distributional  parameters  determined  from  outside  the  market
forces. Marx  did  not  have  the  notion  of  demand  and  supply
schedules, which happens to be the foundation of the  present  day
orthodox theory of prices (see Garegnani, 1976).

As it is quite clear, Marx's two invariance postulates, ie. Sum of pi   =
Sum of li  and sum of P(ci +vi ) = sum of si , are the direct result of  his
of  'average rate of profit'. Defining P = sum of si /sum of (ci +vi ) implies
sum of P(ci +vi )  =  sum of si   and  sum of pi   =  sum of (ci +vi +si ).
Later,  in   1906-7,
Bortkiewicz pointed out that Marx's determination of the  'average
rate of profit' was improper. He argued that in Marx's formulation
the inputs are calculated as labour-values whereas the outputs are
calculated as prices of production, this implies  an  inconsistent
accounting practice. A consistent formulation of the problem  must
use the same accounting procedure on both sides of the  equations.
Thus Marx's average rate of profit was  wrong  because  the  total
capital investment cannot be taken as equal to sum of (ci +vi ) a  priori.
Therefore, the average rate  of  profit  was  an  unknown  in  the
system. Moreover, he showed that once the problem is  consistently
formulated the system turns out to be short of  one  equation  for
the complete determinancy of the prices of production, and when an
invariance condition, ie. some postulate  about  the  relation  of
value to prices of production, is added to the system then  Marx's
two   aggregative   results,   in   general,   would   not    hold
simultaneously. Since Marx had presented his two results  as  sort
of a proof of the correctness of his value analysis, Bortkiewicz's
results  inevitably  turned  it  into  a  'problem'.   Hence   the
transformation 'problem'.

Alejandro Ramos wrote:

> Ajit in #3900:
> "First of all, the determination of what you call the "m" is the central
> problem with Marx's transformation problem."
> What is your definition of "Marx's transformation problem"? It seems to me
> that there is not an universal agreement about what is understood by this.
> Why is the determination of "m" the "central problem" of this... "problem"?
> "That's why assuming that the value of m is "given" can never be taken
> as a solution to the problem, and particularly when it is added that not only
> the real m is unknown but is unknowable."
> So, this problem would not belong to the realm of science? What is this,
> then??
> "This simply confirms the Steedman critique."
> Do you mean the "redundancy" issue here?
> Alejandro
> P.S. If you're very busy, you can perhaps post any of your writings (cited
> in another post) regarding this matter. It's obvious that for people like
> me it's really impossible to get a copy in another way.

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