I'm back from NYC, and here is my critique of Dumenil et al's solution to the
'transformation problem' that I had promissed to Mike Lebowitz before leaving.
I have tried to upload a short section from my dissertation but it has not come
out very well. However, if you read through it, you will get most of the idea.
Because of the uploaded section, this message is long.
Since the uploaded section has not come out well, let me make some additional
comments so that you get interested into it to read through the rest of the
posting.
Dumenil consistently uses the terms VALUE and SUBSTANCE OF VALUE without
defining the terms. Now the terms substance and substance of value are
generally used in Marxist literature without much discussion about what they
mean. Of course, the idea of SUBSTANCE is Aristotelian and there are some
Marxists who would argue that Marx was an Aristotelian philosopher. However, if
the term substance is used in Aristotelian sense then it is incumbent on the
author to make the case that Marx was an Aristotelian philosopher and also that
the idea of SUBSTANCE makes good sense in the case of marx's value problematic.
In anycase, Dumenil's use of the term SUBSTANCE appears to be much more
mundane, even if he thought otherwise. He basically poses the Ricardian problem
of having to maintain the SIZE of the net output constant when prices change
due only to distributional changes; and goes on to assert that "To proceed in
this manner is to implicitly refer a social substance that is conserved through
variations of prices." However, Dumenil never considers the hypothetical case
of one commodity corn model. In the corn model, his idea of "substance"
disappears, since in this case the problem of prices do not exist and the net
output of corn OBVIOUSLY remains constant in the face of distributional
variations. So the problem he is referring to is Ricardo's problem of the
"invariable measure of value" and not the Aristotelian metaphisical notion of
substance. Thus, it seems his rhetoric against Sraffa and neo-Ricardians is
quite disingenuous.
Foley assumes "a closed capitalist commodity producing economy consisting of a
number of different firms producing and selling a number of different commoditi
es. The definitions that follow refer to the operation of this system over a
definite time period, say a year, and presumes that all the commodities
produced are sold." Thus Foley assumes equilibrium prices, closed economy, etc.
This means that his prices are theoretical prices and must be DIFFERENT from
real market prices that can be observed. Yet Foley does not provide any theory
of price determination. All his national income accounting definitions are
based on OBSERVED prices. I'm not sure in what sense Marx's value problematic
can be reduced to an EX-POST macroeconomic accounting problem.
Currently I'm working on a paper on 'transformation problem' and some of my
ideas represented below may change. It goes without saying that all comments
and criticisms would be most welcome.
Cheers, Ajit Sinha
\1cw
\U1STANDARD
\U7GREEK
\U!UNDERLIN
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\^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \@\ \ \ \ \ \ \
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\,
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D. \!Dumenil et al's Formulation\,
\+
\,
\+ \
A group of Marxist economists, led by a French Marxist Dumenil (1983-84)\
\+
and followed by Lipietz (1982), Foley (1982) and \ others, \ have \ rejected \ t
\+
traditional formulation of the transformation problem and \ have \ suggested \ a
\+
alternative. Their basic objection to the traditional approach \ is \ that \ it
\+
interpretation of the value of labor-power and variable capital is \!wrong\1.\,
\+
\,
\+
As we have seen above, in the traditional approach the value of \ variable
\+
capital is derived by determining the value of the real wage \ bundle \ consumed
\+
by the workers during the \ period \ of \ production. \ The \ measurement \ of
\+
investment in variable capital in terms of prices is calculated by multiplying
\+
the real wage bundle by their prices, as it is done for the constant \ capital.
\+
Although this group agrees that values of the commodities and so the \ constant
\+
capital can be consistently determined by the formula, \7L \1= \7L\1A + \ L, \ w
\+
independent of the price system, they claim that the value of labor-power \ and
\+
so variable capital is \!not \ \1independent \ of \ the \ price \ system; \ beca
\+
workers are not paid their wages in terms of \ bundle \ of \ commodities \ but \
\+
terms of money. Before we \ discuss \ the \ import \ of \ such \ critique, \ it
\+
however, essential to investigate the alternative approach put forward by this
\+
group.\,
\+
\,
\+
The alternative approach begins with the fundamental Marxian \ proposition
\+
that production must be defined as metamorphosis of labor into \ material \ form
\+
(production of services can also be conceived, in a sense, as metamorphosis of
\+
labor into material form as well -- see Marx, 1952, \ pp. \ 168-69). \ Thus, \ t
\+
value of the net output must be equal to the live \ labor \ time \ spent \ in \
\+
process of production. As far as this proposition is concerned, there \ is \ no
\+
disagreement with the traditional approach, since in the traditional \ approach
\+
the value of the net output will by definition be equal \ to \ the \ total \ li
\+
labor time spent in the production process. The alternative approach however,
\+
concludes from this, without much explanation or justification, that the \!total
\+
prices of the net output must be equal to total live labor-time or total value
\+
of the net output \1as an obvious proposition of the \!law of value\1. The argu
\+
that the definitional equality of the total live \ labor-time \ with \ the \ tot
\+
value of the net output implies the equality between total prices of \ the \ net
\+
output and total value of the net output is not \ at \ all \ obvious \ as \ Dume
\+
thinks;\,
\+
\,
\+
"The equality between the price and the value of \ social \ production \ must \
\+
established on the basis of the net product, not the gross product, of a given
\+
period. In the framework of an annual period of production, it is clear \ that
\+
all national accounting and economic \ calculation \ addresses \ the \ yearly \
\+
product (disregarding the problem of amortization). It would never \ occur \ to
\+
anyone to take into \ account \ the \ totals \ of \ the \ columns \ and \ rows \
\+
input-output table. Yet this is precisely what equality between total (gross)
\+
prices and total value would mean.\,
\+
\,
\+
The great insight which lies at the basis of the labor theory of value is
\+
the linking of the total labor expended in a given period with the \ production
\+
associated with it, i.e., the net product. The price of this net \ product \ is
\+
equal to the total income of the period or, in the traditional language of the
\+
price-of-production discussion, the sum of wages and profit." (Dumenil, \ 1984,
\+
pp. 441-42)\,
\+
\,
\+
As I have argued above, the value of commodities are \ determined \ in \ th
\+
sphere of production by the formula \7L \1= \7L\1A \ + \ L, \ independent \ of \
\+
system. The transformation problem belongs to the circuit of \ circulation \ of
\+
commodities that lies \ between \ the \ end \ of \ one \ production \ cycle \ an
\+
beginning of another. It is not only the net output but the gross output that
\+
is thrown in the sphere of circulation, this is \ the \ only \ way \ the \ const
\+
capital gets replaced from one production period to another. \ Since \ constant
\+
capital is nothing but commodities, its value is determined by the formula \7L \
\+
\7L\1A + L, independent of the price system. Now if we bound just a part \ of \
\+
total commodities thrown in the sphere of circulation, in this \ case \ the \ ne
\+
output, in terms of prices and their values and leave the rest, in \ this \ case
\+
the commodities constituting the constant \ capital, \ then \ in \ all \ likelih
\+
total prices of the constant capital will diverge from its total value, \ since
\+
prices, in general, diverge from value ratios. As long as \ we \ maintain \ tha
\+
value is neither created nor destroyed \ in \ the \ sphere \ of \ circulation, \
\+
proposition that total price of the net output must equal total value \ of \ the
\+
net output even though it is not true for the total commodities in circulation
\+
is in contradiction to the definition \ of \ commodity \ value \ and \ the \ law
\+
conservation of value.\,
\+
\,
\+
Such contradiction is an outcome of Dumenil et al's misconception of \ the
\+
transformation problem. In the traditional approach not only the value \ of \ a
\+
commodity but also its three distinct elements, c, v, and \ s, \ are \ determine
\+
independent of the price system. The traditional \ transformation \ problem \ i
\+
concerned with an analysis of how the three elements of the commodity value is
\+
reallocated in the sphere of circulation such \ that \ the \ system \ is \ able
\+
reproduce itself over and over again.\,
\+
\,
\+
In the alternative approach, the transformation problem is conceived as a
\+
problem of income distribution similar \ to \ Ricardo's \ problematic. \ Howeve
\+
instead of taking the given bundle of net output and homogenizing it in \ terms
\+
of money commodity as Ricardo did, Dumenil et al introduce an additional \ step
\+
in the Ricardian procedure. They make two separate homogenizations of the net
\+
output: (1) the net output is reduced to the total amount of \ live \ labor-time
\+
spent in the production process, which is then called total value \ added, \ (2)
\+
the net output is also reduced to \ its \ total \ prices \ in \ money \ terms--
\+
Ricardian homogenization. The two \ homogenizations \ are \ separate \ from \ e
\+
other and have their distinct units. The first one is in terms of \ labor-time
\+
and the second one is in terms of \ money \ commodity \ unit. \ By \ imposing \
\+
condition that (1) = (2), i.e., total prices of the net output, say x units of
\+
gold = total amount of the live labor-time, say y units of labor, they \ derive
\+
the \!value of money \1as y/x, which is given in terms of labor-time. \ It \ sh
\+
be noted that the value of money is distinct from the value of money commodity
\+
given by the formula \7L \1= \7L\1A + L. The value of money so derived is then
\+
as the definitional unit for measuring \ the \ value \ of \ variable \ capital \
\+
surplus value. Thus, the total money wage bill equals the value \ of \ variable
\+
capital and \ the \ total \ money \ profit \ equals \ the \ total \ surplus \ va
\+
definition;\,
\+
\,
\+
"To summarize this interpretation: The price of production of the net product
\+
is assimilated to the total amount of \ labor \ expended \ in \ the \ period, \
\+
establishing the 'price-value' \ condition. \ The \ rate \ of \ surplus \ value
\+
interpreted in terms of prices of production; the 'sum \ of \ profit \ = \ sum \
\+
surplus value' condition \ thus \ becomes \ a \ tautology." \ (Dumenil, \ 1984,
\+
445-46)\,
\+
\,
\+
Note that the value of constant capital is not defined by \ the \ value \ o
\+
money but by the commodity value given by \7L \1= \7L\1A + L, \ and, \ in \ gene
\+
value of constant capital will diverge from the money value \ of \ the \ constan
\+
capital. As I have pointed out above, this introduces a contradiction in \ the
\+
definition of commodity value as c + v + s, since the \ different \ elements \ o
\+
the commodity value are \ measured \ inconsistently; \ the \ constant \ capital
\+
measured by the direct and indirect labor time needed to produce the commodity
\+
but the variable capital and surplus value are measured by the value of money.
\+
Dumenil et al neglect this fact because constant capital is not an element \ of
\+
income and as they see it, the problematic of \ value \ is \ the \ problematic \
\+
distribution.\,
\+
\,
\+
Is this round about way \ of \ formulating \ the \ Ricardian \ problematic
\+
distribution of income any better than Ricardo's own formulation? Not really.
\+
As we know, Ricardo's homogenization of net output in terms \ of \ an \ arbitrar
\+
money commodity was not satisfactory because \ a \ change \ in \ the \ distribut
\+
tended to change the size of the net output measured by the \ money \ commodity.
\+
In Dumenil et al's case this problem shows up in an \ inverted \ form. \ Let \
\+
suppose that we change the money commodity from gold to silver. In this \ case
\+
we will get a different set of prices of commodities in terms of \ silver. \ By
\+
imposing the condition that total value of the net output equals total \ prices
\+
of the net output, we can derive the \ value \ of \ silver \ money. \ Now \ let
\+
suppose that the wage rate in terms of silver money is so \ adjusted \ that \ th
\+
workers can and do spend their wages on the same commodities as before, \ i.e.,
\+
the real wage remains fixed. In this \ case \ the \ value \ of \ variable \ cap
\+
measured by the value of silver money will \ not \ be \ equal \ to \ the \ value
\+
variable capital measured by the value \ of \ gold \ money, \ unless \ the \ org
\+
composition of capitals in gold and silver sectors \ are \ the \ same. \ This \
\+
because of the price-value deviation. Thus, in this case the rate of \ surplus
\+
value or the distribution of income would seem to change with a change in \ the
\+
choice of money commodity even though nothing in real terms has changed. This
\+
is the obverse side of the Ricardian coin. Only that the alternative approach
\+
is confused and inconsistent in its formulation. To suggest that the rate \ of
\+
surplus value in Marx's analysis \ is \ contingent \ upon \ the \ choice \ of \
\+
commodity would be a travesty.\,
\+
\,
\+
Now we can investigate Dumenil et al's basic criticism of the traditional
\+
approach regarding the payment of wages in terms of \ money \ rather \ than \ re
\+
wage bundle. This \ criticism \ stems \ from \ a \ fundamental \ confusion \ be
\+
exchange of capital for labor and exchange \ of \ commodities \ between \ sector
\+
Dumenil et al claim that since \ workers \ are \ paid \ in \ money, \ the \ valu
\+
labor-power and variable capital should be determined by money in some \ sense.
\+
However, we argue that whether the wage is paid in \ terms \ of \ money \ or \ r
\+
terms has nothing to do with the transformation problem \ because \ the \ Marxia
\+
theory assumes that the value of labor-power is determined \ from \ outside \ th
\+
system of commodity exchange (see chs 1 and 2). Therefore, the transformation
\+
problem is only concerned with exchange between sectors, i.e., between capital
\+
and capital, and not between capital and labor.\,
\+
\,
\+
Since Marx assumes that wages are advanced to workers and workers do \ not
\+
save, it implies that at the end of a production cycle the total gross \ output
\+
will be exclusively in the hands of \ the \ capitalists, \ because \ the \ previ
\+
period's wage \ advances \ must \ be \ completely \ consumed \ by \ the \ end \
\+
production cycle. Since wage is conceived to be an advance to the workers, the
\+
exchange between capital and \ labor \ takes \ place \ at \ the \ beginning \ of
\+
production \ cycle, \ which \ is \ distinct \ from \ \ the \ \ circulation \ \ c
\+
commodities-- the concern of the transformation problem.\,
\+
\,
\+
Let us determine the meaning of variable capital in this context. At the \
\+
beginning of the circulation cycle the various capitalists have \ gross \ amount
\+
of commodities produced in \ their \ sectors \ that \ contain \ certain \ amount
\+
determined value. The sectors that produce wage goods must sell some of their
\+
commodities to capitalists of capital good sector, this is the \ only \ way \ th
\+
wage good sector can replace its constant capital used up in the \ process \ of
\+
production and be able to reproduce itself. Here the exchange \ ratio \ of \ th
\+
two commodities, capital good to wage good, relates to \ the \ exchange \ betwee
\+
the two sectors. It does not matter at all whether \ the \ capitalists \ in \ t
\+
capital good sector buy the wage goods directly upon the sale of the \ capital
\+
goods and advance the wage goods to their workers for production in \ the \ next
\+
period or take an IOU from the wage good sector upon the sale of \ the \ capital
\+
goods and hand the IOU to their workers instead of the real wage \ goods. \ As
\+
far as the two sectors are concerned it is a purchase and sale \ between \ them.
\+
Therefore, \ the \ investment \ in \ variable \ capital \ by \ various \ sectors
\+
contribute to the flow of value from one sector to another as long as exchange
\+
ratios of commodities (prices) diverge from their value ratios.\,
\+
\,
\+
An analysis of intersectoral flow of commodities was first introduced \ by
\+
Quesnay in his , \!Tableau Economique \1(see Meek, 1963). In \ Quesnay's \ anal
\+
the rent of \ land \ was \ taken \ to \ be \ given \ from \ outside \ the \ exch
\+
commodities. Marx develops the fundamental idea of the \!Tableau \1in his \ sec
\+
volume of \!Capital\1, i.e., in his \ reproduction \ schema, \ in \ detail. \ H
\+
instead of taking the rent as determined from outside the sphere of \ commodity
\+
exchange, Marx takes wages as determined from outside the sphere of \ commodity
\+
exchange to conduct his analysis of intersectoral flow of commodities.\,
\+
\,
\+
A rejection of the transformation problem as an analysis of intersectoral
\+
flow of commodities amounts to \ a \ rejection \ of \ one \ of \ Marx's \ fundam
\+
propositions that wages are determined from outside the \ sphere \ of \ commodit
\+
circulation or the price system. Lipietz thinks that by conceiving \ the \ real
\+
wage bundle as a 'fuzzy set of bundles' he can reject \ the \ interpretation \ o
\+
wages as given in real terms and at the same \ time \ maintain \ that \ wages \
\+
determined from outside of the price system:\,
\+
\,
\+
"But can we reduce labor power to an output requiring as input a vector d with
\+ i
a cost price \7S\1p\ d\ ? \ Such \ a \ formulation \ would \ amount \ to \ a \
\- i
\+
'quasi-slave' mode \ of \ production.... \ But \ in \ fact \ workers \ in \ dev
\+
capitalist society receive a money wage which they can choose 'voluntarily' to
\+
spend according to their needs. \!Certainly \ the \ general \ standard \ of \ l
\+
limits their choice to a certain fuzzy \ set \ of \ bundles, \ and \ the \ value
\+
bundles in that fuzzy set at a given time in the history of class struggle \ is
\+
a basis for the value of labor power\1." (Lipietz, 1982, p. 75, emphasis added)\
\+
\,
\+
Unfortunately, Lipietz cannot have his cake and eat \ it \ too. \ Lipietz'
\+
own formulation of the price system is given by:\,
\+
p = (1 + \7p\1) (pA + wL), (7)\,
\+
which is identical to equation (3) except \ for \ the \ fact \ that \ the \ vari
\+
capital is not defined in terms of bundles of goods as dL but as wL, \ where \ w
\+
is defined as (total money wage bill)/(total prices of the \ net \ output). \ I
\+
equation (7), as in equation (3), there are n equations for n prices \ and \ one
\+
rate of profit to be determined. Therefore, prices can be determined only \ in
\+
relative terms as commodity exchange ratios. There \ is \ no \ single \ commodi
\+
that has the privilege over others to play the role of \ money \ commodity. \ I
\+
other words, any commodity can be arbitrarily chosen to play the role \ of \ the
\+
money commodity in this framework. Therefore, w is contingent upon the choice
\+
of money commodity and is not given to the system as a datum. Only by \ taking
\+
a physical bundle of wage goods as determined from outside \ the \ system-- \ th
\+
'standard of living' \ (the \ notion \ of \ fuzzy \ set \ is \ not \ relevant \
\+
argument), we can determine w by multiplying the \ given \ wage \ bundle \ by \
\+
prices, i.e., pd = w, which is identical to the traditional approach.\,
\+
\,
\+
If we reject this approach of determining w, then \ we \ must \ be \ able \
\+
theoretically \ privilege \ one \ commodity \ as \ money \ commodity \ prior \ t
\+
formulation of the price system, so that we can take the money wage \ as \ given
\+
without having to translate the given real wage basket into money terms. \ But
\+
this is not possible in the formulation given by equation (7), since \ in \ this
\+
formulation prices only mean exchange ratios between commodities \ and \ is \ no
\+
defined exclusively in terms of one commodity. Any attempt \ to \ define \ mone
\+
wage as given from outside and independent of the real wage bundle \ would \ not
\+
only modify Marx's theory of wages but would also imply that the determination
\+
of equilibrium prices and the rate of profit cannot be formulated in terms \ of
\+
simultaneous equations system as it is done in equation (3) or \ (7). \ Without
\+
any doubt, such approach will take us on a separate road from Marxism.\,
\+
\,
\+
"Adam Smith, in contrast to the Physiocrats, restores to its place \ the \ value
\+
of the product as the essential thing for bourgeois wealth; but on \ the \ other
\+
hand he strips off from value the purely fantastic form -- that \ of \ gold \ an
\+
silver -- in which it appeared \ to \ the \ Mercantilists. \ Every \ commodity
\+
\!initself \1money." (Marx, 1952, p.171)\,
\=
