[OPE-L:7693] M-C-M' and the determination of S

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Fri Sep 20 2002 - 19:19:28 EDT

Fred, developments in our two ongoing discussions indicate the need to 
press further into the steps of your summary of your theoretical 
framework.  You'll recognize concerns I've raised in other posts in the 
following, but I try to lay out more thoroughly what I understand to be the 
necessary grounds for these concerns.

>2.  The circulation of capital
>The circulation of capital is of course represented symbolically by:
>         M - C ... P ... C'- M'
>This general formula for capital is not just a helpful illustration.  This
>general formula is Marx's overall analytical framework for Marx's
>theory.  The initial given in Marx's theory is the starting point of the
>circulation of capital, M.  And the main purpose of Marx's theory is to
>explain how this given, presupposed initial M is transformed into (M +
>dM), i.e. the original capital plus a surplus-value, at the end of the
>circulation of capital.  This question applies to the total surplus-value
>produced in the capitalist economy as a whole.

I entirely agree with this formulation and would even want to emphasize 
it.  Marx's starting point is a conception of surplus value such that it 
necessarily originates in production but just as necessarily is realized in 
commodity exchange.  Granting that Marx starts with a "given, presupposed 
initial" magnitude M, he then posits that the appropriation of surplus 
value is pursued in the arena of exchange by using M to purchase 
commodities.  In the circuit of industrial capital, per our previous 
discussion of step 1, this necessarily translates as M = Q*P + w*L, where 
the Q vector and L is dictated by unit labor power input requirements and 
the total output affordable by the given M (more on this below)  This is 
necessarily the case, whether or not Marx chooses to highlight this in any 
given discussion.

By the way, a corollary of the assumption that the magnitude of the initial 
M is *given* is that, given physical input and output conditions, wage 
rates, input prices, the level of aggregate output, and thus the level of 
aggregate surplus labor, is determined, so that the aggregate quantity of 
new labor performed is necessarily a function of the initial M.  To pretend 
that aggregate labor is determined independently of the initial quantity of 
M advanced is to pretend something that simply can't be true, given Marx's 
stipulation that surplus value is realized through the purchase and sale of 
commodities, and thus M = Q*P + w*Lv.  If it is asserted that physical 
input-output relations are *variable* rather than *fixed*, for example, 
then individual commodities do not have uniquely defined labor values; the 
latter will depend on the choice of input mix (in the case of variable 
proportions technology) or the choice of level of output (in the case of 
non-constant returns to scale).

Given that the level of aggregate labor is dictated by the initial M (taken 
as given, per your above representation), physical input requirements, wage 
rates and input prices, the M' resulting from this process is determined by 
the level of output affordable by the expenditure of M and the vector of 
output prices.

>Marx's analytical framework of the circulation of capital is fundamentally
>different from Sraffa's "production of commodities by means of
>commodities".  Marx's framework has to do with quantities of
>money-capital.  Sraffa's framework has to do with physical quantities of
>inputs and outputs.

Descriptively different, perhaps, but not *fundamentally* different, since:

1) per Marx's specification of the circuit of capital, surplus value is 
realized by using M to purchase one set of commodities, and then realizing 
M' by selling another set of commodities.

2) in the specific case of the circuit of industrial capital, the 
commodities purchased must in any case be dictated by the conditions of 
production, i.e. "physical quantities of inputs."  This is what determines 
the Q and L in the expressions C = Q*P and V = w*L (here, L refers to a 
vector of input requirements, rather than aggregate new labor, as in your 
subsequent exposition).  Furthermore, the M' that is realized at the other 
end depends on "physical quantities of ...outputs", since it equals X*P 
(possibly, but not necessarily, with the same price vector P) in any 
case.   So that the "quantities of money capital" that figure in Marx's 
representation are not only entirely consistent with, but *necessarily 
translatable into* expressions involving "phyisical quantities of inputs 
and outputs."  If they were *not* translatable in this way, then Marx's 
theory would simply be incoherent on its own terms, since it would be 
inconsistent with commodity exchange.

3) Sraffian theory typically precedes on the assumption that input and 
output prices are identical.  Marx's treatment in V.I proceeds on precisely 
the same basis, since Marx assumes, beginning in Chapter 6, that commodity 
prices are in all cases proportional to their respective labor 
values.  This assumption is also plausible in the more general case, in 
representing e.g. the hypothetical steady state or simple reproduction of a 
given system of capitalist production and exchange.

In light of the foregoing I don't see the basis for your claim that the 
Marxian and Sraffaian frameworks are *fundamentally* different.

>3.  Theory of value surplus-value
>Marx's theory explains the origin and magnitude of dM on the basis of the
>initial givens of constant capital and variable capital, and also the
>additional assumptions of the quantity of abstract labor currently
>employed in the capitalist economy as a whole (L) and the money value
>added per hour of labor (m).  The product of m and L yields the total
>money value added (or "new value" produced) in the capitalist economy as a
>         MVA = m L.

I don't see that Marx *starts* from this point. This is rather an 
*inference* from given, relatively restrictive initial conditions, namely 
involving a scenario with commodity money in which all commodities exchange 
at their respective values.  As I read Volume I, the argument proceeds 
rather in these steps:

Pre-1:  Labor values are determined by socially necessary labor time, that 
is, physical production conditions.

1.  Chapter 4: Specification of M-C-M' as the circuit of capital, with 
surplus value constituting the increment M'-M corresponding to the 
"valorization" of value, i.e., an increase in total value in circulation.

2.  End of Chapter 5:  Assumption that commodity prices are proportional to 
labor values.  It is impossible to implement this assumption without a 
consideration of "physical quantities of inputs and outputs," since these 
are what determine labor values.  So whether or not Marx explicitly 
mentions it in his subsequent argument, one cannot determine how a given M 
breaks down into C and V without reference to physical input conditions, as 
these will determine both the vectors Q and L and the prices, assumed to be 
proportional to labor values, which are determined in turn by physical 
input/output conditions.

If it is further assumed that money takes the commodity form (which Marx 
does not explicitly assert), then it additionally follows that the factor 
of proportionality between labor values and prices is dictated by the 
inverse of the value of money, which *also* can't be determined without 
reference to physical input/output conditions.

(A corollary of this is that m can't be defined as the inverse of the value 
of money in the case of fiat money, since in that case the value of money 
is zero and m is undefined.)

3.  Chapter 6:  The value of labor power is identified as the value of the 
subsistence wage bundle.  Thus, under the assumption that all commodities 
exchange at their respective values, the wage paid to each unit of labor 
power engaged in production in a given period is the vector product of the 
subsistence wage bundle times the respective labor values times m.

3.  Chapters 7 and 8:  Surplus labor is identified as the source of surplus 
value and "capital advanced" is distinguished into constant and variable 
capital.  The relative proportion of C and V must be dictated by physical 
production conditions, both to determine their input prices and to 
determine how much inputs must be hired; their absolute levels are dictated 
by this proportion and the given quantity of M advanced.  As indicated 
above, this will also dictate aggregate new labor expended, and thus the 
level of S.

Thus, by Marx's own specifications, the flow of determination is:

physical input/output conditions --->  commodity labor values.

Commodity labor values + given initial M + assumption that all commodities 
exchange at value (+ assumption of commodity money)

-->commodity prices, C, V, L, S, m.

To assert otherwise--e.g., to pretend that M is given, labor values are 
determinate, and commodities exchange at their values--and pretend that m 
is somehow analytically prior to the determination of S, or that L is 
determined independently of the initial M, or that Marx's system does not 
depend on underlying physical input and output conditions-- is necessarily 
to be inconsistent with Marx's assumptions in Volume I.

>The sum of MVA and the constant capital consumed (the "old value" or
>"transferred value") yields the value, or the total price, of commodities:
>         P = C + MVA

Rather, P is "yielded" by the initial value of M, the physical input/output 
conditions, and the assumption that all commodities exchange at their 
respective values.  Leave out the latter two conditions, for example, and 
you can't determine what portion of given M constitutes C.

> >From this theory of total price, Marx derived the total amount of
>surplus-value (S) produced within a given period of time.  This derivation
>may be briefly summarized algebraically as follows:

This is backwards.  S is, again, determined by the physical input/output 
conditions and the assumption that all commodities exchange at their 
respective values, which, when combined with the given value of M, dictates 
how much total output (and thus how much L) can be afforded, total price, 
and the portion of total price that goes to C and V.

>         S    =   P  -  K
>              =  (C + MVA)  -  (C + V)
>              =   MVA  -  V
>              =   mL   -  mLn

(Note that the assumption that V=mLn depends critically on the restrictive 
assumption that all commodities exchange at their respective values; this 
will not hold in general, since in the general case individual prices of 
wage bundle goods are not each proportional to values by the factor m given 
by the inverse of the value of money.)

>              =   m(L  -  Ln)
>         S    =   mLs
>where K represents the cost price of commodities (= C + V), Ln the
>necessary labor-time or the time required for current labor to reproduce
>the equivalent of variable capital (= V/m),

see above, in light of which S = mLs is an inference that obtains only 
under special, very restrictive conditions.

>and Ls the surplus-labor time.
>4.  Partial explanation of C and V
>At the high level of abstraction of Volume 1, Marx provisionally assumed
>that the initial givens of constant capital and variable capital are
>proportional to the labor-time embodied in the means of production and
>wage goods, respectively.  Marx made this provisional assumption because
>the price of individual commodities, and hence of groups of individual
>commodities, like the means of production and wage goods, have not yet
>been determined in the analysis of capital in general in Volume 1.  The
>microeconomic assumption of proportionality between price and labor-time
>for individual commodities is the only one consistent with the
>macroeconomic labor theory of value developed in Volume 1.

Agreed, and embodied labor times, and thus commodity prices in V. I, can 
thus only be determined with reference to physical production conditions.

>However, it is important to emphasize that this provisional assumption (or
>partial explanation of C and V) plays no role in the DETERMINATION of
>constant capital and variable capital, and hence plays no role in the
>determination of the total value and surplus-value, which is the main
>conclusion of Volume 1.  The magnitudes of constant capital and variable
>capital are not determined as proportional to the labor-times embodied in
>the means of production and wage goods, respectively.  The physical
>quantities of means of production and wage goods play no role in Marx's
>theory of value and surplus-value.  Instead, value and surplus-value are
>determined (in part) by the magnitudes of constant capital and variable
>capital, which are taken as given, as quantities of money-capital invested
>to purchase means of production and labor-power in the first phase of the
>circulation of capital, whether or not these quantities of money-capital
>are proportional to the labor-times embodied in the means of production
>and wage goods.

In light of the foregoing, these statements are simply and demonstrably 
inconsistent with the assumptions that the initial M is given, that labor 
values are determinate and proportional to commodity prices via the factor 
m (which is itself only determinable from physical production conditions), 
that constant capital represents the expenditure on means of production and 
variable capital represents expenditure on labor power inputs.  One 
**cannot** simultaneously and coherently maintain these assumptions and the 
statements you make here.

Enough for now, have a good weekend,


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