Due to the paper's length, I'm sending it in 3 parts, of which this is the
first. Due to the limitations of email, I've altered notation to eliminate
greek symbols and such.
Andrew Kliman
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Simultaneous Valuation and the Exploitation Theory of Profit are Incompatible
Andrew J. Kliman
Assistant Professor, Economics
Department of Social Sciences
Pace University
Pleasantville, NY 10570 USA
(914) 773-3951
Andrew_Kliman@msn.com
First Draft, January 7, 1998.
For presentation at the IWGVT mini-conference, Eastern Economic Association
Conference, February 27, 1998.
Please obtain author's permission before quoting.
***************
Simultaneous Valuation and the Exploitation Theory of Profit are Incompatible
I. Introduction
Despite their other differences, interpreters of Marx's value theory
universally agree that it claims that the sole source of profit is the
exploitation of workers, i.e., the extraction of surplus-labor. The
proponents of the various interpretations, moreover, all claim to have
replicated this feature of his value theory. The mathematics of their
systems, however, often tells a different story. As I will show, in those
systems in which the prices and values of inputs are determined simultaneously
with the prices and values of outputs, profit may be negative or zero although
surplus-labor is extracted, and profit may be positive although surplus-labor
is negative or zero. In these "simultaneist" interpretations, then,
surplus-labor is not the sole source of profit.
It is well known that the standard version of the dual-system interpretation,
in which values are additive, is incompatible with Marx's theory of profit
when joint products are produced (Steedman (1977)). I will show, however,
that simultaneist interpretations are incompatible with his theory even when
all industries produce single products.
Moreover, all simultaneist interpretations are vulnerable to at least some
aspects of this critique. All of them, I will show, imply that the profit may
be negative although surplus-labor is extracted. In the case in which
production does not require human labor, all of them also imply that profit
may be positive although no surplus-labor is extracted. (In those
interpretations which define the value of the wage as the labor-time needed to
replace wage goods, the coexistence of positive profit and negative or zero
surplus-labor is possible also under much weaker conditions.)
What has limited recognition of this incompatibility until now is theorists'
nearly exclusive focus on cases in which positive "profit" and positive
"surplus-labor" (as defined by simultaneist interpretations) do happen to
coincide. Proponents of the standard, simultaneous dual-system interpretation
have focused on those cases in which a positive physical surplus of every
use-value is produced in each period. Proponents of more recent simultaneist
interpretations have focused on those cases in which the aggregate price of
the "net product" is positive in each period. As I will show, theorems meant
to demonstrate that positive surplus-labor and positive profit imply one
another cannot be generalized beyond these cases. Moreover, I will argue that
such conditions are much more restrictive and much less plausible than is
usually thought.
II. The "Fundamental Marxian Theorem"
The distinctive features of the standard version of the simultaneous
dual-system interpretation of Marx's value theory are, first, that it defines
commodities' values as vertically integrated labor coefficients. Second, it
construes wages in the "price" system as the price of the wage goods workers
receive, and wages in the "value" system as the value of these wage goods.
Third, "surplus-labor" is defined as living labor extracted minus the value of
these wage goods.
A set of theorems of Okishio's (1993a, 1993b) have been dubbed the
"fundamental Marxian theorem" (FMT) by Morishima (1973). The FMT is often
cited as having shown that, according to this interpretation, the extraction
of surplus-labor is necessary and sufficient for the existence of profit when
no joint products are produced (see, e.g., Howard and King (1994:230, 239)).
Yet the FMT in fact depends crucially on a condition which will be shown below
to be extremely restrictive: in every period, a positive physical surplus of
every use-value is produced. That is, more of each use-value is produced in
every period than is used throughout the economy (including for workers'
consumption) in the same period.
In this interpretation, "profit" is simply the vector of physical surpluses
valued at end-of-period (replacement) prices. Using the usual input/output
notation, **footnote 1** the (column) vector of physical surpluses is E = (I -
A - bl)x, so simultaneist profit is
m = pE,
where p is a row vector of unit prices. Unit values are defined as the (row)
vector of vertically integrated labor coefficients v, so surplus-labor, s, is
the living labor extracted minus the "value" of wage goods: s = lx - vblx.
But since v = l(I - A)-1, v(I - A) = l, and thus lx = v(I - A)x.
Surplus-labor can thus be expressed as s = v(I - A)x - vblx = v(I - A - bl)x,
or simply as
s = vE.
Thus, in this interpretation, "profit" and "surplus-labor," pE and vE, are
simply one and the same vector of physical surpluses valued in two different
ways.
It is then obvious that the FMT holds when a positive physical surplus of
every use-value is produced, i.e., when all elements of E are positive. Given
only that no prices or "values" are negative and some of both are positive,
both the aggregate price and the aggregate "value" of the physical surplus
vector, "profit" and "surplus-labor," must also be positive. Because all
physical surpluses are positive, it does not matter that prices and values
differ, or by how much; a set of strictly positive physical surpluses valued
according to either must be positive.
It is, however, equally easy to see why the FMT fails to hold unless all
physical surpluses are positive. Once there is even a one-unit negative
physical surplus of even one use-value, it matters that values and prices
differ. The aggregate worth of the physical surplus vector can then be
negative when valued at prices, even though it is positive when valued at
"values," and vice-versa.
Assume, for instance, that 1 more unit of good A is used throughout the
economy than is produced; the physical surplus of A is -1 unit. Assume also
that there are 1000 other goods, and that a physical surplus of 1000 units of
each of them is produced. If the unit "value" of each good is 1, then
simultaneist surplus-labor equals 1*(-1) + 1*1000*1000 = 999,999. Yet if the
unit price of the other goods is 1 and the price of A is 1,000,001, then
simultaneist profit equals 1,000,001*(-1) + 1*1000*1000 = -1. Conversely,
were A's unit "value" equal to 1,000,001 and its price equal to 1, then
surplus-labor would equal -1 and profit would equal 999,999. This proves
that, in this interpretation, surplus-labor is neither sufficient nor
necessary for profit to exist.
This is, of course, a very unrealistic example. Yet as subsequent examples
will demonstrate, the FMT fails to hold even if both price-value differences
and negative physical surpluses are very small in percentage terms.
III. The "New Interpretation" and Simultaneous Single-System Interpretations
In the past two decades, a number of other simultaneist interpretations of
Marx's value theory have also emerged. In the context of the present paper,
the key difference between the standard, simultaneous dual-system
interpretation, on the one hand, and both the "New Interpretation" (e.g.,
Duménil (1983), Foley (1982)) and the simultaneous single-system
interpretations (e.g., Wolff, Roberts, and Callari (1984), Lee (1993), Moseley
(1993), Ramos and Rodriguez (1996)),**footnote 2** on the other, concern their
definitions of wages and surplus-labor.
Rather than defining wages as the price or value of wage goods, these latter
interpretations construe wages as the sum of money paid to workers. To assess
whether surplus-labor is extracted, money wages are converted into the
equivalent sum of labor-time (or living labor extracted is converted into a
money equivalent). These simultaneist interpretations typically convert money
sums into labor-time sums by dividing the former by the economy-wide ratio of
the aggregate "net product" at replacement prices to living labor extracted:
SMELT = p(I - A)x/lx
I call this ratio SMELT, to indicate the "simultaneist monetary expression of
labor-time." The authors in question interpret it as the amount of money
value that represents one unit of labor-time.
In these interpretations, "profit" is defined as the vector of physical net
products valued at end-of-period (replacement) prices, minus the wage bill:
m = p(I - A)x - wlx,
where (I - A)x is the net product vector and w is the money wage per unit of
living labor extracted. "Surplus-labor" is defined as living labor minus the
labor-time equivalent of the money wage:
s = lx - (1/SMELT) wlx.
Multiplying both sides of this last definition by SMELT, we see that SMELT*s =
SMELT*lx - wlx = p(I - A)x - wlx, or, equivalently,
m = SMELT*s.
This result has led proponents of the "New" and single-system interpretations
to claim that they yield an exact correspondence between surplus-value and
profit. Not only is the extraction of surplus-labor necessary and sufficient
for the existence of profit, as proponents of the dual-system interpretation
also claim, but the magnitudes of surplus-labor and profit are strictly
proportional.
That profit is proportional to surplus-labor, however, does not allow us to
conclude that the extraction of surplus-labor is either sufficient or
necessary for profit to exist. A key problem with this claim is that the
factor of proportionality, SMELT, need not be positive. If the "net product"
valued at replacement prices is negative, then so is SMELT. Simultaneist
"profit" is therefore negative although surplus-labor is positive. This
proves that, in these interpretations, surplus-labor is not sufficient for the
existence of profit.
Clearly, this possibility discloses a serious conceptual flaw in these newer
simultaneist interpretations. The flaw stems from their claim that the
aggregate price of the "net product" is the monetary expression of the value
added by living labor.**footnote 3** This claim leads to perverse results
when the price of the "net product" is not positive. Note, for instance, that
when the price of the "net product" and therefore SMELT are negative, these
interpretations imply that a fall in the money wage rate will lead to a fall,
rather than a rise, in the amount of surplus-labor extracted!
The proportionality of surplus-labor and profit also fails to imply that
surplus-labor is necessary for profit to exist. As Dmitriev (1974)
discovered, if we imagine a fully automated economy that produces a positive
"net product" of all use-values — and if, in addition, prices in such an
economy exist and are positive — then simultaneist "profit" is positive, even
though no labor and thus no surplus-labor is extracted.**footnote 4** Note
that SMELT = infinity in this case, so that SMELT*s = (infinity)*0, which
leaves profit undefined. By assumption, however, it is positive.
In reality, of course, human labor is indeed used in production and, if the
aggregate price of the "net product" happens to be positive, then positive
profit and positive surplus-labor (as defined by these interpretations)
coexist. The relevant issue, however, is not whether they coexist, but why.
Unless the theory in question precludes the possibility that the aggregate
price of the "net product" could be positive although no human labor was used
in producing it — and those under consideration seem not to do so **footnote
5**— then we must conclude that it admits the possibility of positive "profit"
without surplus-labor.
NOTES:
1. A = [aij] is a square matrix of input/output coefficients; aij is the
amount of good i used to produce one unit of good j. b is a column vector of
wage goods per unit of living labor, l is a row vector of living labor
requirements per unit of output, and x is a column vector of outputs. I is the
identity matrix.
2. Note, however, Ramos's (1997) critique of simultaneism.
3. See Kliman (1997) for other criticisms of this concept.
4. Dmitriev also claimed to have proven that positive profit can exist
without human labor. Kliman and McGlone (1995), have shown that this proof is
fatally flawed — Dmitriev tacitly assumed that prices are positive when he in
fact needed to prove it in order then to show that profit is positive. It
remains true, on the other hand, that if prices in a fully automated economy
are positive, then "profit" as defined by simultaneism is positive, even
though no surplus-labor is extracted.
5. Foley (1997:19, emphasis in original), in particular, has noted that his
interpretation "is completely general, in that it is consistent with any
theory of price formation …."