Careful readers may have noticed that, although I have argued that all
physical surpluses in every period must be positive for the FMT to be true, I
have proven only that they must be non-negative. I will now show that they
must indeed all be positive.
Assume a two-economy with a zero physical surplus of means of production (good
1), and a positive physical surplus of the consumption good (good 2). This is
the familiar example of two departments in simple reproduction, in which the
means of production produced exactly replace those used up. Now imagine that
the price of good 2 is zero. Simultaneist "profit" is thus
m = p1*0 + 0*E2 = 0.
To prove that this case contradicts the results of the FMT, it is also
necessary to show that surplus-labor, as defined by the simultaneous
dual-system interpretation, can be positive. Thus, imagine that good 2 is
produced by means of living labor alone, and that Department II workers
receive less of good 2 as wages than they produce. The amount of labor-time
needed to reproduce their means of subsistence is less than the amount
extracted from them; surplus-labor in Department II is therefore positive. If
the real wage rate and the intensity of labor are the same in both
departments, then clearly surplus-labor is also extracted from Department I
workers. Thus, unless all physical surpluses are strictly positive in every
period, this interpretation implies that positive surplus-labor can be
extracted without yielding profit.
The key assumption here is that the price of good 2 is zero, which may seem to
be an unimportant curiosity. Yet the equalization of simultaneist profit
rates may require that one or more goods have a zero price. In other words,
the scenario outlined above may be the equilibrium solution.
Examine Table 3. The (equalized) real wage rate is 0.5 units of good 2 per
hour of labor. The unit "value" of each commodity, according to the
interpretation in question, is again 1, so the top set of figures represent
both physical and "value" magnitudes. Given the physical quantities, no set
of positive simultaneist prices will result in an equalized profit rate. The
only equilibrium solutions in which one price is positive and neither is
negative are those in which p1 > 0 and p2 = 0. At these prices, the
equalized profit rate is zero. Yet surplus-labor is extracted in both
departments.
--------------------------------------------
Table 3
POSITIVE SURPLUS-LABOR BUT ZERO SIMULTANEIST PROFIT
(with equalized wage rate, and equalized profit rate, non-negative physical
surpluses, and simple reproduction in every "period")
PHYSICAL AND "VALUE" QUANTITIES
===============================
Good 2 Living Surplus-
Dept. Good 1 (Wage) Labor Labor Output
I 2 1 2 1 2
II 0 3 6 3 6
tot. 2 4 8 4
PRICES AND PROFITS
==================
Costs
Unit ----------------------- Total
Dept. Price Good 1 Good 2 Total Price Profit
I 1 2 0 2 2 0
II 0 0 0 0 0 0
tot. 2 0 2 2 0
-------------------------------------------
All this occurs without a negative physical surplus of either good. There is a
zero surplus of good 1 (1 unit used, 1 unit produced) and an 2 unit surplus of
good 2 (4 units paid as wages, 6 units produced). Thus, the non-negativity of
all physical surpluses in every period, even under the strictest equilibrium
assumptions, is unable to guarantee that "profit" will be positive when
"surplus-labor" is positive, as these terms are defined by the simultaneous
dual-system interpretation. All physical surpluses must be strictly
positive.
VII. The Temporal Single-System Interpretation
The results to this point have been negative. It might therefore be thought
that, no matter how Marx's value theory is interpreted, surplus-labor turns
out not to be the sole source of profit. This is not the case; the temporal
single-system interpretation (e.g., Ernst (1982), Carchedi (1986), Kliman and
McGlone (1988), Giussani (1991-92), Freeman (1995), Maldonado-Filho (1997),
Ramos (1997)) does imply that surplus-labor is both necessary and sufficient
for profit to exist. More precisely, although negative (positive) nominal
profit and positive (negative) surplus-labor can coexist, real profit is
positive (negative) when surplus-labor is positive (negative).
According to this interpretation, "surplus-labor" is defined, just as in the
newer simultaneist interpretations as living labor minus the labor-time
equivalent of the money wage:
s = lx - (1/TMELT[t])w[t]lx.
Note, however, that variables are now defined within historical time (the
subscript t stands for the start of period t; thus t+1 is the end of period
t). In particular, TMELT[t], the temporalist monetary expression of
labor-time,
differs from SMELT in that the relation between money and labor-time at the
times
of input and output are not constrained to be equal.
"Nominal profit" is interpreted as m(N) = p[t+1]x - p[t]Ax - w[t]lx. "Real
profit,"
however, deflates sales revenue (p[t+1]x) at the end of the period in order to
remove the effect of inflation in the monetary expression of value:
m(R) = (1/[1+i])p[t+1]x - p[t]Ax - w[t]lx,
where i is the rate of inflation in the monetary expression of value, i.e.,
the relative change in TMELT:
i = (TMELT[t+1] - TMELT[t])/TMELT[t].
TMELT[t+1] is defined as the ratio of the money price of output of period t to
the
sum of dead and living labor used to produce it:
TMELT[t+1] = p[t+1]x/([1/TMELT(t)]*p[t]Ax + lx)
= TMELT[t]*p[t+1]x/(p[t]Ax + TMELT[t]lx),
so that 1+i = TMELT[t+1]/TMELT[t] = p[t+1]x/(p[t]Ax + TMELT[t]lx). Hence,
m(R) = (p[t]Ax + TMELT[t]lx) - p[t]Ax - w[t]lx = TMELT[t]lx - w[t]lx,
and therefore,
m(R) = TMELT(s).
This looks very similar to the proportionality between surplus-labor and
profit that was derived from the newer simultaneist interpretations. We saw
that, despite that proportionality, these interpretations implied that
surplus-labor was insufficient and probably unnecessary for positive profit to
exist. The problem is that the simultaneist monetary expression of labor-time
can be negative, zero, or infinite. An examination of the equation
determining its temporalist counterpart, TMELT, shows to the contrary that if
the
initial condition TMELT[0] is positive and finite, then the subsequent terms
of the
J-series will be positive and finite as well if prices are positive. The
proportionality between surplus-labor and "real profit," together with this
result on TMELT, imply that
surplus-labor is both necessary and sufficient for the existence of positive
"real profit," according to the temporal single-system interpretation.
VIII. Conclusion
It is now generally conceded that, in simultaneist value theory, value theory
plays no role in explaining the dynamics of capitalism (see Duménil and Lévy
(1997:16)). Yet many simultaneists seem untroubled by this. They argue that
value theory is not meant to play that role. Instead, the "core of the
explanatory power of the labor theory of value lies in the analysis of
exploitation" (ibid.) and, they maintain, their theories do show that profit
arises from the exploitation of workers. In particular, the FMT has often
been cited as proving that, in simultaneist interpretations of Marx's value
theory, profit will be positive only if surplus-labor has been extracted.
This paper has demonstrated, to the contrary, that simultaneism and the
exploitation theory of profit are incompatible. The FMT, grounded in the
standard simultaneous dual-system interpretation, holds only when a positive
physical surplus of every use-value is produced in every "period," a postulate
that this paper has exposed as extremely implausible and completely
unnecessary for social reproduction to take place. It has also been shown
that the extraction of surplus-labor is insufficient and probably unnecessary
for the existence of profit according to the more recent "New" and
simultaneous single-system interpretations. A choice must be made between
simultaneism and the exploitation theory of profit.
Yet if simultaneist value theory plays no role in explaining the dynamics of
capitalism, and if it is also incapable of explaining the origin of profit (a
putatively "static" problem), one is entitled to ask whether it has any role
to play at all. In contrast, temporalist value theory, which provides a
value-theoretic fabric for the explanation of capitalism's dynamics, also
succeeds in coherently locating the origin of profit in the extraction of
surplus-labor.
Thus, what the present paper reveals is that Marx's value theory is far more
of a "package deal" than has hitherto been recognized. The attempts to
fragment it into "dynamic" and "static" aspects, and to reject the former
while embracing the latter, do not succeed. When his value theory is given a
static interpretation, not only do his explanations of dynamic events, such as
the falling tendency of the profit rate, come out wrong, so does his
explanation of an important "static" event, the secret of profitmaking! This
suggests that, contrary to the established wisdom of the last century, Marx's
value theory is internally consistent, even to the point of being an
inseparable whole.
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