# [OPE-L:4430] "A Contribution ...," Part III

andrew klima (Andrew_Kliman@msn.com)
Tue, 18 Mar 1997 11:51:31 -0800 (PST)

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The Constancy of the "Vintage" Labor Unit Values

The vintage labor notion thus seems to be able to rescue the simultaneist
"labor theory of value": the simultaneist profit rate is replicated, and this
is accomplished without doing violence to the simple facts of economic
dynamics. This rescue operation does, however, come at a price.

A constant price, to be precise. Dividing the total value figures in Table 2
by the corresponding corn output figures, we see that the unit value of output
always equals 2. Dividing the constant capital figures by the corresponding
corn input figures, we arrive at the same result. This is by no means an
accidental consequence of this particular illustration. It holds generally.
Equation (2') implies that Wt/Wo = Ht/Ho, so that Wt/Ht = Wo/Ho. According
to (1'), the unit value of the commodity in period t is WtTt = (WtLt)/(1 -
at) = Wt/Ht, which equals Wo/Ho, a constant. Thus, according to the vintage
labor notion, **the unit value of the commodity never changes, no matter how
much productivity varies**. Likewise, the unit value of constant capital can
never change. We have seen that (3) implies that Wt-1Kt = (WtLtat)/(1 - at).
The unit value of constant capital is (Wt-1Kt)/at, which thus equals (WtLt)/(1
- at) = Wt/Ht = Wo/Ho.

Therefore, according to the vintage labor notion, the value of the commodity
is not determined by labor-time – variations in the labor-time needed to
produce it fail to influence the magnitude of the commodity's value.
Moreover, even the relation between value of constant capital and value added
is determined independently of labor-time. Since Wt/Ht = Wo/Ho, the value
added per unit of output, WtLt, equals (Wo/Ho)HtLt = (Wo/Ho)(1 - at).
Similarly, since the total value per unit of output equals Wo/Ho, the
remaining portion of value, the constant capital-value per unit of output,
Wt-1Kt, equals (Wo/Ho) - (Wo/Ho)(1 - at) = (Wo/Ho)at. Hence, the *sole*
influence on the relation between value transferred and value added, according
to the vintage labor notion, is at, the physical "capital/output" ratio.

Table 4 illustrates these results for the production of one unit of the
commodity, assuming that Wo = 1 and Ho = 0.2. We see that the value of the
commodity always equals 5, no matter how much the labor needed to produce it
varies. The relation between value transferred and value added, moreover, is
the same in periods 1 and 5, 2 and 6, etc., even though the amounts of labor
needed to produce the commodity differ quite markedly, because the physical
"capital/output" ratios are the same.

Table 4

STATIONARITY OF "VINTAGE" LABOR UNIT VALUES

t at Lt Ht Wt Wt-1Kt WtLt WtTt
1 16.00 0.02 0.061 0.306 0.1 4.9 5
2 197.00 0.34 0.003 0.017 1.7 3.3 5
3 0.01 0.66 34.000 170.000 3.3 1.7 5
4 3.00 0.98 0.007 0.033 4.9 0.1 5
5 6.00 0.02 0.163 0.817 0.1 4.9 5
6 0.05 0.34 13.200 66.000 1.7 3.3 5
7 82.00 0.66 0.004 0.021 3.3 1.7 5
8 20.00 0.98 0.001 0.005 4.9 0.1 5

What accounts for these results? According to Marx, commodities' values
vary inversely with productivity:

"The value of a commodity would therefore remain constant, if the labour-time
required for its production also remained constant. But the latter changes
with every variation in productivity. … The value of a commodity, therefore,
varies directly as the quantity, and inversely as the productivity, of the
labour which finds its realization within the commodity" [Marx 1977, pp.
130-31].

When, for instance, productivity doubles from one period to the next, the unit
value of the commodity falls in half. This, however, is only true if the
labors of the two periods are *weighted as equal*. According to the vintage
labor notion, on the contrary, a unit of labor of the latter period produces
double the value that a unit of labor produces in the former period, which
exactly cancels out the decline in labor-time per unit of output, and thus the
commodity's value remains unchanged.

The Monetary Expression of Use-Value

Professor Foley seems not to have recognized that, if his notion that labor
of different "vintages" are incommensurable is right, then the very measure
for which he has become famous, the "value of money" or its reciprocal the
"monetary expression of value" (MEV), is wrong. To be sure, one may take the
ratio of money value added to the actual living labor extracted from
productive workers, but according to the vintage labor notion, the latter is
not the amount of *value added* measured in labor-time. Labors of different
productivities, in this view, produce unequal amounts of value, so the
relation between money value added to total value added is not the same as the
money value added divided by living labor. In any given period, this does not
matter – any given period may be taken as the "base period" – but if the
amounts of living labor actually extracted are incommensurable, then so are
the ratios that have them as their denominators (or numerators), and the
procedure for which Professor Foley is noted cannot produce a consistent time
series.

To correct this problem in conformity with the vintage labor notion, the
amounts of living labor extracted in different periods need simply to be
weighted according to their use-value productivities. In the case of a single
sector, where Pt is the output price of period t, measured in money per unit
of output, the measure of the monetary expression of value that Professor
Foley has heretofore employed is

mev(t) = (Pt[1 - at]Xt)/(LtXt)

whereas it should be, according to the vintage labor notion,

mev(t) = (Pt[1 - at]Xt)/(WtLtXt).

Once this is done, what are the implications? As we have seen, WtLt =
(Wo/Ho)HtLt = (Wo/Ho)(1 - at), so that the corrected MEV is equivalent to

mev(t) = (Pt[1 - at]Xt)/([Wo/Ho][1 - at]Xt).

Accordingly, the base period's MEV is mev(0) = (P0[1 - a0]X0)/([Wo/Ho][1 -
a0]X0) = (P0)/([Wo/Ho]). If we set Wo so that the base period's MEV = 1, we
have 1 = (P0)/([Wo/Ho]), so that Wo = P0Ho. This then implies that

mev(t) = (Pt[1 - at]Xt)/(P0[1 - at]Xt).

Notice that labor-time has disappeared from the denominator of the MEV. In
its place is P0[1 - at]Xt, which we may call the "real net product," since it
is the net product expressed in "real," "constant-dollar" terms. In other
words, it is a measure of *physical* production in period t. And thus, the
MEV has been transformed from a measure of the relation between money value
and labor-time value into a measure of the relation between money value and
*use*-value. It has become a monetary expression of use-value, an index of
inflation (in the non-Marxian sense).

To make this even more clear, note that by dividing the money value of the
net product by the MEV, we should arrive at its labor-time value. Using the
MEV that Professor Foley has heretofore employed, we would have (Pt[1 -
at]Xt)/{(Pt[1 - at]Xt)/(LtXt)} = LtXt, so that the labor-time value of the net
product is the living labor expended. Using his corrected MEV, however, we
have (Pt[1 - at]Xt)/{(Pt[1 - at]Xt)/(P0[1 - at]Xt)} = P0[1 - at]Xt, so that
the "labor-time" value of the net product is the constant-dollar measure of
*use*-value produced, the "real net product."

Analogous results can be obtained in the multisector case, by using the
procedures employed above and the measures developed in footnote 6.

Marx on Values and Productivity

Marx, of course, did not think that commodities' values always remained
constant; perhaps hundreds of passages could be brought forth to prove this,
but the matter seems too obvious to bother. The attempt to reconcile the
determination of value by labor-time with simultaneous valuation and, more to
the point, with the capital-productivity theory of the profit rate that
underlies the Okishio theorem, by means of the notion of vintages of labor, is
therefore a stillbirth.

It may be helpful nonetheless to produce textual evidence that more directly
demonstrates that, according to Marx's concept of valuation, the value
produced by a given amount of labor is independent of the use-value
productivity of that labor. In the second section of the first chapter of
*Capital* I, a work that Marx himself saw through to publication in one
original and two different revised editions, he writes the following:

"Two coats will clothe two men, one coat will only clothe one man, etc.
Nevertheless, an increase in the amount of material wealth may correspond to a
simultaneous fall in the magnitude of its value. This contradictory movement
arises out of the twofold character of labour. ... Useful labour becomes,
therefore, a more or less abundant source of products in direct proportion as
its productivity rises or falls. **As against this, however, variations in
productivity have no impact whatever on the labour itself represented in
value**. As productivity is an attribute of labour in its *concrete useful
form*, it naturally *ceases to have any bearing* on that labour as soon as we
*abstract* from its concrete useful form. The same labour, therefore,
performed for the same length of time, always yields the same amount of value,
**independently of any variations in productivity**. … For this reason, the
same change in productivity which increases the fruitfulness of labour, and
therefore the amount of use-values produced by it, also brings about a
reduction in the value of this increased total amount, if it cuts down the
total amount of labour-time necessary to produce the use-values. [Marx 1977,

Earlier in the same chapter, when first discussing the magnitude of value, he
had written: "How, then, is the magnitude of this value [of a useful article]
to be measured? By means of the quantity of the 'value-forming substance',
the labour, contained in the article. This quantity is measured by its
*duration* ... [Marx 1977, p. 129 emphasis added]. In Marx's theory,
therefore, the labor that creates new value therefore creates it in proportion
to the "duration" of labor, "independently of any variations in productivity."

Thus, when Marx begins to discuss the law of the tendential fall in the
profit rate, he makes clear that he is dealing with the profit rate as a ratio
of labor-times – actual labor-times – and not the productivity of labor in
use-value terms: "We entirely leave here aside the fact that the same amount
of value represents a progressively rising mass of use-values and
satisfactions, with the progress of capitalist production and with the
corresponding development of the productivity of social labour and
multiplication of branches of production and hence products [Marx 1981, p.
325]. It should be noted that, according to the vintage labor notion, on the
contrary, the same amount of value always represents a constant mass of
use-values. The total value of a mass of products is always strictly
proportional to their total mass.

Indeed, the concept that a unit of labor-time always produces the same amount
of value is the cornerstone of Marx's law of the falling rate of profit (which
is the very reason why one needs to make the value created by labor vary with
productivity in order to obtain a "labor theory of value" that conforms to the
Okishian results). As Marx notes, in an example that assumes a labor force of
two million, a constant length and intensity to the workday, and a constant
rate of surplus-value:

the total labour of these 2 million workers **always produces the same
magnitude of value**, and the same thing is true of their surplus-labour, as
expressed in surplus-value, always produces the same magnitude of value. But
as the mass of constant (fixed and circulating) capital set in motion by this
labour grows, so there is a fall in the ratio between this magnitude and the
value of the constant capital [Marx 1981, p. 323, emphasis added].

In another passage discussing the falling rate of profit, Marx contends, in
opposition to the vintage labor notion, that

In so far as the development of productivity … reduces the total quantity of
labour applied by a given capital, it reduces the number by which the rate of
surplus-value has to be multiplied in order to arrive at its mass. Two
workers working for 12 hours a day could not supply the same surplus-value as
24 workers each working 2 hours, even if they were able to live on air and
hence scarcely needed to work at all for themselves [Marx 1981: 355-56].

According to the vintage labor notion, two workers working for 12 hours a day
could supply *more* surplus-value than 24 workers each working 2 hours, if the
use-value productivity of the former were more than twice that of the latter.

Finally, Marx puts the matter most succinctly, when he writes, in opposition
to the Ricardian and post-Ricardian view, that "Nothing is more absurd, then,
than to explain the fall in the rate of profit in terms of a rise in wage
rates, even though this too may be an exceptional case. … The rate of profit
does not fall because labour becomes less productive but rather because it
becomes more productive [Marx 1981, p. 347]." No simultaneist interpretation
is able to make sense of this idea. In both the traditional and vintage labor
interpretations, the maximum profit rate is always a measure of the average
physical productivity of capital, as the neoclassicists would call it, and the
only other determinant of the profit rate is income distribution. According
to the TSS interpretation, however, when productivity rises, the value of
constant capital not artificially devalued as it is in the traditional
simultaneist interpretation, nor is the value added by living labor
artificially revalued upward, as it is in the vintage labor version. And
without the artificial decline in the denominator of the profit rate or the
artificial rise in its numerator, rising productivity can definitely make the
profit rate fall when value is determined by labor-time, as Table 3
demonstrated.