Does the LTV have a mechanism? (continued)
===============================
[Note: Heading towards the home stretch now, though it might take a
couple more postings than I thought. Thank you for your patience. I
intended to send this message hot on the heels of the last one in
case anyone was in danger of biting his/her fingernails to the quick,
but got caught by a hiccup in the pen-l mail system, whereby this
posting bounced back to me a few times. Thanks to the folks at
csuchico for a quick fix.]
1. Here is a gift horse whose mouth we shall have to examine
carefully.
2. Capitalists *don't* calculate labor-contents. But they *do*
calculate profit rates, and act on those calculations, so there is a
theoretical warrant for the idea of a *tendency* towards the
equalization of the rate of profit. Now, under certain conditions (the
rate of profit is "small" and/or the dispersion of the value composition
of capital across industries is limited), the equalization of profit rates
will produce a tolerable approximation to relative prices = relative
labor-values.
3. So we *can* produce a mechanism for the LTV (as
approximation) after all -- only it is "parasitic" on the mechanism for
generating Sraffian prices, which justifies the idea that the LTV is
theoretically redundant! (I think that Gil Skillman may have something
like this in mind.)
4. But this is wrong. Farjoun and Machover show that if the LTV is
cast in a probabilistic form, one can derive a stochastic version of
price-value proportionality without appealing to a uniform rate of
profit (indeed, a uniform rate of profit is inconsistent with their
stochastic framework).
5. The probabilistic version of the LTV goes like this. Define
"specific price" as the ratio of money-price to labor-content (or labor-
value) in any given transaction. (Following both Smith and Keynes, F
and M find it convenient, in the definition of specific price, to express
money-price not in the monetary unit of account itself (dollars,
pounds) but in units of the average wage.) Specific price is conceived
as a random variable, and the question is, What does its distribution
look like? On the basis of very general statistical considerations,
having to do with the fact that an economy is a system with very high
"degrees of freedom," and very general facts such as the stability of
the shares of labor and capital in total value-added over time, F and
M leverage their way to some relevant inferences.
6. First of all, they infer that specific price has a mean value of about
2. (That is, on average, an embodied labor-content of n hours sells
for 2n times the average hourly wage.) On somewhat less secure
ground (but still very plausibly, IMO), F and M go on to infer that the
distribution of specific price is likely to be approximately Normal
(leaving aside industries whose products' prices have a high rent
element), and will have a relatively "small" standard deviation -- they
guesstimate about 1/3. (As a proportion of the mean this is small, for
instance, compared to the standard deviation of profit rates as a
proportion of their mean.)
7. If the dispersion of specific price is indeed "small," this is to say
that labor-values will be quite good as predictors of price -- if not for
individual commodities, narrowly defined, then for collections of
commodities such as a typical firm's set of inputs, or the workers'
consumption bundle. In arriving at the conclusion that the standard
deviation of specific price is "small," F and M *do* appeal to
considerations relating to the rate of profit, but not -- once again -- to
its uniformity, or even approximate uniformity. They rely on (a) the
Normality assumption, plus (b) the idea that there must be a *very*
low probability of specific price being less than one, i.e. of finding a
commodity selling for a price that does not suffice to cover the cost of
all the labor-power used directly and indirectly in its production (never
mind taxes and interest charges). Thus, in effect, they rely upon the
idea that there are systematic forces causing (and enabling) capital to
shun continuing losses (so that pre-tax and pre-interest loss-making is
a very low-probability event).
8. Thus F and M supply a definite mechanism supporting a stochastic
version of the LTV, that is *not* parasitic on the Sraffian uniform-
profit condition. Notice, however, that this mechanism is in a sense
"statistically emergent." It is certainly not the direct result of agents'
paying attention to the labor-content of commodities in the mode of
Smith's hunters; and it would seem to be "invisible" to methodological
individualism. On the other hand, the "probability law" in question
clearly must be realized via the interactions of a multitude of capitalists
(and workers). The situation is analogous -- this is still Farjoun and
Machover -- to statistical mechanics. The ideal gas laws, for instance,
are "statistically emergent" from the interaction of millions of individual
molecules.
9. But here is a further concern for future treatment. Suppose you
grant the above, at least for the sake of argument. You may still
wonder: But after all, what is really special about labor? Couldn't you
do the same sort of statistical number using oil-content, timber-content
or what-have-you? Why is the LTV of any more intrinsic significance
than the OTV or the TTV?
End of seventh message.
==========================
Allin Cottrell
Department of Economics
Wake Forest University
[EMAIL PROTECTED]
(910) 759-5762
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