[OPE-L:8111] Re: 'Testing Marx or why the law of value holds'

From: clyder@gn.apc.org
Date: Wed Dec 04 2002 - 04:24:26 EST

Quoting gerald_a_levy <gerald_a_levy@msn.com>:

> Andy, responding to Paul  C, in  [8096] wrote:
> > Re your 8093.
> > > > (1) I would be very interested to know your theoretical explanation
> > > > for the correlations that you obtain.
> > > This is a very difficult question.
> > > At one level I would explain it by saying that labour is
> > > overwhelmingly the main non-produced input to capitalist commodities,
> > > and as such it will tend to drive the price system. It is the signal
> > > that shows through the noise of random market fluctuations.
> > Do you mean that wages are more stable than other major costs 
> > due to the fact that labour-power is non-produced?
> The article by Paul and Allin, "Does Marx Need To Transform?"
> (http://www.wfu.edu/~cottrell/vol3.pdf), used input-output data for
> the UK economy in 1984  (published in 1988).   It is not surprising that
> wages were more 'stable' than the prices of other commodities during
> that year.  Remember  Margaret Thatcher? (boo! hiss!)  In the US, also, 
> wages were relatively flat do in large part to the 'concessions movement' 
> initiated by capital.   Here we had Maggie's evil twin brother Ronald
> Reagan (boo! hiss!) as President and Neo-Liberalism was on the 
> ascendancy internationally.
> In solidarity, Jerry

Why the Law of Value Holds - in the style of F&M

I want to address again the question of why prices tend to be
proportionate to values.

I said that I thought the reason was that the labour input to
production was

a) not a produced commodity within the capitalist system

b) a major element of the direct costs of each industry

Gerry paraphrases this as wages being 'stable', but this
is not quite what I mean. What I am saying is that ratio
of aggregate wages to net national product is very close
to the ratio of necessary labour time to total labour time,
and that this in conjunction with points a) and b) constrains
prices to follow values.

Why is the ratio of wages to national product close to
the ratio of necessary to total labour time?

Basically because of regression to the mean.

Given the net national product in Euro and the total number of
hours worked we can deduce the number of minutes
necessary to produce one Euro of national income, call this M.

If we multiply the price of any commodity i  by this number
we get its current exchange value E[i] in terms of national labour.
For any given commodity this exchange value will be
either above or below its actual labour content L[i], according
to whether it is selling above or below value. We know that
E[i]/L[i] must have a mean value of 1, since commodities selling
above and below value must cancel out. Let the standard
deviation of E[i]/L[i] be S.

The necessary labour time is given by the labour content of
the commodities consumed by workers - the labour content
of the wage bundle as the neo-ricardians put it. Now if workers
just lived on a single commodity corn, as occurs in some
neo-ricardian models then expected the standard deviation of wages
relative to necessary labour content would also be S, but
in fact the wage bundle contains thousands of different
commodities. Each of these commodities has a selling price
that is either above or below value, but by the law of large
numbers the standard deviation of the wage W times M
from the actual labour content of the wage bundle will
be much smaller than S.

For instance in a simulation run with the individual commodities
selling up to 20% above or below values I found that
for a wage bundle of 10 commodities I got a 3.5% deviation
of price from value, for 100 commodities a 1.8% deviation,
for 200 commodities a 1% deviation and for 1000 commodities
a 0.3% deviation.

Thus in a real economy with a big wage bundle we can assume
that the wage bill multiplied by the labour equivalent of money
will be very close to the actual necessary labour time.

Now consider all industries. Each of these has a selling
price in labour hours made up of a wages commonent which
is almost exactly equal to the V in labour time used by Marx
in volume I of capital, plus a component C for constant capital,
plus some random profit - determined by market conditions.
For most industries C will again be made up of a large
bundle of commodities and as such will, by the same argument
as applied to wages tend to be purchased for a price very
close to its value. The exception will be a few industries that
process a single raw material - these will have a C which in
money terms will deviate more from value than is normal.

Empirically it is a fact that for most industries labour is the
major cost. We know that the cost of labour WM is very close
to Marx's v or necessary labour time, and also that for
most industries CM will also be close to Marx's c.
That leaves only profit as a random element causing
prices to deviate from values.

But we have reason to believe that there will be a constraint
on the dispersion of profits.

The profit of any individual firm will be influenced by a whole
host of factors - a collection of random un-correlated pressures.
We would therefore expect firms' markups over prime costs
to be normally distributed, as this is characteristic of things
which are the result of a sum of random pressures.
We know the mean of this random distribution - it is
given by the mean markup ratio or rate of profit on turnover.
We would expect this to be of the order of 10 to 20% for typical
economies. We also know that if the mean is say 0.15, that very
little of distribution - say less than 10% of all firms will be
making a loss in an average year - since firms dont survive
long once they start making a loss. Thus we have the mean
of the normal distribution say 0.15, and we know that less than
10% of the distribution falls below 0.0. This is enough to
fully constrain the standard deviation of the distribution
and in practice to make it fairly narrow. This is because
a normal distribution has only two free variables, so two
constraints are enough to characterise it.

It will of course, be understood by those skilled in the
craft, that the figures 10% and 20% above are rough
indicators for the sake of argument.

Thus we have a results that
1.  the standard deviation of the rate of profit on turnover
     has to be small,
2. the price of each product is made up of three components
    wages, constant capital and this random profit markup
3. money wages can be expected to be very highly correlated
    with necessary labour
4. constant capital in money terms will also be strongly
    correlated with constant capital in terms of labour albeit
    not so strongly as wages are to necessary labour
5. thus prices are made up of two components that
    are very close to labour values, plus a random markup whose
    dispersion is narrow

It follows that prices are constrained to be close to labour

The argument above draws heavily on the arguments of
Farjoun and Machover, though I have considerably 
simplified some of the statistical logic.
This type of argument is unfamiliar
to most Marxian economists since the vast bulk of the
Marxian literature makes little use of  arguments about
statistical distributions. However Marx does in one or
two places in Capital use the concept of regression to
the mean - for instance in arguing that the size of a workforce
is an important factor in reduce labour to average social
labour. Ricardo's argument for why the deviation of prices
from values should on average be around 5% also
pioneered this sort of argument.

Michael is of course quite right when he points out that
scientific investigation always takes place within a problematic,
and that the questions one asks are one of the preconditions
of the results one obtains. They are not however the sole
precondition, brute reality is the other. Our problematics
constrain our ability of interrogate reality, they do not
constrain reality itself.

What I found refreshing about reading Farjoun and Machover
almost 20 years ago, was the way that they broke with the
problematic that had dominated Marxian economics for
decades and allowed new questions to  be asked.
Their problematic has opened up a new research program
which is, I believe, proving more productive than the
rather tedious debates about the transformation problem
that were going on before that.

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