I want to reply to several postings that
have come up on this issue. The first was
Andrews point that in computing labour contents
from i/o tables one has to deal with data supplied in
price form, and that therefore one is using prices
to predict prices.
Secondly I want to deal with Alejandro's points to
the effect that one must use production prices rather
than values to approximate market prices, since production
prices are at the right level of abstraction.
Do Labour coefficients presuppose market prices?
------------------------------------------------
There is a real problem relating to the adequacy
of the statitistics currently available for testing
Marxian value theories. In principle what one would
like to have would be
1. A matrix of product flows in use value terms.
2. A vector of current commodity prices.
3. A vector of labour expended per industry.
4. A vector of gross outputs per industry in use
value terms.
Such a collection of vectors and matrices would be
very large for a real economy, probably containing
of the order of millions of distinct products. Although
it is now within the capability of technology both
to collect such matrices and to perform iterative
approximations to labour values using them, we dont
have access to them as the statistics are not
currently collected.
What we do have access to are aggregate i/o tables
which group whole industries together as if they
produce a single product. For something relatively
homogenous like electrical energy, grouping a whole
industry together could still allow you to have the
entries in use value terms - so many megawatts of
electricity used in car production, so many megawatts
used in plastics production etc. But when one groups
a whole industry like plastics into a single column
one is effectively aggregating all of the different
plastics PVC, polyurethane, polyethelene etc into
a single composite product : plastic. The only way these
can be aggregated is if they are converted into a
common unit, which, in a capitalist economy is money.
Thus aggregate i/o tables are constructed in terms of
monetary valuations of the product flows between sectors.
This then appears to create the problem that as soon
as you try to extract from the i/o table a set of labour
values, these have been contaminated by the market prices
prevailing when the table was constructed. This would
appear to vitiate any attempt to compare market prices
with labour values.
I wish to argue that this objection is overstated. It has
some limited validity - relating to the contamination
arising from differences in wage rates - but as a general
principle it is false.
Aggregation and units of measurement
------------------------------------
Although the output of the plastics industry is measured
by government statisticians in $ terms, it is true that
one could also aggregate it in other ways - by weight or
volume for example.
If the plastics industry has an output of $2000,000,000 it
also has an ( unknown output ) of x million tons. If one
aggregates by weight, then the relative proportion of PVC
in the output will be different from when one aggregates
by price, but as an aggregate figure we are not really
interested in the sub-components of the aggregate.
It is also true that one could measure the output in weight
terms in either imperial or metric tons without affecting
the principle of the measurement.
Each figure given in the i/o table can thus be considered
as decomposable in the following fashion
$A = B (units of measure) x C ( $ per unit measure )
A is the quantity in dollars shown in the table, B is a
quantity in some natural unit of measure - tons of coal, watts
of electricity, litres of petroleum
etc, and C is the price in dollars per ton of coal etc.
Clearly one can scale ones units of measure provided that
one scales the units in which prices are measured at the
same time. So that a figure for a cell in the
iron colum could be seen as, Light Tools use
$1000,000 iron = 100,000 kilos iron x 10 ( $ per kilo)
could also be expressed as
$1000,000 iron = 220,000 lb iron x 4.545 ( $ per lb )
since the natural units are arbitrary we can choose
the unit of measure to be that amount of the substance
in question that is produced annually. If the gross
product of the iron industry is shown as:
$4billion iron = 1 ironunit iron x 4 billion($ per ironunit)
where we have implicitly defined 1 ironunit to be
400,000,000 kilos. Using these 'ironunits' one can then
re-express the cells of the i/o matrix in terms of
use values in iron units. The intersection of the
Iron column and the Light Tools row can now be expressed
as
0.00025 ironunits
and similarly for all cells in the product flow matrix,
they become numbers in terms of specific units of a use
value.
We then take the gross output row and express it as
1 in all cases and at the same time obtain a price vector
equivalent to the original gross output vector. We then
take the mean hourly wage rate for the economy and
divide the row representing industrial wage bills
by this.
This then gives us what we initially required to test
the theory, points 1 to 4 above. Further calculation
can then proceed without reference to market prices.
We have made an implicit arbitrary choice of units in
which we measure the outputs of the industries in
setting them to be measured in terms of the gross
output of the industry. But the method would be
unchanged if, instead of making the gross outputs all
1, we had drawn the gross outputs in usevalue terms
from a table of random numbers, so long as we make corresponding
adjustments to our initial price vector.
The point is that the choice of use value units in which
prices or values are expressed is entirely arbitrary.
Given any such initial choice we can transform an i/o table
in money into an i/o table in use value terms using these
units.
There is still a source of aggregation error that is
immediately apparent in dividing through the wage row by
the mean hourly wage, in that wage rates differ between
industries. This however, can be explicitly corrected
for. But, it is in principle no different from the
aggregation problems that are present for any other
row of the matrix. If we defined our units of plastic
in terms of volume, then the plastics use of the consumer
electronics industry which uses a lot of foam polystyrene
would be understated relative to that of the garment industry
which uses predominantly higher density plastics, by
the procedure described above. But these are errors
that arise from aggregation rather than the nature of
the units of measure.
Values are at the wrong level of abstraction
--------------------------------------------
Alejandro makes two main points here:
>First of all, when "market prices" are analized it is
>obvious that in a lot of cases we have "rents". This factor
>should be not explained as a simple "random" factor,
>because involves "structural" conditions of the economy. So
>there is a fraction of the economy in which "market prices"
>are not competitive at all.
This point is certainly correct, as is very evident
once one looks at which industries tend to be outliers
in the market price/value distribution. For the economies
that I have looked at the most prominent of these is
petroleum production and petroleum refining. Both of
these are plausibly affected by rent factors.
One gets appreciably better correlations between market
prices and either values or prices of production if these
industries are excluded.
>Secondly, let us look at the remaining "competitive"
>fraction. In this case the "centre of gravity" (or
>"attractor") CANNOT be "value". A couple of quotations from
>Vol III, Ch. 10:
>
> The ASSUMPTION that commodities from different
> spheres of production are sold at their values
> naturally means no more than that this value is
> the CENTRE OF GRAVITY around which price turns
> and at which its constant rise and fall is balanced
> out. (Penguin, p. 279; capitalization added)
>
>After "explaining" the categories of "market value",
>"individual value", etc., Marx says:
>
> What we have said here of market value holds also
> for the PRICE OF PRODUCTION, as soon as this TAKES
> THE PLACE OF MARKET VALUE. The price of production is
> regulated in each sphere, and regulated too according
> to particular circumstances. But it is again the
> CENTRE AROUND WHICH THE DAILY MARKET PRICES
> REVOLVE, and at which they are balanced out in
> definite periods. (Penguin, p. 280;
> capitalization added.)
>
Marx said this, but is it true.
It depends crucially on how strong the tendancy for the
rate of profit to equalise is. If this tendancy is weak, then
prices of production will not be the center of gravity
around which prices will oscillate. This is particularly
true if there is a tendancy of the wage/profit ratio
per industry to equalise. Farjoun and Machover suggest
that the tendancy for the wage/profit ratio to equalise
is stronger than any tendancy for the rates of profit
to equalise. Empirical measurements are certainly not
inconsistent with this hypothesis.
Remember that what Marx puts forward in volume 3 of
capital is both a hypothesis about what happens -
profit rates equalise - and a mathematical procedure
for calculating the consequences of this. In focussing
solely upon the mathematical procedure, you may lose
sight of the hypothesis that makes it relevant. If
the initial hypothesis is mistaken, or seriously overstated,
there is little point in getting to worked up about
the finer details of the mathematical procedure.
Paul Cockshott
wpc@cs.strath.ac.uk
http://www.cs.strath.ac.uk/CS/Biog/wpc/index.html