Alan reports an interesting experiment in which he constructed
random i/o tables and computed the ratios between values and prices
of production in them, finding the two to be highly correlated.
This is a test that I have wanted to perform for some time and
I am glad to see that it has produced the anticipated result.
I say anticipated, since one can deduce that this would be the
result from the argument advanced by Machover in a book that
Alan himself edited a dozen years ago. Machovers essential argument
was that the pathological examples that Steedman and his followers
construct, are only feasible in very small i/o tables. Once the
table gets up to a few hundred square, the following effects cut in:
a) the inputs to each industry are drawn from a large random sample of
commodities each of which is independently distributed with respect
to its price of production/value ratio. The law of large numbers
predicts that the expected mean price of production/value ratio
of this aggregate commodity will be 1 and that the standard deviation
will be small. This indicates, that were prices of production to
exist, the errors arising from not transforming the inputs would
be low. It also immediately establishes a positive correlation between
prices of production and values.
b) since labour enters into all products to a greater or lesser extent,
and since the rate of profit is normally <<1, this sets strict limits
on the possible deviations of prices of production from values. It was
on the basis of this argument that Ricardo settled on the labour theory
of value as being 93 orrect. Machover gives more precise estimates
in his paper.
Alan is probably right to say that the reason why labour is the substance
of value rather than cheese or brown paper being the substance of value,
has to do with the degree of inter-connected ness of the branches of the
economy. Labour is a universal, polymorphous resource, used in all branches,
few other products get near it in these respects.
Alan, please note that to hold to the classic labour theory of value does
not imply that all prices are exactly values, it is to imply that values are
an attractor for prices - it determines what they oscilate around.
Paul Cockshott (wpc@cs.strath.ac.uk)