[OPE-L:3535] Re:returns to scale

From: Paul Cockshott (wpc@dcs.gla.ac.uk)
Date: Fri Jun 23 2000 - 06:49:36 EDT

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At 12:09 22/06/00 -0400, Rakesh wrote:

>Paul C wrote:
> This matrix has
> >properties which include projecting out a vector associating a number
> >- a labour value - with each product.
>If the matrix is defined, then labor values are redundant for the
>determination of relative prices and the average rate of profit. You are
>simply sidestepping the question about the determinateness of the matrix
>before the configuration of relative prices. I.e. the untenable assumption
>of constant returns. You are ignoring the criticism of Jesus Albarracin in
>Ricardo, Marx and Sraffa, eds. Mandel and Freeman.

I dont recall having read that particular article in the collection. If I
have time
I will get it out of the library to check it.

I agree that if the matrix is defined and the distribution of income is defined
and --- and this is critical -- we assume an equal average rate of profit
industries, then labour values are irrelevant to determining the relative

However I am very dubious about the reality of price of production theory
as applied to competitive capitalist economies. It is my impression from the
existing empirical work that it remains to be established that the rate of
profit is independed of the organic composition of capital. Allin and I have
a paper comming out in the Cambridge Journal that shows that for the
US and UK economies the rate of profit is roughly inversely proportional
to organic composition except for a few monopolistic industries.

If you drop the assumption of a rate of profit that is uncorrellated with
organic compositions, then you are back to a volume 1 or a Ricardo chapter
1 theory of value. In which case labour values turn out to be very relevant
for the determination of prices.

> >My assertion is that the matrix exists objectively and determines
> >what the values are.
>This is to treat the technical coefficients as givens as relative prices
>are reconfigured by a change in the distribution of income (I am going
>here by Meek's old review of Sraffa's book and Meek does not even mention
>the problem here).

I think that it is absolutely essential to take the technical coefficients as
our starting point.

It is technical coefficients that differentiate a developed from an undeveloped
economy. Alexandro Valle's work on the relative labour values of maize in
the US and Mexico shows that there is a huge discrepancy, Maize production
requires almost an order of magnitude more labour in Mexico than the US.
This difference is determined by the existence of real things in the US that
do not exist in Mexico - millions of expensive pieces of agricultural
and by differences in climate.

Historical materialism takes the forces of production as its starting
point. It is
these that constrain the range of what is possible in a society. Such
can only change relatively slowly and by immense expenditures of labour.

> I suggest this kind of transformation procedure makes no
>sense at all, while the temporal, sequential, macro method of treating the
>initial money sum of capital does make sense. And it does not make our
>beloved labor theory of value redundant.

I have several objections to this:
1. The whole literature on this is based on what seems to me to be a highly
artificial time period analysis, rather than using continuous
time. I have yet to see any of the advocates of this theory construct a
true dynamic model, which when simulated is capable of reproducing
their results - in particular is capable of generating the equal rate
of profit ( rather than imposing this from outside as a constraint).

2. There is no clear theorisation as to what an initial sum of money capital
means as the social level.
Does is mean the stock of cash in the hands of the public?
Does it mean the sum of bank deposits?

3. However one defines the stock of money in what sense is it initial? At any
instant in time there is a really existing stock of means of production and an
assignment of credit and debit balances to individuals and firms by the banking
system. Whilst the stock of means of production has a non zero sum, the
sum of all monetary entries tends to cancel out. The banking system can
increase the stock of credit balances by creating corresponding debit
balances, so there is in no sense a fixed initial purchasing power.

Over time, the technology matrix changes, and values change in consequence,
but I dont think that this invalidates the treatment of the economy at any
instant in terms of linear models.

I accept that the general rule for capitalist economies is for returns to scale
to increase, but such increasing returns to scale correspond to change in
the technology matrix over time. In electrical power generation, larger
tend to be more fuel efficient, so there was a historical tendancy to increase
the scale of the turbines used from 180Mw , 500MW , 660MW etc.
However these changes came in over a period of many years and are
better treated as changes in technology. At any given year if you wanted
to add 5,000MW to the grid, you had a range of sizes of sets that you
could chose from, you would tend to chose some multiple of the largest
size of set. At any given point in time the production processes can be
realistically represented as a linear or integer programming problem.

Gil raises the question as to whether values should be based
on average or marginal labour required.

I would strongly argue that one should use average labour
required otherwise your national accounts in labour terms do
not add up.

If you express national accounts in terms of labour flows per
annum, you are using the dimension 'persons'. I would say that
a criterion for the accounts be realistic is that the number of
persons that you get for the net value product should be equal
to the number of workers multiplied by the fraction of the year
that they are actively working. Call this P, the average number
of workers active at any one instant.

If you were to adopt Gils assumption of decreasing returns to
scale and his assumption that you should use marginal labour
inputs - i.e., the least productive producer in each industry
is taken to regulate the value of the product, then the value
in labour time of the net national product per unit time will exceed P.

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