Re: [OPE-L] Ajit's Paper on Sraffa and Late Wittgenstein

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Thu Jun 08 2006 - 17:40:36 EDT

Assume an arbitrary numeraire equation that fixes the scale of the
price system. In Sraffa's model prices are money units per units of
commodity-type. In a circular flow representation of Sraffa's
equations the price of money-capital is no different: it is money
units per unit of money-capital, with dimensions $/$, equivalently a
dimensionless ratio.

Note that this does not imply that a capitalist can supply
money-capital for a nanosecond and receive its price.

At this point you are surely conceding that what you call
the price of money capital has dimension t^-1

Continuing with the dimensional analysis: in Sraffa's model quantities
are measured in units of commodity-type. So quantities of the
money-capital commodity are measured in money units. If we wish to be
explicit about the length of time represented by the production period
then the dimensions are money units per unit of time.
No this is not right. The production rates are in units of tons
of corn per year. The prices are in oz of gold per ton of corn.
The revenue flow from sales is tons of corn /year x oz gold / ton corn
and hence oz gold per year. 

If we consider a two year production period, the prices do
not change, but it we consider a two year period the profit
will double - this is because the profit is a rate per year,
thus what you call the 'price of money' is not a price at all.

>  "It is not until capital is money-capital that it becomes a commodity,
>  whose capacity for self-expansion has a definite price quoted every
>  time in every prevailing rate of interest."
>  Marx, Capital Vol. 3.
>  ---------------
>  Paul
>  Marx is being vulgar here.

I'm not sure what to make of your comment. My feeling is that Marx is
concerned to explain all the value forms of the capitalist economy,
from the simple to the most esoteric and fetishistic. 
Marx has no theory of the rate of interest.


Money-capital is
a form of value that requires explanation in terms of underlying
labour-time transfers. Sraffa's labour-value accounting cannot do this
job because it does not count the labour-time worked to produce the
goods that are bought with the profit-income from the sale of
money-capital. Sraffian labour-value accounting gets struck at prices
of production and cannot advance to the analysis of higher forms of
value. I think that rather than cherry-picking from Marx those aspects
which we find agreeable or disagreeable, we should try to understand
the unity and consistency of this theoretical framework.

For example, once Sraffa's labour-cost accounting error is fixed, r is
also equal to Marx's S/(C+V), which has dimensions
labour-hours/labour-hours, also equivalently a dimensionless ratio.

It is important to distinguish the flow rate of profit from the
stock rate of profit. The flow rate refers to the proportion
of current labour that it devoted to the production surplus goods 
relative to the remainder of social labour. The stock rate
refers to the number of people producing surplus goods  divided
by the number of person years required to construct the capital stock.
The flow rate is a dimensionless quantity, the stock rate has
dimension 1/t . Marx does not always distinguish  clearly
between the two because he still uses single production period
analysis for most of his work.

Each index tells you something useful about the economy, but
they tell you different things.

>  In the circular flow model there is both working-capital and
>  commodity-capital. However, there is not an identifiable "point in
>  time" when a firm both owns the working-capital and the
>  commodity-capital that was bought with it. That would not make any
>  sense.
>  -----------------------
>  Paul
>  It makes sense because of the stochastic nature of transactions
>  which requires cash balances to ensure reproduction ( see my draft
>  on money which you have ).

You must not have carefully read what I wrote. The stochastic nature
of transactions is not relevant. I am modelling an exchange economy:
money is exchanged for goods. At the completion of the transaction an
economic agent cannot have both the money spent and the good received.
The point is that each capitalist is both a buyer and a seller.
If one capitalist buys inputs another sells them, on average
they are all buying and selling at the same time. The rate will
be stochastic, the deviations in cash balances from the mean
will be subject to noise with a Poisson spectrum.


 What has introducing money-capital go to do with a requirement
to model partial stocks and unfinished goods within a production

The point is that Sraffa does not have money capital, he only
has commodity capital. If you introduce money capital you have
to augment the Sraffian accounts which deal only with labour
inputs and inputs of means of production, with an additional
column on each side of the equation. On one side it represents
the stock of coin held by firms in order to start out production,
on the other side it represents the stock of coins that the firms
have after production has continued. In your simple case this
will be the same in each case, but if we allow an industry producing
the numeraire and assume that this is gold or silver, the stock
of gold will go up each cycle.


My feeling is that you are introducing extraneous matters, which may
be relevant for deepening the model. But for the purposes of critique
I am content to work within Sraffa's single production framework.

Best wishes,

I am not introducing it. You introduced the concept of money capital.
I am just pointing out that if you introduce this concept then
your accounting system has to be made more complicated.

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