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

From: Ian Wright (wrighti@ACM.ORG)
Date: Thu Jun 08 2006 - 13:03:38 EDT

```Hi Paul & Allin

>  All production flows could be so qualified, but not his prices
>  whose dimension will remain units of numeraire per unit of x.
>  Your treatment of r as a price is still inconsistent since
>  it is of dimension \$t^{-1}\$

You think there is a dimensional problem because you conflate the
price of money-capital with profit income.

The price of money-capital, like the price of any commodity, is an
exchange ratio against money. It has got nothing to do with time.

In contrast, profit income is the monies received in exchange for
quantities of money-capital. The quantity of money-capital supplied is
quantitied by the length of time of the production period.

These are two different things. Capitalists do not receive the price
of money-capital, they receive profit income in exchange for
quantities of it.

If that is too compressed the following expands on the above.

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. Quantities of
money-capital fund the period of production. The buyers of
money-capital, that is the firms, require money-capital in definite
proportions that is constrained by the material process of production.
Hence, in the circular flow the rate of profit is *both* a price and a
function of the maximum eigenvalue of the input-output matrix
augmented by workers consumption.

The price of money-capital is certainly a very interesting theoretical
object, and given the capital controversies, this is hardly
surprising. But not inconsistent. The circular flow concept of
money-capital preserves Sraffa's insights regarding the rate of
profit. Once you've fully assimilated theorems 5.1, 6.1 and 6.2 of the
paper you will understand this point. The price of money-capital is
equivalent to the rate of profit of Sraffa's surplus equations.

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.

Imagine a capitalist supplies a quantity of 10\$ of money-capital to
fund production for a year. The prevailing rate of profit is r=10%. So
the price of money-capital is r=0.1\$ per \$. What is the profit income
the capitalist earns on the investment during the year? Like any other
commodity we multiply the quantity by the price. In this case it is 10
x r, or 10\$/year x 0.1 \$/\$ = 1 \$/year.

That interest is earned per annum does not imply that the price of
money-capital is related to time.

>  "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. 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.

>  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.

>  In reality production is of course not smooth. Hence, within a
>  production period, a firm will have a partial stock of working-capital
>  and a partial stock of commodity-capital and unfinished goods etc.
>  This level of detail is abstracted from in linear production theory.
>  ------------------
>  Paul
>  It is in Sraffa, I agree, but by introducing money capital
>  as a category which is not there in Sraffa you have to deal
>  with it.

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

>  As I said in private email earlier that throws
>  you into the deep end of joint production, since each
>  production process has as output a commodity, and a stock
>  of cash.

You'll need to explain better why introducing the concept of
money-capital to an input-output model necessitates joint production.

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,
-Ian.
```

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