# Re: [OPE-L] workers' consumption and capitalists' consumption

From: Ian Wright (wrighti@ACM.ORG)
Date: Wed Jun 07 2006 - 16:45:52 EDT

```Hi Ajit

Apologies for the delay in getting back to you.

> Ian, now I'm almost convinced that you are making a
> conceptual error. Take for example Sraffa's two-sector
> subsistence example:
> 280 qr. wheat + 12 t. iron --> 400 qr. wheat
> 120 qr. wheat +  8 t. iron -->  20 t. iron
> This is self-replacing subsistence economy. Here you
> have no problem with the price solution of 1/10.

Yes.

> Now, let's make it a surplus economy by making one sector
> more productive such as
> 280 qr. wheat + 12 t. iron --> 400 qr. wheat
> 120 qr. wheat +  8 t. iron -->  30 t. iron
> So the system has 10t. of iron as surplus and let us
> assume that the capitalists consume the 10 t. of iron,
> so it is a system of simple reproduction. Now, how do
> you solve for prices in this system?

The same way as Sraffa, when this economy is represented by Sraffa's
surplus equations. However, prices are solved in terms of a
higher-dimensional homogenous system of equations when this economy is
represented as a circular flow. The price solutions are the same in
both cases.

> Sraffa says that
> you write the system as:
> [280P(w) + 12P(i)](1+r) = 400P(w)
> [120P(w) +  8P(i)](1+r) =  30P(i)
> This solves for r and P(w)/P(i)

Yes. Note that the extra 10t. of iron for capitalist consumption is
already treated as a nominal cost in these equations.

> But you want to put the 10t. of iron back on the left
> hand side of the equation so that it becomes like the
> first subsistence equations. However, the question is
> how do you allocate the 10t. of iron to the two
> sectors?

The short answer is that the 10t of iron is not allocated to the two sectors.

In the circular flow representation of this 2-commodity economy there
are 4 sectors: 2 for iron and wheat, 1 for worker households and 1 for
capitalist households. The 10t. of iron is allocated to a single
sector, the capitalist household sector. It is not directly allocated
to either of the iron or wheat sectors. However, I don't think this
affects the underlying point you are trying to make.

> You agree that it has be to allocated in
> terms of the profits received by the capitalists in
> the two sectors and the rate of profits on the value
> of capital investment must be equal. But then there is
> no way of finding how to allocate the 10t. of iron to
> the two sector capitalists unless you solve Sraffa's
> equations.

Yes that is true.

Capitalist consumption coefficients (in contrast to capitalist
consumption) is the vector of real consumption per unit of
money-capital supplied.

I think you mean to say that "there is no way of finding" the
capitalist consumption coefficients unless we know the prevailing
prices of production. That's because capitalist consumption is per
unit of money-capital supplied, but money-capital supplied depends on
prices. Is this a correct interpretation of your point? If so, I agree
with you, but not with the conclusion you draw from this.

Consider the following: if we start from Sraffa's surplus equations
then we do solve Sraffa's surplus price equations in order to
construct the circular flow representation. The money-capital
coefficients and the capitalist consumption coefficients are
determined upto the choice of numeraire equation. Hence, from this
starting point, the circular flow matrix has a degree of freedom and
is parameterised by a numeraire equation. There is an infinite set of
circular flow representations corresponding to the infinite set of
Sraffian price solutions. If a numeraire equation is specified then an
element from each set is chosen. Their price and quantity solutions
are mutually consistent.

This manifests in a simple way in the corn-economy example in the
appendix of my paper, which will be easier to follow compared to
Sraffa's 2-commodity example.

Sraffa's lower-dimensional surplus equations are embedded in the
higher-dimensional circular flow.

> But once you have done that the 10t. of
> iron must be treated as 'surplus' and cannot any
> longer be treated as cost.

Here I do not quite understand you. The 10t. of wheat is already a
nominal cost in Sraffa's surplus equations. That's because the surplus
is nominally distributed.

However, perhaps your concern is with real costs. The 10t of wheat can
be treated as a real-cost, despite the money-capital and consumption
coefficients being dependent on the numeraire equation. This is a
subtle point, but prices cancel when constructing the technique
augmented by capitalist consumption. Again, this can be clearly seen
in the corn economy numerical example. This matches our intuition --
as real-costs cannot depend on the scale of the price system.

> That's why Sraffa said that
> once surplus emerges in the subsistence system, the
> system becomes self-contradictory. This conceptual
> error of your must show up in your mathematics. And as
> I have suggested in my previous mail, I think your
> system must be short of one equation. Cheers, ajit

I think there is probably an important underlying point that is
motivating your remarks, which you have not yet managed to
communicate. Maybe you are concerned that because the rate of profit
manifests as a price in the circular flow then this will upset
Sraffa's critique of naive marginalism. For what it's worth, I think
his circularity critique is not threatened, although I have not spent
time on this aspect.

Best wishes,
-Ian.
```

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