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

From: Ian Wright (wrighti@ACM.ORG)
Date: Tue Jun 06 2006 - 13:45:53 EDT

Hi Ajit

Thanks for continuing the discussion.

> Yes, but counting inputs and outputs at the factory
> gate will most likely leave you with non-equilibrium
> situation. Your condition that the situation must be
> in equilibrium introduces the notion of demand into
> the model, which is a subjective aspect.

Here is what I interpret you as saying: Sraffa counts inputs and
outputs at the factory gates, but specifically ignores how the surplus
is physically distributed. That's why there is no "demand" is his

However, Sraffa does introduce at least one subjective element into
his model: he counterfactually imposes a constraint of uniform profits
in order to deduce prices of production, contingent on a wage-profit
trade-off. Unless the surplus is actually bought, so there is
sufficient effective demand for the surplus, and the nominal price of
production accounts balance, then Sraffa's prices are ideal or
counterfactual prices. In your interpretation of Sraffa are prices of
production counterfactual or actual prices?

Regarding the "objectivism" of counting inputs and outputs. If you
watched the inputs of groceries at the door of my household over a
week you'd see I consumed 3 apples and 1 loaf of bread. This
consumption can be objectively counted by the man from the moon. How
much enjoyment I got out of that consumption, or what I may have
alternatively preferred, is irrelevant to the construction of an
input-output table. My suggestion here is that, in terms of counting
inputs and outputs within a "production period", there is not an
important difference between factories and households. Factories
"demand" goods, that is receive inputs, and so do households. Of
course worker and capitalist consumption is contested. But what's that
go to do with counting inputs and outputs?

Sraffa's objectivism is in some ways a cartoon objectivism, or at
least when reduced to the metaphor of a man from the moon. It requires
a great deal of theoretical baggage to identitfy different types of
commodities in an economy, which manifests as aggregration problems in
the Leontief approach to national income accounting. As you know, it
isn't a simple matter of dispassionately counting inputs and outputs
of well-defined commodity types between well-defined industrial

This aside may be taking us far from the main points.

> Secondly, you
> cannot argue that the observed inputs and outputs at
> the factory gate, which specifies your methods of
> production, will give you the correct price solutions
> in the case of the system finally adjusting to the
> equilibrium unless you assume constant returns to
> scale.

When did I mention processes of adjustment?

> Finally, if you are arguing from the
> perspective of 'every effect must have sufficient
> cause',which you appear to be doing, then you will
> have to specify the sufficient cause for the return to
> capital investment that you are simply presupposing in
> your model. I'll say something more about your
> interretation of Sraffa's objectivity later.

There are no causes, ordering or causality in a state of
self-replacing equilibrium. It's merely a  system of mutually
consistent simultaneous equations. Why is there a requirement for a
theory of the cause of profits?

I think you have an underlying idea that is motivating your remarks
which I do not as yet grasp.

> But Sraffa's self-replacing state does not imply
> "equilibrium" in the case of a system that always
> produces surplus. The equilibrium condition is an
> extrenous condition imposed by you on Sraffa's system.

I agree that equilibrium is arguably absent from Sraffa's system. As
you know, there isn't consensus on the equilibrium/non-equilibrium
interpretation of Sraffa's book. To paraphrase Joan Robinson: Sraffa
only gives us half an equilibrium system to stand on.

The metaphor of the circular flow, in which every output is also an
input, implies self-replacing equilibrium, whereas the metaphor of an
undistributed surplus, in which some outputs are not fully distributed
and contingency is introduced, implies a novel distributional event,
i.e. non-equilibrium. My guess is that the interpretative ambiguity in
the literature reflects a real ambiguity in PCMC: these two metaphors
clash. If the surplus is undistributed the circular flow is
interrupted. You can't have your equilibrium and not have it at the
same time.

I agree that I intrepret Sraffa's system in terms of equilibrium, in
the sense that I ask: how does the surplus get physically, rather than
just nominally, distributed in a self-replacing state? I'm happy to
accept that this is a special case of Sraffa's theoretical scheme.
(However, unless this is done, I think there are unsolved difficulties
in Sraffa's theory. That is a side-issue.)

A further motivation for adopting this approach is to initially
investigate the theory of value under well-specified conditions of
simple reproduction, because this is a simple case, but also because
the neo-Ricardian critique of Marx's theory of value has been
conducted under the rubric of equilibrium interpretations of Sraffa's
system, not non-equilibrium interpretations. For example, the TSS
school would be very surprised to hear that Sraffa, after all, was a
non-equilibrium theorist!

> I'm willing to grant you both the constant returns
> assumption and the equilibrium assumption if you say
> that an interpretation of Sraffa is not your purpose
> but rather you are interested in deducing certain
> properties of Sraffa's system under these two
> assumptions--that would be fair enough.

I do not accept that I need to assume constant returns because at no
point is the scale of production changing. But I am happy to accept
that I am deducing properties of Sraffa's system under the given
restrictions. An interpretation of Sraffa is not my purpose --
although a critique is.

But are you willing to accept the obverse of this position? Absent a
full specification of a state of self-replacing equilibrium then it is
not possible to calculate labour values, and real-costs in general.
Hence, nothing much can be said about the value controversy. As I
mentioned, just as price determination requires the exogenous
distribution of nominal income, real-cost determination requires the
exogenous distribution of real income. We can dig deeper into the
reasons why, if you think it might help.

> But then how come you are not short of one equation?
> In your system, the aggregate of the column must be
> equal to the right hand side of the corresponding row,
> which means only n-1 independent equations but you
> need to solve for (n-1) prices plus the rate of
> profits r. Since I'm not a mathematical person like
> yourself, I'm urging you to check for this one more
> time.

I'll explain why in a reply to your new message about this, although
some of the below is related.

> Commodity capital is not in the form of money but in
> the form of commodities only. During the period of
> production all your inputs including commodity wages
> are commodity capital in the hands of the firms. After
> the production period the gross outputs are the
> commodity capital in the hands of the firms, some of
> this capital could be converted into revenue.

OK, I assumed you meant working capital, rather than commodity
capital, because you raised the issue of double counting. I assumed
you were talking about double counting of money amounts. But now I
think you might be projecting a money-commodity interpretation onto
the circular flow, which is not quite right, as I'll try to explain.

I'm a little hesitant to interpret simultaneous equations in terms of
the "beginning" of the period and the "end" of the period, but

The working capital (which is money) in firm accounts, received from
capitalist households, is spent on commodity inputs at the beginning
of the period. At the end of the production period there is zero
working capital and some commodity capital, about to converted into
revenue. The math does not imply that there is both working capital
and commodity capital in the hands of the firm at the same time, just
as the price and quantity equations do not imply that there is both
means of exchange and the bought item in the hands of the purchaser at
the same time.

> You don't know the "gross revenue" unless you know the
> prices. But they are not yet determined in your model.

Yes that is true. Here's something to chew on: both the money-capital
coefficients and capitalist consumption coefficients have a free
variable and are undetermined upto the choice of numeraire equation.
Hence, the circular flow matrix is parameterised by a numeraire
equation. There is a choice: leave it parameterised, or specify the
numeraire equation. It makes no difference. I have left the system
parameterised to more closely follow Sraffa's approach, whose
objectivism seems not to extend to counting inputs and outputs of
nominal money, in particular the supply of money-capital from
capitalist households to fund production. The interesting twist is
that the formula for real-costs in the circular flow, when specialised
to calculate labour-values, is independent of the numeraire equation.
This is certainly an obscure technical point, but also interesting and

Another point to bear in mind is that the circular flow and Sraffa's
system are formally equivalent, merely different representations of
the same economy. We could start with the circular flow and yield
Sraffa's surplus equations. So when you express concern about the
number of equations etc. in the circular flow, at the same time you
are expressing concern  about Sraffa's surplus equations.

> The book keeping exercise is not yet possible. The
> firms have gross physical outputs, and that's all you
> know that they have. You cannot know what is the money
> equivalent of this gross output (and here by money
> equivalent I mean its value in terms of the numeraire
> commodity. If you are thinking in terms of paper money
> then you have additional problem of specifying the
> values of those papers)before you have solved the
> system of equations.

I am thinking in terms of paper money that has no intrinsic value and
is conserved in exchange.

> If money is a commodity, which is part of the
> input-output matrix, then obviously it is the
> numeraire commodity and its price is fixed at 1,
> because it is a numeraire commodity. The idea that it
> has another "price" which is equal to "r" is, I think,
> a conceptual contradiction.

I don't think you've fully assimilated the role of money in the
circular flow representation. You are conjoining the concept of a
money commodity with a numeraire equation. If we exogenously fix the
scale of the price system by specifying a numeraire equation we are
not at the same time defining a money-commodity. For example, I might
choose the numeraire equation w=1, which sets the wage rate to unity.
But this doesn't imply that it is labourers who are exchanged for
goods in the market ... all it implies is that the wage rate is 1 unit
of nominal money units, e.g. 1$.

The Sraffian price equation is determined upto a numeraire equation,
which may refer to  many commodities. The notion of a numeraire
commodity, which is a money-commodity, with price fixed at 1 is a
regression to old-school Bortkiewicz, which I think really muddles
things up and is therefore best avoided.

> If I understand you correctly, conceptually what you
> are doing is to say that "r" of Sraffa's system should
> be treated as cost.

Yes, it has a real cost, because in simple reproduction the
profit-income is spent, which commands workers to perform actual
labour to produce capitalist consumption goods. It is not just a
nominal cost.

> At certain level, this is nothing
> but restating Adam Smith who also insisted that proft
> was a necessary cost.

Great, at least I'm not on my own here ... !

But I don't accept the term "necessary". It is ambiguous. Production
can occur without a capitalist class. Under capitalist conditions,
however, production occurs with profit-income.

>But that should not change the
> accounting of Sraffa's system. I think there has to be
> some mistake of mathematics in your system and you are
> the best suited to catch it.

I'm not proposing any changes to Sraffa's price accounting. I'm
working within his theory. These considerations however do change
Sraffa's labour-cost accounting, implicit in his belief that prices
are proportional to labour values only at zero profits.

There is always the possibility of error, on all sides. I am not that
confident to think it impossible that I have made a mistake somewhere.
The only way to find out is by testing the arguments.

> Now I'm running out of time to write about Sraffa's
> 'objectivism', so I might take an opportunity to do so
> in the next mail. It seems you are relying on Kurz and
> Salvadori's interpretation of one of Sraffa's notes on
> the nature of surplus. I'm not sure whether you have
> read the whole passage, as they quote only a small
> part of a long piece.

No my access to it is only through Kurz and Salvadori. I'd be
interested to read the whole passage.

Best wishes,

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