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

From: Ian Wright (wrighti@ACM.ORG)
Date: Sun Jun 04 2006 - 16:34:27 EDT

Hi Ajit

Thanks for taking the time to provide feedback -- I really appreciate it.

> As a matter of fact, if this exercise turns out to be right, then
> the talk of labor theory is superfluos since in this
> case labor inputs can be substituted with
> commodities—as Sraffa's ch. 1 does.

Do you mean that in this case any commodity type can form a real-cost
basis? If so I agree.

However, I don't think it possible to establish a theory of value
without dynamics, so I'm comfortable with this conclusion. The
real-cost results cannot establish Marx's theory of value, although it
can show that the neo-Ricardian criticism of it misses the mark.

> Now the question is how do you do it, and can it be
> done ? Now, to turn Sraffa's surplus system into a
> subsistence system you first reduce Sraffa's wage
> laborers into horses (some people out there who know
> duddly da of Sraffa but think that they have all their
> phoney baloney criticisms worked out should note that
> Sraffa's wages are 'money' wages and not
> commodity-bundle wages) . On this basis you throw the
> wage part from the net output side back to the input
> side, which is more faithful to Marx.

Yes. Except treating the real wage as an input needn't imply that the
wage is "subsistence" (I'm not sure what the can mean, by the way).
Closing Sraffa's system -- i.e. throwing the net output back to the
input side -- does imply self-replacing equilibrium however.

> Then your next step is to argue that within capitalist system, a
> capitalist will not invest unless there is a return to capital assured.

I don't rely on counterfactuals. If I imply that I do then I've made a
presentational error, so my apologies if so. I'm trying to take
Sraffa's (original) objectivism to its logical conclusion, for example
only counting inputs and outputs at the "factory gates" and ignoring
subjective motivations. In a state of self-replacing equilibrium,
capitalists supply working capital for the production period and
receive a return that they spend in the market for consumption goods.
Such material exchanges of goods and money can be counted.

> Thus there is a price to capital
> investment and profit is its price that must be paid
> to bring about that investment. This, of course, is
> the inducement theory and brings your approach close
> to the Austrian approach to capital theory.

My guess is that a state of self-replacing equilibrium will radically
under-determine the theory of value, as you've already suggested. I
think different people will prefer different interpretations of the
very same mathematics.

The concept that profit is the price of money-capital follows as a
logical necessity from Sraffa's starting point -- on condition that
(i) we decide to model a state of self-replacing equilibrium, and (ii)
we fully specify that state, by specifying the physical distribution
of the net product.

If I'm an Austrian then so is a special case of Sraffa ...

> Now, without going into any details, here I would like you
> to think of two questions. (1) Can you determine the
> price of investment on the basis of the inducement
> theory of price of capital investment ?—In your paper
> you first determine the rate of profits from Sraffa's
> surplus equations and then throw them back on the
> input side at a later stage, which creates a
> conceptual contradiction in your model.

I will try to think, but I don't quite follow you, especially as I
don't think there is any inducement theory here. Perhaps the following
remarks might help the discussion.

Sraffa's surplus equations, subject to certain technical restrictions
necessary to interpret the equations as representing a state of
self-replacing equilibrium, are equivalent to the closed system of
equations (the "circular flow"). We can map back and forth between the
two representations of the same economy.

In the circular flow representation, the rate of profits is determined
simultaneously with the  distribution of real income, including
capitalist consumption. In this representation, there cannot be any
talk of ordering, such as "throw them back on the input side at a
later stage". The solutions of the system of simultaneous equations is
mutually determined all at once.

It may appear that the rate of profits is determined from Sraffa's
surplus equations and then later thrown back on the input side only
because I carefully deduce the circular flow representation from
Sraffa's starting point. The ordering appears in the deduction of
Sraffa's system to circular flow. But each step of the deduction
exists "all at once" -- as this is a system of simultaneous equations.
The step-by-step deduction simply brings out information that already
existed in the starting point.

We can look at this another way. Alternatively, we could have started
from the circular flow representation and then later "opened" the
system to yield Sraffa's surplus equations (and some new kinds of
surplus equations -- but this is a detail).

> Now, let me turn to your novel idea of bringing 'money
> capital' and price of 'money capital' in the model. I
> think here you have gone wrong. Let me explain why ? I
> think the fundamental mistake you commit is that you
> forget that there is something called 'commodity
> capital' in the hands of the firms all the time and
> therefore they do not need 'money capital' advancement
> from the capitalists' households for production.

Could you define "commodity capital"? Do you mean an amount of money,
the "working capital" for the period of production? Or do you mean the
actual physical input goods that are transformed by labour into the

I'll assume that you mean an amount of money.

In which case, "commodity capital" and "working capital" are probably
synonyms in this context.

> Let us suppose that your numeraire commodity is the money
> commodity.

There is no money commodity. Only symbolic money throughout. But I
don't think this affects the point you are trying to make.

> After the production period is over all the
> firms will hold their gross outputs, including the
> firms producing the numeraire commodity. These firms
> will use their numeraire commodity to buy other inputs
> from other firms and also labor power and those
> laborers in turn will again use their money to buy
> other consumption goods. This puts the money in the
> hands of other firms who in turn go about buying
> inputs from other firms and also labor power. Thus the
> money commodity circulates through the system, and
> given your assumption of simple circulation schema,
> gets completely absorbed in the system as inputs or
> and consumption, including consumption by the
> capitalists. Thus there is no need for an infusion of
> money capital for the system to go around. As a matter
> of fact your procedure amounts to double counting the
> capital investment.

I think this is an misinterpretation that is unfortunately easy to
make. I think the problem is that the meaning of money-capital is
quite subtle.

The first point to note is that there is not an additional infusion of
money from capitalists into the system. Rather, the circulation of
money is more complex compared to simple commodity production. There
is now an additional circuit of money between firm and capitalist
accounts, and a new function of money, the ability to command a

The gross revenue held in firm accounts is transferred to capitalist
accounts, the owners. A part of this money is simulaneously
transferred from capitalist accounts to firm accounts to cover the
input costs of the "next round" of production. This is the working
capital (or commodity capital) held in firm accounts. Only the
residual is retained by capitalists to spend on consumption goods --
their profit. So there is a *net* transfer of money from firms to
capitalists. All this is consistent with Kalecki's principle that
capitalists earn what they spend. You may think there is
double-counting if you interpret the transfers between firms and
capitalists in gross terms. But at no point is there both
money-capital in capitalist accounts and working capital (or
commodity-capital) in firm accounts. Rather, it's the very same
"physical" money.

The subtle issue is the change in the function of money, from means of
exchange in the price equations, to money that is a commodity with a
price (money-capital) in the input-output matrix. This functional
change of the very same physical money is dependent on the property
relations that exist in the capitalist firm, sketched in 4.2.

Introducing money amounts to the input-ouput matrix is not novel (e.g.
Leontief), but this concept of money-capital probably is. However, the
concept of money-capital logically follows from Sraffa's starting
point. It cannot be avoided once the physical distribution of the
surplus is specified.

If there is double-counting then I'd expect this to manifest as a
mathematical contradiction. I'd be interested if one can be found.

> I hope in the light of my two recent papers you would
> make some changes to your representation of Sraffa's
> system. Your matrix equations assume constant returns
> to scale, but Sraffa's does not—notice Sraffa's
> equations are always in terms of gross outputs and not
> in terms of unit outputs.

I don't think that matters, unless I've missed something. As long as I
do not vary the scale of production while keeping the technical
coefficients unchanged, then I am not assuming constant returns.

> The case of 'beans' are not
> important. In Sraffa's context, which takes a given
> system at any point of time, if 'beans' exist then he
> has to take that into account and show that if the
> rate of profits go beyond a certain rate in the basic
> goods sector then the system cannot maintain equal
> rate of profits and all positive prices at the same
> time. I would say, giving up equal rate of profits is
> no big deal in this case. But in your case, since you
> are taking long-term equilibrium case, 'beans' should
> simply disappear as the capitalists producing beans
> will find it more profitable to quit bean production
> and move into producing something basic.

I think you're missing something more important here. You think
"beans" should disappear because you assume that the rate of profit is
determined by the basic subsystem. In a fully specified state of
self-replacing equilibrium the rate of profit is not determined by the
basic subsystem, it is determined by the system as a whole. The
"beans", in this case, are "blocking goods" or, to use a biological
term, "limiting factors" on the rate of growth of the system. The
crucial question is whether the "beans" are also inputs. We do not
know the answer to that if we stick with Sraffa's undistributed

All kinds of confusions arise if we uncritically apply Sraffa's
surplus representation to model a state of self-replacing equilibrium.
Either the surplus is fully distributed or the circular flow is
interrupted; in the latter case we (arguably) have no idea what is
going to happen next, although we can make some statements about
prices if we decide to specify the distribution of nominal income.

Ajit, I hope we can continue this exchange, if you have the time and

Best wishes,

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