# [OPE-L:7469] QRE: Sraffa on Prices and Money

From: A.B.Trigg@open.ac.uk
Date: Thu Jul 25 2002 - 16:20:31 EDT

```Gil.
Great to get a quick reply. My vertical/horizontal comment is I concede
rather lose. Let me set out what I mean in a two sector input-output table,
if you will excuse the email algebra. p1 and p2 are money prices for each
sector, Q1 and Q2 gross outputs (physical units), F1 and F2 physical final
demands. The a's are technical coefficients aij.

sector 1:  (p1)(a11)(Q1)+(p1)(a12)(Q2)+ (p1)(F1)=(p1)(Q1)
sector 2:  (p2)(a21)(Q1)+(p2)(a22)(Q2)+ (p2)(F2)=(p2)Q2)

OK, so reading horizontally we can divide the first row by p1 and the second
by p2. This would leave us with a physical quanity system.

Prices can be determined separately by looking vertically at the first two
columns, and the value added rows of the input-output table containing wages
and profits. The quantity terms Q1 and Q2 cancel out there.

What I am grasping towards is to say that this input output table is in
money terms. The money final demands as represented by p1F1 and p2F2 can
drive this system as Kalecki argues, but we can say that this impact is made
up of the real effects (F1 and F2, which determine the overall scale) and
the distributional effects (as determined by the prices p1 and p2 in the
price model).

I can't see why the quantity theory of money is needed, though can be
convinced. It doesn't effect the structure of this model whether final
demand is financed by fiat money or commodity money.

Am not suggesting that we bring in demand functions into Sraffa. Didn't
Sraffa see the PCM as only one part of a general system, with him
concentrating on prices and distribution? The quantity system would be an
extra model bolted onto PCM, which is left internally consistent. Prices
would not be determined by demand and supply. Only quantity, in the quanity
model, would be driven by demand.

Any thoughts welcome. This is not fully thought through.

Andrew.
> -----Original Message-----
> From:	Gil Skillman [SMTP:gskillman@mail.wesleyan.edu]
> Sent:	25 July 2002 20:40
> To:	ope-l@galaxy.csuchico.edu
> Subject:	[OPE-L:7467] Re: RE: Re: Re: Re Aoki on K and M on money
>
> Andrew writes
>
> >Hello Gil and Rakesh.
> >I am coming in late here on this one, but is it not wise to distinguish
> >between quantity and price systems in a Sraffian, or any, framework.
> Sraffa
> >assumes the quantity of output is given and looks at prices and
> >distribution.
>
> Not only wise, but necessary.  In the standard representation I've been
> discussing so far, constant returns to scale (the case most favorable to
> labor value theory, for reasons I discussed on OPE-L long ago in the
> context of KIII, Ch. 10) are assumed, which implies that quantity levels
> factor out of the price of production equations, assuming commodity
> money.  If you assume fiat money and want to discuss the connection
> between
> money supply and prices, you may need to introduce the quantity equation
> MV
> = PQ, which means that quantities have to be brought back in (I was saving
>
> this step until Fred had a chance to reply to my scenario involving
> quantity money).
>
>
>
> >  But a quantity model can also look at the scale of output,
> >which is where money comes in through the impact of investment on
> >quantities, through a Kalecki type multiplier (or as is fashionable the
> >supermultiplier). These quantity relationships could hold regardless of
> >whether prices are sequential or simultaneous.
> >
> >You can either look at an input-output table vertically, in which case
> >quantities are cancelled out, or horizontally in which case prices are
> >cancelled out.
>
> I can't quite translate this comment.  Strictly speaking, prices won't
> show
> up in an input-output table. And even if we adduce prices to convert such
> a
> table to a system of prices of production equations, I don't yet see the
> sense in which prices might be "cancelled out."
>
> >Both dimensions can be explored separately in a Sraffian
> >system. (If we determine quantities and prices together then isn't this
> what
> >the neoclassics do with their demand and supply diagram?)
>
> Indeed so.  But to do this in a Sraffian framework you'd have to add
> demand
> functions, something that Sraffa was trying to avoid.
>
> Gil
>
>
>
> >Let me know if this makes any sense.
> >
> >Andrew (Trigg)
> >
> > > -----Original Message-----
> > > From: Gil Skillman [SMTP:gskillman@mail.wesleyan.edu]
> > > Sent: 19 July 2002 20:08
> > > To:   ope-l@galaxy.csuchico.edu
> > > Subject:      [OPE-L:7432] Re: Re: Re Aoki on K and M on money
> > >
> > > Rakesh, you write
> > >
> > >
> > >
> > >       re 7430
> > >
> > >       Hi Gil,
> > >       Money can have no other role than numeraire in a system of
> > > simultaneous equations.
> > >
> > >
> > > As I think Gary mentioned earlier, there is a potential equivocation
> here
> > > with respect to the term "simultaneous."  It's true that the standard
> > > Sraffian framework involves a system of equations that might be solved
> > > "simultaneously" to yield values for some subset of prices of
> production,
> > > profit rate, and wage rate.  It does not follow, however, that the
> > > equations in this system must represent economic processes that
> *occur*
> > > simultaneously.  Quite to the contrary, it is possible (and has been
> done)
> > > to introduce time-specific variables in the Sraffian framework, which
> > > among other things makes it possible to reflect the function of money
> as a
> > > store of value--making it more than simply a numeraire good.
> > >
> > >
> > >
> > >       (1) The equation for money appears alongside all the other
> > > commodities in such a formalization, and  the contradiction between
> > > commdities on one side and money on the other is thereby elided. But
> this
> > > is the basic abstraction of a monetary production economy. It is an
> > > emasculation of of Marx's theory of money to treat it as any other
> > > commodity except that it alone is set to equal one in an algebraic
> > > solution.
> > >
> > >
> > >
> > > No more than it is an "emasculation of Marx's theory" to posit that
> > > commodities exchange at their respective values--a condition he
> clearly
> > > rejects as empirically descriptive or analytically general yet imposes
> as
> > > of the end of KI Ch. 5--or that workers are necessarily paid a wage
> > > corresponding to the value of labor power--a condition he assumes
> > > beginning in Ch. 6 but subsequently relaxes in his analysis of
> capitalist
> > > accumulation in Ch. 25.  The point is that these additional aspects of
> > > money are simply *not at issue,* and thus *nowhere invoked,* at the
> level
> > > of abstraction pursued by Marx in KIII Ch. 9, to which the Sraffian
> > > analysis most directly speaks.
> > >
> > >
> > >
> > >
> > >       (2) Once one has put himself in the simultaneous straightjacket,
> it
> > > seems impossible to make a logical transition to a level of
> abstraction in
> > > which the features of money which are temporally based can be
> assimilated.
> > > Through the introduction of money even C-M-C separates sale and
> purchase
> > > by time. But there is no time in the Sraffian formalization and thus
> there
> > > is no capitalism. The formalization thus does not capture the
> essential
> > > features of its purported object.
> > >
> > >
> > > I believe this claim is built on the confusion between mathematical
> and
> > > temporal simultaneity noted above.  It *is* possible to introduce time
> in
> > > the Sraffian formalization, and indeed has been done.  Thus, if one
> were
> > > to read Marx in KIII, Ch. 9, as insisting that output prices were
> > > determined "later" than input prices for the corresponding goods, and
> were
> > > thus generally unequal to them, this complication could readily be
> > > incorporated into the Sraffian framework.  But I don't think he
> insists on
> > > this.
> > >
> > >
> > >
> > >
> > >       For these reasons, I am sympathetic to the TSS interpretation in
> > > which the givens are in the form of money and all variables are time
> > > subscripted. There then seem to be no logical problems in moving to
> what
> > > we are calling other levels of abstraction. Of course I wish the TSS
> > > members were present here to continue this argument at the level of
> > > sophistication which it deserves.
> > >
> > >
> > > Fair enough.  I'll just note again that there is absolutely no barrier
> to
> > > time-subscripting variables in the Sraffian framework.
> > >
> > >
> > >
> > >       I shall not re-engage your ch 5 criticism (which I had recently
> > > mentioned) except to say that we are both agreed that putting out
> > > manufacture can be a form of surplus value production. By the way
> there is
> > > an important exchange between Michael Zmolek and Robert Albritton
> > > putting out mfg in recent issues of the Journal of Peasant Studies.
> > >
> > >
> > > Interesting.  If you have a moment, could you summarize the key point
> or
> > > points at issue in that exchange?
> > >
> > >
> > >
> > >       Needless to say, I don't believe there is a transformation
> problem
> > > which requires the money-less, atemporal Sraffian formalization to
> solve.
> > >
> > >
> > >
> > > Perhaps, but as I read it the discussion between Gary and Fred
> involves a
> > > narrower question:  is it logically coherent, in general, to insist
> that
> > > the rate of profit is determined analytically *prior* to prices of
> > > production?  And one can use a Sraffian formalization *with* money,
> that
> > > is no more or less explicitly temporal than Marx's analysis in KIII,
> Ch.
> > > 9, to establish that this claim is *not* logically consistent in
> general.
> > > To put the point another way, since Marx nowhere *rules out* the
> > > possibility of a steady state in which respective input and output
> prices
> > > are equal, even if temporally separated, this Sraffian demonstration
> is
> > > unavoidably relevant to Marx's--and Fred's--categorical claims.
> > >
> > > Gil
> > >
> > >
> > >
> > >
> > >       Yours, Rakesh
> > >
> > >
> > >
> > >
> > >               Rakesh, thanks for bringing the Aoki article to my
> > > attention.  I hadn't known about the 1933 MS of Keynes's theory, and
> found
> > > Aoki's discussion of the overlaps and contrasts with Marx quite
> > > interesting.  But for what it's worth, so far as I can see nothing
> Aoki
> > > wrote suggests a refutation of my earlier comments on the
> applicability of
> > > Sraffa to Marx, **at the level of abstraction at which Sraffian
> analysis
> > > engages Marx's analysis.**  Aoki notes that both Marx and Keynes
> > > understand money to play a more complex role in a capitalist economy
> than
> > > simply serving as a medium of exchange, and that this more complex
> role
> > > allows for the possibility of capitalist crisis.
> > >
> > >               But first, none of these more complex aspects of money
> are
> > > at issue in the portion of Marx's analysis under discussion with Gary
> and
> > > Fred, roughly corresponding to Marx's argument in KIII, Ch. 9.  I
> might
> > > add, in anticipation of what follows, that nor are these more complex
> > > aspects of money at issue in Marx's analysis of the "contradictions"
> in
> > > the circuit of capital in KI, Ch. 5. If you allow  Marx to abstract
> from
> > > these complexities at this stage, then it seems to me a similar
> latitude
> > > should be allowed to the Sraffian framework when it addresses the same
> set
> > > of questions at the same level of generality.  Second, I see no
> evident
> > > impediment to incorporating the more complex functions of money in a
> > > Sraffian framework if this is called for in some more all-encompassing
> > > abstraction of capitalist processes, and see no reason to believe that
> > > doing so would reverse the valid indictments of Marx's analysis made
> > > possible by the Sraffian framework.
> > >
> > >
> > >                       My argument with Gil has been that Marx is not
> > > attempting a logical transition from simple commodity production to
> wage
> > > labor relations of production in chapters five and six.
> > >
> > >
> > >               It would be pointless to re-engage this argument, but I
> will
> > > just note for the record that contrary to your claim here I never
> argued
> > > that Marx is attempting such a logical transition.  My main point is
> that
> > > (whether or not you understand Marx to be positing a fully elaborated
> > > capitalist economy at every step of his argument in KI, Part 2), Marx
> > > explicitly developed logical basis for invoking *price-value
> > > proportionality* (i.e. the analytical hypothesis that commodities
> exchange
> > > at their respective values) as the necessary theoretical starting
> point
> > > for analyzing surplus value is (1) evidently invalid, involving a
> > > fallacious inference about necessary conditions from a premise
> concerning
> > > sufficient conditions; (2) contradicted by at least one version of the
> > > circuit of capital that meets all of Marx's conditions for the
> existence
> > > of surplus value; and (3) essentially misleading about the systemic
> > > conditions that make it possible for capitalists to appropriate
> surplus
> > > value.
> > >
> > >               But other than noting what my real argument on this
> point is
> > > for the record, I don't mean to pursue this critique further in this
> > > forum.  There is a very different set of questions at stake in the
> > > exchange between Fred and Gary.
> > >
> > >               Gil
> > >
```

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