General Equilibrium Economics [Was: Re: marginalism

[Gunnar Tómasson <gunnar.tomasson@xxxxxxxxxxx>]

Barkley:

Re. the following:

> Thus, [von Neumann's] model was intended for contingent use
> within time frames within which inputs did not
> exhaust.  I see no reason to declare his model
> ridiculous because of that.

Comment:

Briefly, here is why I take the opposite view.

1.  The Walrasian General Equilibrium mode of "reasoning" was picked up by
other mathematical neo-classical economists while Walras was still working
his way towards what, in due course, became his final word on the subject
matter.

2.  As reproduced in Appendix Note in Don Patinkin's 'Money, Prices, etc.',
Walras conclusion was to the effect that the general equilibrium model
exemplified by the Laplacian construction of Newtonian Mechanics has NO
place in observation-based theoretical economics - what Samuelson would
later call "operationally meaningful theorems."

3.  Of course, Walras did not put it so bluntly; instead, he acknowledged
that the model required that the conditions of general equilibrium be held
to obtain at ALL POINTS IN TIME in real-world market economies - a
proposition which is NOT disputed in the Laplacian construction of Newtonian
Mechanics.

4.  But the damage was done - his neoclassical peers NEVER looked back at
Walras' mature grasp of the LOGIC of the general equilibrium model with the
result that, when Keynes surveyed their handiwork, he could write without
fear of contradiction that "Walras's theory and ALL OTHERS along those lines
are little better than nonsense." (Letter to Hicks, December 9, 1934 - cited
by Skidelsky, 'The Economist as Saviour', p. 615)

5.  In 'Foundations of Economic Analysis', Samuelson preached the OPPOSITE
view:

"In fact, any sector of economic theory which cannot be cast into the mold
of such a system must be regarded with suspicion as suffering from
haziness." (Atheneum, New York, 1979, p. 9)

6.  But Samuelson sought to have it BOTH ways:

(a) embrace the half-baked "general-equilibrium" approach of Walras'
neo-classical peers, and

(b) dismiss the LOGIC of the Laplacian general-equilibrium model as spelled
out by Walras late in life (# 2-3 above).

Of course, Samuelson did not put things so bluntly.  Instead he ASSERTED
that "The concept of an equilibrium system outlined above is applicable as
well to the case of a single variable as to so-called _general equilibrium_
involving thousands of variables.  Logically the determination of output of
a given firm under pure competition is precisely the same as the
simultaneous determination of thousands of prices and quantities.  In every
case _ceteris paribus_ assumptions must be made.  The only difference lies
in the fact that in the general equilibrium analysis of, let us say, Walras,
the content of the historical discipline of theoretical economics is
practically exhausted." (Op. cit., p. 8)

I take it that by "the content of the historical discipline of theoretical
economics [being] practically exhausted", Samuelson is acknowledging the
implications of the LOGIC of the Laplacian General Equilibrium model which,
if conceded in forthright fashion, he could not have (effectively) dismissed
as a matter of PERSONAL judgement on the part of either Walras or himself.

And where does all this leave us today?

In their writings on the subject matter, both Samuelson and Friedman have
claimed methodological kinship between physics and economics.

I submit that this claim is without foundation in fact.

Gunnar




----- Original Message -----
From: "Barkley Rosser" <rosserjb@xxxxxxx>
To: "Gunnar Tómasson" <gunnar.tomasson@xxxxxxxxxxx>; <pkt@xxxxxxxxxxxxxxxx>
Sent: Tuesday, October 28, 2003 1:47 PM
Subject: Re: marginalism


> Gunnar,
>      It is well known that von Neumann's model
> is a cost of production/reproduction model
> somewhat like that of Marx's and other classical
> economists.  It does not depend on marginalism
> or scarcity of anything at all, as you note.  However,
> obviously, von Neumann recognized that the
> theoretical infinity of inputs was ultimately absurd.
> Thus, his model was intended for contingent use
> within time frames within which inputs did not
> exhaust.  I see no reason to declare his model
> ridiculous because of that.
>       Certainly there are other theories of value
> besides those derived from marginalism.  One
> can even apply marginalism in the model above,
> except that it is a waste of time because in a
> linear model the margin equals the average, so
> one can simply use the latter and dispense with
> the former.
> Barkley Rosser
> ----- Original Message -----
> From: "Gunnar Tómasson" <gunnar.tomasson@xxxxxxxxxxx>
> To: "Barkley Rosser" <rosserjb@xxxxxxx>; <pkt@xxxxxxxxxxxxxxxx>
> Sent: Tuesday, October 28, 2003 1:40 PM
> Subject: Re: marginalism
>
>
> > Barkley:
> >
> > Re. the following:
> >
> > >      Just for the record, I have various problems
> > > with "marginalism," and am not frequently some
> > > great defender of it.  But, the idea that its biggest
> > > problem is some alleged "unlimited" supply of
> > > resources is the least of its problems in my view.
> >
> > Comment:
> >
> > Below is an extract from an old working paper of mine on related issues.
> >
> > Gunnar
> >
> >
> >
> > (i)                 General equilibrium
> >
> >
> >
> > The mathematical genius, John von Neumann, is recognized as the foremost
> > pioneer in the construction of general equilibrium models in the
twentieth
> > century.  In a recent book, his model was summarized briefly as follows:
> >
> >
> >
> > "In a new [1937] breakthrough John von Neumann first formulated a
balanced
> > and steady-state growth of a general economic equilibrium and proved the
> > existence of a solution.  The breakthrough did not lie in the subject
> > matter, which was still allocation and relative price in general
> equilibrium
> > using maxima and minima.  Indeed, all economists can appreciate the
simple
> > beauty, yet high degree of generality, characterizing the von Neumann
> model.
> > There is substitution in both production and consumption.  The model
"can
> > handle capital goods without fuss and bother," as
Dorfman-Samuelson-Solow
> > put it.  There is explicit optimization in the model: the solution weeds
> out
> > all but the most profitable process or processes.  There are free and
> > economic goods, indeed the solution tells us which will be free and
which
> > economic." [106]
> >
> >
> >
> > Economists in the modern mainstream macroeconomics tradition have
analyzed
> > von Neumann's model from the point of view of mathematics, neglecting to
> > test it for analytical coherence and consistency along the following
> lines:
> >
> >
> >
> > 1.                  von Neumann assumed "that the natural factors of
> > production, including labour, can be expanded in unlimited quantities."
> > [107]
> >
> > 2.                  He also defined a "free good" to be one whose supply
> > exceeds the need for it.
> >
> > 3.                  Thus, "free goods" within von Neumann's model may be
> > "free" one day and "non-free" the next, although he did not make that
> point.
> >
> > 4.                  Since all factors of production "can be expanded in
> > unlimited quantities" by assumption, von Neumann's model has built into
> its
> > premises the conclusion that all goods may in time become "free" goods.
> >
> > 5.                  Since time is not an essential feature of any
general
> > equilibrium model, why should only one or some rather than all goods be
> held
> > to be "free" and not "economic"?
> >
> > 6.                  Speaking of a mathematical equation relating to the
> > subject matter, von Neumann said: "[Its] meaning is: it is impossible to
> > consume more of a good G in the total process than is being produced.
If,
> > however, less is consumed, i.e., if there is excess production of G, G
> > becomes a free good and its price y = 0." [108]
> >
> > 7.                  von Neumann recognized that there was mathematically
> > nothing to preclude all goods from being available in infinite supply so
> > that all goods would be "free."
> >
> > 8.                  von Neumann declared this mathematical possibility
to
> be
> > "meaningless." [109]
> >
> > 9.                  In principle, a mathematical model can only yield
> > conclusions, which are already implied by its premises.
> >
> > 10.             Therefore, when von Neumann found it "meaningless" that
> all
> > goods could be "free goods," he effectively declared the premises of his
> > model to be "meaningless."
> >
> >
> >
> > 106.                  Hans Brems, Pioneering Economic Theory, 1630-1980,
A
> > Mathematical Restatement, The Johns Hopkins University Press, Baltimore
> and
> > London, 1986, p. 299.
> >
> > 107.                  John von Neumann, 'A Model of General
Equilibrium',
> > 1938, reprinted in Precursors in Mathematical Economics: An Anthology,
ed.
> > by W. J. Baumol and S. M. Goldfeld, London, 1968, p. 297.
> >
> >
> >
> >
> >
> >
> >
> > ----- Original Message -----
> > From: "Barkley Rosser" <rosserjb@xxxxxxx>
> > To: "Clifford Poirot" <cpoirot@xxxxxxxxxxx>; <pkt@xxxxxxxxxxxxxxxx>;
> > <william_b_ryan@xxxxxxxxx>
> > Sent: Tuesday, October 28, 2003 12:17 PM
> > Subject: Re: marginalism
> >
> >
> > >      Just for the record, I have various problems
> > > with "marginalism," and am not frequently some
> > > great defender of it.  But, the idea that its biggest
> > > problem is some alleged "unlimited" supply of
> > > resources is the least of its problems in my view.
> > > Barkley Rosser
> > > ----- Original Message -----
> > > From: "Clifford Poirot" <cpoirot@xxxxxxxxxxx>
> > > To: <pkt@xxxxxxxxxxxxxxxx>; <william_b_ryan@xxxxxxxxx>
> > > Sent: Tuesday, October 28, 2003 11:47 AM
> > > Subject: Re: marginalism
> > >
> > >
> > > > In some ways resources are even more constrained in the longer run
as
> > > > population pressure and increased energy use bumps up against
limits.
> > > >
> > > > -----Original Message-----
> > > > From: Barkley Rosser [mailto:rosserjb@xxxxxxx]
> > > > Sent: Tuesday, October 28, 2003 11:17 AM
> > > > To: william_b_ryan@xxxxxxxxx; pkt@xxxxxxxxxxxxxxxx
> > > > Subject: Re: marginalism
> > > >
> > > >
> > > >       "The new approach to economics"???  Is
> > > > this something you cooked up or something you
> > > > picked up from reading the late Julian Simon?
> > > > Very simply, in the short run many resources are
> > > > limited.  It takes time to drill new oil wells or increase
> > > > output rates from old ones.  It takes time to dig new
> > > > coal mines or other mines.  So, marginalism is
> > > > certainly relevant in the short run.
> > > >      It becomes less so in the long run, although
> > > > even there, it is false that resources are "unlimited,"
> > > > although many that may be constrained in the short
> > > > run are not very constrained in the longer run.  Ironically
> > > > those that are really in the shortest supply are not the
> > > > non-renewable ones, but the so-called renewable ones.
> > > > Once you have driven a species to extinction it is gone
> > > > forever.  Unlike methane, we will not find it on Jupiter.
> > > > Barkley Rosser
> > > > ----- Original Message -----
> > > > From: "William B. Ryan" <william_b_ryan@xxxxxxxxx>
> > > > To: <pkt@xxxxxxxxxxxxxxxx>
> > > > Sent: Saturday, October 25, 2003 10:56 AM
> > > > Subject: marginalism
> > > >
> > > >
> > > > > ***>Price is where marginal benefits + utility (aka
> > > > > market cost) = cost. (The whole point of marginalism
> > > > > and STV) Cost is another term for price.  So...price
> > > > > + utility = cost is circular logic.  Circular logic
> > > > > is impossible, therefore supply and demand is
> > > > > junk.<***
> > > > >
> > > > > Your argument is invalid not because marginalism is
> > > > > not invalid, but because you have falsely described
> > > > > marginalism.  Marginalism is invalid because it is
> > > > > premised on the false assumptions that resources are
> > > > > scarce and demand is unlimited, so the two must
> > > > > intersect.  Marginalism is perfectly logical premised
> > > > > on those assumptions.
> > > > >
> > > > > The new approach to economics is premised on the
> > > > > facts that resources are permanently abundant and the
> > > > > physical capacity to consume is permanently limited.
> > > > >
> > > > > Resources become abundant through continuing
> > > > > discovery, development and innovation.
> > > > >
> > > > > And it is physically possible to consume only so much
> > > > > per unit time.  The limit to consumption is the point
> > > > > of satiation.
> > > > >
> > > > > --
> > > > >
> > > > > "smithaa02" <sadf@xxxxxxxx> wrote:
> > > > > >
> > > > > >"Capitalist Pig" <root@localhost.> wrote in message
> > > > > >news:lnfipvksijllub6jk84ucisvlb8anmdj92@xxxxxxxxxx
> > > > > >> On Thu, 23 Oct 2003 22:32:23 -0500, "smithaa02" <sadf@xxxxxxxx>
> > > wrote:
> > > > > >> >
> > > > > >> >I've debunked marginalism, STV, and supply and demand all
> > > > > >> >in one.
> > > > > >> >
> > > > > >>
> > > > > >> Wow, I'm impressed!
> > > > > >
> > > > > >You should be...
> > > > > >
> > > > > >>
> > > > > >> >
> > > > > >> >Price + utility can't equal price for that is circular logic.
> > > > > >> >
> > > > > >>
> > > > > >> I wouldn't call it circular logic, I would call it a mistake. I
> > have
> > > > > >> no idea how you could come up with such silly definition.
> > > > > >Price is where marginal benefits + utility (aka market cost) =
> cost.
> > > (The
> > > > > >whole point of marginalism and STV) Cost is another term for
price.
> > > > So...
> > > > > >price + utility = cost is circular logic.  Circular logic is
> > > impossible,
> > > > > >therefore supply and demand is junk.
> > > > > >
> > > > > >
> > > > >
> > > > >
> > > > >
> > > > >
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