Re: gross substitution and existence proofs

["Alan G. Isaac" <aisaac@xxxxxxxxxxxx>]

I don't have Arrow & Hahn in front of me,
but gross substitutability is not generally
used in existence proofs. It is often invoked
in uniqueness proofs, however.
Alan G. Isaac


Paul Davidson wrote:
>
> In their book, GENERAL COMPETITIVE  ANALYSIS (1971), Arrow and Hahn
> demonstrate that the gross substitution axiom is a sufficient condition to
> demonstrate the EXISTENCE of a general equilibrium (full employment). and
> if the gross substitution axiom is dropped then, according to Arrow and
> Hahn, ALL known existence proofs are "jeopardized".  Consequeently, the
> gross substitution axiom is an essential property of classical analysis
> where, in equilibrium, all markets clear simultaneously.
>
> Arrow and Hahn  then go on to state (pp. 356-7) That "The terms in which
> contracts are made matter. In particular, if money is the good in terms of
> which contracts are made, then the price of goods in terms of money are of
> special significance. This is not the case if we consider an economy
> without a past or future....IF A SERIOUS MONETARY THEORY comes to be
> written, the fact that contracts are made in terms of money will be of
> considerable importance" [emphasis added].
>
> Post Keynesian Macroeconomic Theory develops a model where contracts are
> written in terms of money, where the economy is moving from an irrevocable
> past ot an uncertain future, and where elasticity of substitution between
> money and the products of industry is zero (i.e., the gross substitution
> axiom is not accepted as a ubiquitous force). In such a system, as Arrow
> and Hahn indicate, one can not prove the existence of a full employment
> equilbirum that can be achieved by any  possible free market relative price
> vector.
>
> Paul
>
> Paul Davidson
> Holly Chair of Excellence in Political Economy
> University of Tennessee
> SMC523
> Knoxville, Tennessee 37996-0550
> office phone# (423)974-4221
> fax# (423)974-1686
> home phone # (423)573-9160
> email: pdavidson@xxxxxxx
> http://econ.bus.utk.edu/Davidson.html