Re: gross substitution and existence proofs

["J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>]

     Alan is correct.  Gross substitutability is the
sufficient condition for uniqueness in the pure
exchange model (no production).
     Convexity, as Peter Dorman has noted,
and continuity are the key conditions for existence.
Barkley Rosser
-----Original Message-----
From: Alan G. Isaac <aisaac@xxxxxxxxxxxx>
To: POST-KEYNESIAN THOUGHT <pkt@xxxxxxxxxxxxxxxx>
Date: Thursday, April 15, 1999 5:26 PM
Subject: Re: gross substitution and existence proofs


>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
>