gross substitution and existence proofs

[Paul Davidson <pdavidson@xxxxxxx>]

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