About the "missing equation"

[Dimitris Konstantareas <dimit@xxxxxxxx>]

Today, the overwhelming majority of the profession believes that the
aggregate supply of output is vertical, if not in the short run, definitely
in the long run. Keynes, more than 60 years ago, argued that the facts from
experience constitute "prima facie" evidence [G.T., p.9] against this
classical view of the word. However, his alternative to the orthodox
paradigm failed, at the end, to displace orthodox economics, -not only from
the field of theory, but from the policy field as well. The reason, turns
out to be, the alleged lack of choice-theoretic microfoundations on the
supply side of his system. This much and more along these lines is
encrypted on the one face  of the "Keynes  and the Classics" coin.
The "Introduction" that follows belongs to a paper that I plan to send out
for publication. The paper is an outgrowth of one I published in 1987 in
the  "York's Studies in Political Economy". It can be found at
<http://msc05.atkinson.yorku.ca>. It is the result of a reading of the
other side of the "coin". According to it, the letter of the General Theory
does not fit in the framework of the excess labor supply law. Subject to
this law Keynes' theory of aggregate supply lacks, by definition,
microfoundations. However, such a conclusion can be true only if this law
is above any logical objection.  Even if that were true, still we should
know how Keynes dealt with the supply issue. Is it too late then for a
re-examination of the supply side of Keynes' economics? Your answer and
comments would be greatly appreciated. (Apologies for the size of the
"message").

                                                 KEYNES AND THE CLASSICS I;
                                                  towards the "missing
equation"

 Introduction

Keynes criticized the classical theory, for a missing equation problem [G.T
], but Professor Milton Friedman(1973) turned this around. Friedman,
somehow (we shall see how) found that the criticism applies only to Keynes'
General Theory model. Worse than that, Friedman believes not only that
Keynes' model is "one equation short", but that Keynes, at the end, came to
admit that much; Keynes "himself" said "we are one equation short"
[Friedman 1978]. And Keynes did say that. But then how did he come -at the
same time and in the same book, to strongly believe that his theory is
"general" in contrast to the classical theory, with small "c" [GT., p.3]?
On the basis of a defective model? Did he really offer an
one-equation-short model in the place of another model -that he criticized
for the same problem?
We all know that Keynes distinguished between voluntary and involuntary
unemployment, rather than between high and low unemployment. High and low
unemployment could be of the same "color", but the same is not true with
voluntary and involuntary unemployment. The former is compatible with the
"second" postulate of the classical theory [GT, p.6], while the latter is
not. Thus, if high unemployment is involuntary, in Keynes' strict sense
[GT.,p.15], the application of the classical theory to this unemployment
would be "fallacious" [GT., p.16]. For, under the second postulate, Keynes'
"third" kind of unemployment is inadmissible.
To accommodate the case of involuntary unemployment, one needs to first
"throw over" the second postulate of the classical doctrine. If we begin
with the Classical Model and then relax the labor-market equilibrium
condition, the second postulate would no longer be enforced, but it would
neither really be thrown over. For, without any further ado, the resulting
model would be one equation short. Thus one would have to recall the
equilibrium condition. This may mean either that the second postulate is
indispensable to the analysis in general, or it is indispensable to the
classical analysis only. Keynes, of course, argued the latter. That may
mean that, before throwing over the "axiom of parallels", he had worked out
the necessary "non-Euclidean geometry", viz., involuntary-unemployment
analysis, to fill the gap of the system.
If involuntary unemployment is by Keynes' grand design incompatible with
the second postulate, then the throwing over of the postulate presupposes
the existence of an involuntary-unemployment analysis. Our failure above to
throw over the postulate by relaxing the equilibrium condition -in the
context of the classical model, exemplifies this point. A more dramatic
exemplification of the same point is offered by the equilibrium
macroeconomic theory that emerged after the publication of Keynes' General
Theory, and because of it. Notwithstanding any contrary views or beliefs,
all this theory turns out to be compatible with the second postulate. Thus,
the unemployment of all these models is voluntary or frictional. That is,
in the big and closed "book" on Keynes' General Theory the term
"equilibrium with involuntary unemployment", although frequently
encountered, lacks any analytical content. There is no, that is, pure,
impure or ad hoc equilibrium model of involuntary unemployment, in the
"book"! This may explain why all these equilibrium models, "Keynesian" or
not, come of necessity to agree with the second postulate, comprehensively
defined. But this does not explain how Keynes came to the position to
challenge the postulate and introduce his theory as "general".
If the General Theory had not been published more than 65 years ago. If its
"new" ideas had not attracted the interest of the best minds of the
profession. If Keynes' case was not "appraised "reappraised" and, since the
mid 1970's, firmly closed, one, on the basis of the above discussion, might
have come to the conclusion that whatever Keynes said against the classical
theory must be founded on a non-classical equilibrium analysis of
unemployment. Straightforward thinking points to such a conclusion. Keynes
cannot possibly had claimed that his theory is general in contrast to the
classical theory, on the basis of a classical theory of unemployment! He
cannot possibly had offered a model of voluntary unemployment for the
"problems" of involuntary unemployment: he cannot possibly had committed
the very fallacy he asked others to avoid. He cannot possibly had
criticized the classical theory for a missing equation problem, without
first having an involuntary unemployment model. Of course, such conclusions
are natural after giving Keynes the benefit of the doubt. Such conclusions,
though, come to head on collision with the "habitual modes of thought and
expression" on Keynes' accomplishment.  Was then Keynes given the benefit
of the doubt, during the debate of his case? More precisely, was he taken
literally and, thereby, seriously on the main objectives of his work? The
answer to both questions turns out to be categorically negative.
 Keynes' case was appraised, reappraised and finally closed, or better
given up, within the  Walrasian formulation of the excess labor supply law
(hereafter the Law), under alternative rationality restrictions and
wage-adjustment hypotheses. The Law, as we shall see, does not admit
involuntary unemployment in Keynes' sense, at any theory level -pure,
impure or ad hoc. This explains why in the "book" that came out of the
historic "Keynes and the Classics" debate and Leijonhufvud's [1968]
re-appraisal of this debate, no such model exists. This, though, does not
answer the question about the way Keynes arrived at the conclusions he
arrived at about his theory and the classical. Do these conclusions follow
from a model of involuntary unemployment? If they do-as they should, due to
the interference of the Law and possibly other related received theory,
Keynes' model must had been missed, during the debate of his case.  Whether
this is true or not, is a question that cannot be answered in the present
paper.
The purpose of the present paper is to challenge the propriety of the
appraisal and reappraisal of Keynes' case within the framework of the Law,
and that way raise the expectation or "rational" belief in the reader's
mind that if Keynes' General Theory contains any "new" ideas on the supply
side of the system, they must had been missed by his "fellow
economists".  Thus, in Section I, I shall present a formal statement of the
Law. In Section II, I shall critically present the verdict of the debate
with its incredible implications on Keynes as a logician cum economist.
Section III is devoted to the definition of involuntary unemployment, its
pitfalls and its incompatibility with the Law. Section IV concludes the paper.