The full force of the Sonnenschein, Mantel, and Debreu (SMD) result is
often not appreciated. Without stability or uniqueness, the intrinsic interest
of economic analysis based on the general equilibrium model is extremely
limited. Morishima (1964) was very clear, when he said, concerning
stability, ‘If economists successfully devise a correct general equilibrium
model, even if it can be proved to possess an equilibrium solution, should
it lack the institutional backing to realize an equilibrium solution, then the
equilibrium solution will amount to no more than a utopian state of affairs
which bear no relation whatsoever to the real economy.’ But, for macroeconomists,
uniqueness is also important. ‘Comparative statics’ in which
one compares one equilibrium with another one, predicated on a change in
the parameters, makes no sense in the presence of multiple equilibria. Now
it is clear why macroeconomists find as the usual way out of this problem
the assumption of a ‘representative agent’ since this obviously generates a
unique equilibrium, which will be associated with the prices which make
the individual unwilling to move from where he is. However, as I have
said, the assumption of such an individual is open to familiar criticisms
(Kirman 1992; Stoker 1995) and recourse to this creature raises the basic
problem which I have mentioned and which was encountered on the route
to the place where general equilibrium has found itself: the problem of
aggregation. In fact, we know, as I have already pointed out, that in general,
there is no simple relation between individual and aggregate behaviour,
and to assume that behaviour at one level can be assimilated to that
at the other is simply erroneous. Just to give an elementary example, from
the standard assumptions on individuals, it follows that each of their
demand for goods satisfy the ‘Weak Axiom of Revealed Preference’
(WARP); that is, if in some situation, an individual chooses alternative
‘x’ when he could have chosen ‘y’ he will never choose ‘y’ when ‘x’ is
available. But, unfortunately, if we sum the demands of two individuals,
both of whom satisfy WARP, their aggregate demand may not satisfy it.
Thus even well-behaved individuals do not, in sum, necessarily have wellbehaved
demands.