4 Uniqueness, stability and the ‘representative agent’
To see what is going on, suppose for the moment that we put to one side
the debate as to what constitutes rationality and that we accept the standard
axioms of rationality for economic agents and wish to build our
macromodels on that basis. Why would this pose a problem? The
simple answer is that, even under these very restrictive assumptions,
there is no guarantee that the economy would ever attain the equilibrium
states which are analysed in such detail by macroeconomists. In other
words, the key to the problem lies in the stability of the equilibrium
states. We make the usual rationality assumptions for our individuals
because this enables us to prove the existence of equilibrium states.
These can be shown to be characterized by an efficient allocation of
resources by the well-known ‘fundamental theorems of welfare economics’.
It is often asserted that somehow, an economy in equilibrium, if
knocked out of that state, will return to it, as a result of some adjustment
process. Typically, the Walrasian tatonnement process, which increases the prices of those goods for which demand exceeds supply and decrease
the prices of those for which the opposite is true, has been used as an
example. Let us assume for a moment that we define some such process,
which adjusts prices when they are not in equilibrium. This would not help
us at all, because the fundamental problem is that the conditions which are
known to guarantee the stability of such a process cannot be obtained
from assumptions on the behaviour of the individuals. To be absolutely
clear, what Sonnenschein (1972), Mantel (1974) and Debreu (1974)
showed is that there is no hope of a general result for stability nor
indeed of uniqueness of equilibria, if we wish to build a model based
only on individuals who satisfy the standard axioms of rationality.