The above argument was based on the extremely restrictive
assumption that every member of the population of participants has
the same amount of financial resources. If we drop this assumption
we may at the same time also drop the implicit assumption that
every participant expects one and only one definite price. This
is,in fact, rather artificial. In reality he probably considers
several alternative prices and perhaps attributes greater or
lesser probability to one or the other alternative. If this
variety of expectations has any practical consequence it will mean
that he divides his resources according to the prices"on which he
speculates”, acting as a bull in relation to one part and as a
bear in relation to the other, the proportions depending on the
probability he attributes to the various expectations. In fact the
participant may be regarded as a divided personality consisting of
various parts each of which holds the same amount of wealth (a
standard unit which may be determined by the minimum unit which
can be traded).Again these expectations of the various
"subpersonalities” may be ordered statistically and combined with
the orderings of the other participants. In probabilistic terms
this will mean a convolution of the various frequency
distributions of the individual expectations. The resulting total
frequency distribution for all participants together will show
just how much funds are associated with each expected price. This
is a cumulative frequency distribution as before but without the
restrictive assumption of equal resources for each participant.The
shift from bull to bear or vice versa may now take place within
the resources of one and the same person or it may take place
between persons.
The distribution function just described may now be used to define
and measure uncertainty. The measure of uncertainty in the group
of participants in a market is given by the variance of the price
expectations . This cannot be observed directly but it will show
itself through the strength of the price response which a certain
additional offer or demand from outside (an exogenous
disturbance)will produce. If expectations are closely concentrated
a small change in the price will shift a large volume of financial
resources from bull to bear or the other way round. If they are
spread out widely a large change in price will be necessary in
order to shift a modest amount of resources. It has to be noted,
however, that the strength of reaction will also depend on whether
the price initially is in the middle of the distribution (near the
mode) or nearer to one of the tails.
The peculiarity of the above definition of uncertainty is that it
does not apply to an individual but to a group. Instead of being
psychological it is a social concept.
The above analysis can also be seen as an alternative to
traditional concepts of supply and demand. Instead of two
different functions relating the same two variables we have only
one function. The supply (offer) and the demand are exogenous
quantities. The ticklish point in the analysis is the
identification and definition of "exogenous”. We have assumed
implicitly that the amount of bonds is given and invariable. The
new entrant into the market who brings in a new demand or a new
supply must therefore indirectly find the necessary adjustment in
the quantity of the no-bonds, that is money, which is assumed to
adjust automatically in Kaldorian fashion.