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.