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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.