21 
In the course of his life-carreer, the individual moves from one 
position to another. It has been repeatedly described how the 
hierarchical advance during the life-time leads to skewed income 
distribution^/ /, and, in fact, may give rise to a Pareto distri 
bution; this is shown in the example treated at the very beginning 
of this paper. 
The position reached by an individual influences, however, also 
the inital position and the progress of this heirs. The stochastic 
process thus continues over the generations. This has been studied 
by sociologists under the title of "social mobility" /4/. 
In order to lend just a little more concreteness to our theory, 
let us consider a special hierarchy, that of the managers. Their 
income distribution has been studied by several authors /13, 15, 
16 or 3/ and we shall refer to the very simple but illuminating 
picture given by H.Simon /3/. He assumes that each manager can control 
directly a certain number of subordinates and no more; this number 
is called the span of control. If this span of control is the same 
on all levels, then the employment at various levels of the hierarchy 
from top to bottom will increase in geometric proportion. 
He further assumes that each manager gets a salary which is determined 
as a certain proportion (larger than unity) of his subordinate's