21
In the course of his life-carreer, the individual stoves 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 lnltal 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 subordinated