vv 
ir i/ / V' 
0 
hit 
V 
The salary thus decreases geometrically as go from 
top to bottom. 
In terms of algebra: 
n: span of control 
b: managers 4 ' salary in proportion to that of his 
^Subordinates 
•T 
L: level of the hierarchy (counting the base as unity) 
N(L): number of managers at level L 
C(L): Salary at level L 
N©: number of managers at the base level 
A: Salary at the base 
The salaries under the assumptions given conform to Pereter h'otAjhZo’ S 
distribution. Simon bases his model on empirical facts (Roberts' 
SoJtxOvu, 
regression of top manager's* on the size of firm, regression 
J 
coefficient 0, 3^, which would correspond to the value of 
and Davis' Pareto distribution of managers' salaries in General 
Motors, Pareto coefficient 3). 
i 
The above demonstration is ourelv deterministic, but if jwe" 
we regard the span of control as the reciprocal of a probabi^ \