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^ \