22
salary. The salary thus decreases geometrically as we go from
top to bottom.
In terms of algebra:
n: span of control
b: manager's salary in proportion to that of his direct
subordinates
L: level of the hierarchy (counting the base as unity)
N(Ii): number of managers at level L
C CD: Salary at level L
No: number of managers at the base level C, - A
.'A'l/t 'T'V
N(L)
w , ~ L
/Vi ^
L-i
(V
PJ
A: Salary at the base
AAv N -
oi, ^
/■A, c A)
(y
N - A" C ,
The salaries under the assumptions given conform to Pareto's
distribution. Simon bases his model on empirical facts (Roberts'
regression of top manager's salary on the size of firm, regression
coefficient 0,37, which would correspond to the value of y&L
and Davis' Pareto distribution of managers' salaries in General
Motors, Pareto coefficient 3).
The above demonstration is purely deterministic, but if
we regard the span of control as the reciprocal of a probability