## Full text: Income Distribution: Line of Reasoning (Fassung 1)

```<')
<*-)
0*1
t\
Simon on executives
-'JV
L
First assumption: A constant span of control at all levels of
the hierarchy, ^THis ought really to he a random variable.}
This leads to: jj^S) size ( number of executives^according to
Simon, but a reasonalle measure would bi
capital or sales)^(L) level of the hierarchy^]
In S = L In n + constant,
Second assumption: & constant ratio between a man's salary and that
of his subordinate.^b^ (also that ought tojbe a random variable )-
That is used to determine the salary of the top executive in
('fafrd j !
terms of those at other levels:
In C = L In b + eonstant^
By elimination of the level L we obtain
n _ In b tv
In C = , , , , In b
— In S + cpnstant - constant —
the salary of the top(official »')Manager is a function of size of
company^ ^
that is the xsxizx relation empirically observed by Roberts.
It might be hoped that Roberts relation also holds more
generally for all organisations like hospitals, city administrations
etc. although the measure of size becomes again more prob/elematic
(employment? which would however not fit automatized corporations).
Simon now passes to another empirical observation, made by Bavis,
The frequency distribution or density of executive's salaries
at General Motors in 1936 Wfas a -^arato distribution:
f°' :
C' = m N~ 0 *^ f C': salary , N;number of executives receiving (P '
O/
The number of markers at level L' from the top is
N ( L' ) = n L '" 1
Simon now writes from assumption 2
C'(L') = M b 1 L '
1 . AJi
but his M must be logically equal to the to^/salary C, although he
does hot say so.
The equation obtained by eliminating L' is therefore
inc '"4H- lnK
U W■ , ^ V
jfa. N =\L , -l)fa**'
■fa, £* ~ fa~ M
6m, &
'tv
```

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