# Full text: Income Distribution: Line of Reasoning (Fassung 2)

```Simon n executives
First asoumpt ons A constant span of control at all levels o r
the hierarchy. n fHis ought oally to be a random v riablo.
This leads to: S else ( number of executives according to
Simon, but a reasonable mo .'..sure would b&
capital or sales) L level of the hierarchy
lrx S = L In n + con tant
Second assue tion: A constant rati ; bet .eon a eon's . :alary and that
of his subordinate, b (also that ought lobe a random variable )
C
That is used to determine the alary f the top executive in
terns >f these at other levels:
In C *■* L In b + constant
By elimination of the level L we obtain
1 U ^ In 1) 1u
——— In S + constant - constant
In n Ir. n
the ovlory of the top(official »)&ano£cr is a fancti n of oise >f
company
that is the rsmtxx relation empirically bservo by Leberta.
It mi I t be hoped that Robert" relati n also holds more
enerolly for all organisations Ire Los itala, city a minis rati ns
etc. alth ugh the measure of sise becomes again more r belomatic
(a-.-'loyaent? which would however not fit automatic d cor -ora ions).
Simon new passes to another empirical observation, a e by Davis,
The froquo.-oy distributi n or density of executive’s sal ...ieo
at General oiors in 193^ > ! as a 1 arete distribution:
C* <=» n IT C’ sal ry , IT number of executives receiving 6’
The number of mangers 1 level L’ from the top is
II ( L’ ) . n L ’’ 1
Simon new w ites from assumption P.
/ . 1-L’
C’(L’) = I£ b
but his II must be logically equal to the topsal ry C, although he
doon not say so.
The equation obtained by el :i.minuting L* i therefore
In b
In n
In C’
In H + In C
```

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