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 ) 
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 
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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