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

```Bo to that the two empiric 1 rel ti no ere of an entirely
different kind. One hot rrainer the top salary in
various c.nspanies. The other determines the salary
'jQZ’rirGroouV.ng to the frequency with whi'oh'it i3 paid in
a certain c n. any ( the r ore nat r 1 ray of putting it
would be IT - m* C" 5
•imongs point b-cafor in that with ..is expIon-.ti n the
oranoior is the same in thetwo very different e uati ns
.hich .squares with the empirical be?: resu' t.
Simons th ory follows the pattern of the usual Pareto
cxt>lan tion • the two exponential distributions -
but it is unsatisfactory because, like Roys omplanaii n of
1 .normal distributi n , it does not contain the tire ole nnt.
e auot got history iito it.'
A way y which it can enter* the sise ,f orqanioati no prows
with time.
Incidentally the oiyo distributi. n of oonpanlos in already
pareto distributed, therefore the top sal -:ry would bo do
•istribute- , sindo it is a linear functi n of t c tide.
Elaboration of the algebra* Sub3titutiaG froQ 3 in 7*
1 r In b . „ , lnb
in 0 *> r 1 ' :— In I« +
In n
In b
In n
( In - constant] ) + constant 2
In C 1 «* ( In If + In S -constant.) + onsiant,,
In n * «•
The results of -imon imply that th e same parameter In b/ In n
occurs in both relations and the fact that the parameter is
err irlcdlly the same servos him as confirr ation.
Ho has inplioitly assumed tha the -ammeter is the same for
all companies, that is implied in his argument.
'0 stuck to this assumption in e.crivin the gneral distribution 9
which can c more conventionally put as follows*
In 35 » Tn‘"§ In C' - In 3 +constant1 - ^ cknstan 12
In n
IT
C»
s"
exp(oonstant1 -c nctenth )
If wo n w mix the above distribution of V. with the fro uoncy function
of S, the sise distributi n wo ov hi to get the frequency ;f
sal rior: for the ?h- le industry. The distribution f S is Pareto.
```

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