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 
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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