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

Note that the two empirical relations are of an entirely 
different kind. One determines the top salary in 
various companies. The other determines the salary 
corresponding to the frequency with which it is paid in 
a certain company ( the more natural way of putting it 
would be N = m' C -5 tL* 
Simonas point ( howefer ( is that with his explanation the 
parameter is the same in thejtwo very different equations 
which squares with the empirical isx result. 
Simon's theory follows the pattern of the usual Pareto 
explanation - the two exponential distributions - 
but it is unsatisfactory because, like Roys esplanation of t 
lognormal distribution , it does not contain the time element. 
We must get history iito it. v 
A way by which it can enter: the size of organisations grows 
with time. 
Incidentally the siye distribution of companies is already 
pareto distributed, therefore the-top salurj would bo so ‘ 
rH-a^ri bo ted, s-inde—irt^-drs—a—linear —function of the s i z W7~7 ^ 
Elaboration of the algebra: 
Substituting from 3 in 7• 
('LOln b . _ T 
In ^ --n’T"" 1 " r - In N 
In n 
In n 
( In ^ _ constanti ) + constant 
In "b 
In C' =“ t ( In N ^ In S -l-constant.) + constant,, j 
-*-^1 n I i0l0 ^r 
The results of Simon imply that th e same parameter In b/ In n 
occurs in both relations and the fact that the parame&er is 
empirically the same serves him as confirmation. 
He has implicitly assumed that the parameter is the same for 
all companies, that is implied in his argument. 
We stuck to this assumption in deriving the gneral distribution 9 
which can be more conventionally put as follows: 
In N § In C 1 In S ^constanti j xX chnstant2 
In b 
N = C ' 
exp(constanti -constant2 ) 
If we now mix the above distribution of N with the frequency function 
of S, the size distribution^we ought to get the frequency of 
salaries for the whole industry. The distribution of S is Pareto.

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