Josef Steindl 
August-September 1972 
The Personal Distribution of Income 
When D.G. Champernowne showed how you can explain the 
Pareto law hy a stochastic approach he very naturally 
chose as an example the distribution of income, because 
that is the classical case. It appears now that the approach 
is more easily applied to firms, towns or wealth.-) 
The case of income is the hardest, so that the great 
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pioneering paper £*& while fully demonstrating a powerful 
new method, has not entirely disposed of the individual 
problem which it was dooignod - to -o-olve♦ 
Champernowne's Model 
I shall give a simplified version of Champernowne's model 
7 
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which will throw a new light on its relation to other 
models of the Pareto law. 
The income of a person is the state of the system, and 
its evolution is described by a Harkov chain. The stochastic 
matrix of income transitions from one year to the next, in 
desperate simplification, looks as follows; 
0 
1 
2 
5 
4 
5 
6 . 
0 v 
q 
p 
1 
q 
P 
2 
q 
P 
5 
q 
P 
q 
p 
'5 
q 
p 
• 
• 
• 
• 
♦ 
• 
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CO 
CD 
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