Josef Steindl
August-September 1972
The Personal Distribution of Income
When D.G. Champernowne showed how you can explain the
Pareto law by 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
pioneering paper cy while fully demonstrating a powerful
new method, has not entirely disposed of the individual
tff
m w.
problem,which it was designed to solve.
Champernowne's Model
I shall give a simplified version of Champernowne's model
4 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 Markov chain. The stochastic
matrix of income transitions from one year to the next, in
desperate simplification, looks as follows:
income in year t + 1
0
1
2
3
4
3
6 • •
0
q
p
1
q
P
2
q
p
3
q
P
4
q
p
5
q
p
•
•
•
•
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