## Full text: The Personal Distribution of Income

```To find tiie tail of the steady state distribution P(y^) we
sum C£) from ft to cc and obtain p*. Thus
1 i x 1
m PCy*) -\ia p ) e ln 7 k
and, putting -h - ^ In p = oC we have
In P(7ft) * -oC ln 7/o C3)
Evidently the crucial feature of the model is the geometric
distribution of the recurrence time. This relates here to
the life-time of the persons as income receivers; since
promotion is automatic, the age of the system is measured
in income classes K. The age, or spent life-time, is
geometrically (approximately exponentially) distributed..
Since the income is also an exponential function of K ,
the Pareto law results from an elimination of time K from
1)
the two exponential functions. '
This is exactly the same pattern of explanation as was used
(3 - 2./, 2.1, 23 _
in other fields by Simon £ 4ft/ and myself and
in, _ *#■_ '
which is'directly descended from Tule / iyy, who used it
2.
to explain the frequency of species in genera. According to
-i "N V
'Although Champernowne's x model is more complicated than the
above the essential features remain the same (orriy^ o in
the solution is replaced by the solution of a difference
equation).
```

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