4
To find the tail of the steady state distribution P(y^) we
sum (2) from X to oo and obtain p K . Thus
In P(y^) = In p . ^ In y K
„'I
and, putting -h In p = oC we have
In P(y^) - -oc In 7k 0)
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 i£ ,
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
l% - 2.^11/23
in other fields by Simon cW and myself and
[yv tM--
which is^directly descended from Yule CJj who used it
2.
to explain the frequency of species in genera. According to
^Altfbqugh Champernowne' sNo^odel is more complicasted than the
above^x^he essential feattip^s remain the same (oitiy p in
the solution is replaced by b, the solution of a difference
equation).