4
_
To find the tail of the steady state distribution P(y^) we
sum (2) from ft to and obtain p . Thus
-1
In P(y~) = In p . ^ In
and, putting -h“ In p * o( we have
In P(y- : ) * -oo y#, (3)
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 ft. The age, or spent life-time, is
geometrically (appronimately exponentially) distributed,
^ince the income is also an exponential function of ft ,
the Pareto law results from an elimination of time ft from
the two exponential functions. '
This is exactly the same pattern of explanation as wsg used
in other fields by Simon J and myself /^2, 13, 147 anci
t
which is^directly descended from Xule /~15_7, who used it
1
to explain the frequencj of species in genera. According to
mmmmmmm ^ *TVv y ‘
‘^Although Champernowne's model is more complicated than the
above:, the essential features remain the same (only p in
the solution is replaced by b, the solution of a difference
equation).
&u t Ay '
/y -0efa&ti/x. fa* S-fi- t d"
c4 ■