Full text: The Personal Distribution of Income

To find the tail of the steady state distribution P(y^) we 
sum (2) from ft to and obtain p . Thus 
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 
which is^directly descended from Xule /~15_7, who used it 
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 
&u t Ay ' 
/y -0efa&ti/x. fa* S-fi- t d" 
c4 ■

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