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 
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 
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 

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