Full text: Konvolut The Personal Distribution of Income 1

To find the tail of the steady state distribution P(y^) we 
sum (£) from X, to oo and obtain p . Thus 
(3) 
1x1 P <7 K ) = _cC 
Evidently the crucial feature of the model is the geometric 
distribution of the recurrence time. This relates hers 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. 7 
This is exactly the same rattern of explanation as was used 
* - i/;it, 2 3 _ 
in other fields by Simon £ 1#/ and myself and 
which is'directly. descended from Tule CJ i wil ° used it 
2. 
to explain the frequency of species in genera. According to 
'Although Champernowne's x model is more complicated than t 
above^the essential features remain the same (oniy^u in 
the solution is replaced by t, the solution of a differs: 
'equation).
	        

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