Full text: Konvolut The Personal Distribution of Income 1

I 
4 
To find the tail of the steady state distribution P(y^) we 
sum (/) from & to oo and obtain p . Thus 
1 \ 1 
3-n H7 K ) -^la p ) E 1» J B 
«-I 
and, putting -h In p = oC we have 
In P(y^) = -cC In 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 K. The age, or spent life-time, is 
geometrically X a PP rcsiinai:e -7 exponentiallyf distributed. 
I / I lit i \ l 
Since the income is also an exponential function of K » 
the Pareto law results from an elimination of time K from 
5' 
the two exponential functions. 
This is exactly the same pattern of explanation as was used 
m .. L* \ t ^ ^ 
/ 2. i, 1 
in other fields 
t)v 
- _ —7 y - _ 
by Simon £ Jp and myself -43/ and 
which is-directly■descended from Tule 1# J, who used it 
(IQ2H> 2. 
to explain the frequency of species in genera. According to 
'Although Champernowne's^model is more complicated than the 
above, v -the essential features remain the same (only, o in 
the solution is replaced by b, the solution of a difference 
equation).
	        

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