Full text: The Personal Distribution of Income

6 
• ( , V 
The solution of the equation is X k = b (b<l). 
The steady state distribution of the population according 
ir t • • • • Tr 
to rank is (l-b)b and the tail of the distribution is b . 
The steady state solution in Champernowne's case is thus 
equivalent to the simplified case treated further above, 
if p is replaced by b. 
The aim of the preceding considerations is to show that 
Champernowne's explanation of the Pareto law is basically 
the same as that of Simon (1957)and myself (1965) which 
goes back to the model of Yule (1924) who used it to 
explain the frequency of species in genera. 2 According to 
this approach size distribution is a transformed age 
distribution and the pattern of the Pareto law occurs so 
often simply because of the empirical importance of 
exponential growth which makes both the age distribution 
and the transformation function exponential. Owing to the 
conceptual density of Champernowne's model the two 
elements of rank in the hierarchy and income as a function 
of rank are merged into one. 
There is,however, a difference (which relates to the 
interpretation rather than to the form ) between 
Champernowne's model and the others:Since physical persons 
sooner or later die the age or rank in his model is 
limited while in other models, of firms or of wealth,for
	        

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