Full text: The Personal Distribution of Income

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. 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 
example, there is a probability of virtually infinite 
life.The steady state in these models is made possible 
only by the continuing new entry of small units. 
Further developments. 
Champernowne's work has inspired another model (Rutherford 
1955)in which personal age has been introduced 
explicitly.This still leaves important questions 
unanswered. Income is not a very suitable variable as the 
state of a Markov chain. It does not embody the influence 
of the past (Polya's "influence globale"),so that 
yesterdays state tells you all you need to know about the 
past. More important, the model is confined to the life 
cycle of an individual from entrance to exit. But the 
relevant stochastic process goes far beyond that.When 
somebody starts in life his chances of receiving certain 
incomes are already settled to a large extent by the 
condition of his parents:By their wealth,status, 
connections,reputation and the education or training they 
have been able to give him. 3 In other words the entries 
and exits in the life cycle model are linked by 
inheritance and similar elements, and the stochastic 
process continues over the generations. 
The arguments point to an obvious conclusion: We must 
relate the chances of getting certain incomes to the 
amount of wealth and to other factors which are in a wider 
sense "inherited". In this way we can link the income to a 
suitable state variable which is evolving in a long run 
process through the generations. By following such a path 
we shall also be able to answer the question why income

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