4
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