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of wealth and income. This could be used then to
understand and interpret the empirical joint distributions
of income and wealth. For this purpose one would no doubt
require data which are more conveniently arranged than the
published material used above, and for this reason alone
it would go beyond the modest scope of this paper.
Footnotes.
1 The difficulties arising from the discrete
representation of a continuous income variable
(Cramer,1969,p.62)in the matrix need not concern us
here.They do not exist since we relate the classes of the
matrix to rank in a hierarchy.
2 Champernowne apparently did not know Yule's paper. It
was Simon's merit to have brought it to the attention of
economists.Unfortunately he used it in a form which
obscured its essence which is the interplay of two
exponential,or geometrical,distributions resulting from
two stochastic processes.
3 Champernowne was, of course, aware of these facts,as his
thesis of 1937 shows (Champernowne 1973).His formalised
model of 1953 is,however,not well suited to reflect all
the economic factors so well stated in 1937.
4 As far as the other factors,in other words,the
explanations of earned income, are concerned, I can only
vaguely indicate the direction in which I think a theory
might be developped. The high earned incomes concern e- /
managers,professional people artists and sportsmen. In
most cases these people can be ranked in a hierarchy which
in the case of managers depends on the scope of their
activity,i.e. on the size of the firm,while in the case of
the artists and sportsmen what matters is the size of the
audience which they serve. The modern media have created
ever larger audiences and accordingly greater incomes. A
relevant theory of the high earned incomes (and the Pareto
distribution is relevant only for them) will have to start
from this concept of hierarchies pertaining to scope which
gives another interpretation of Champernowne's matrix
which,in his own presentation, is more adapted to income
formation in a burocratic hierarchy.
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