24 
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 accrue to 
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.