5 
this approach, size distribution is a transformed age 
distribution, and the pattern of the Pareto law appears* 
so often simply because of the empirical importance of 
exponential growth which makes both the age distribution 
and the tranformation function exponential. Owing to the 
conceptual density of Champernowne's model the two 
elements of life- cycle and promotion are merged into 
one. 
(which resides 
There is, however, a difference^in the interpretation not 
in the form) between Champernowne's model and the others: 
Since physical persons sooner or later die, the age in 
his model is limited, while in the others (relating to 
firms or wealth) there is always the probability of 
virtually infinite life which accounts for a very 
2.2, 
peculiar character of the steady states concerned 7• 
Further developments 
We may consider the following stages in the treatment of 
the income distribution: 
I. Champernowne's model. ^ 
II. Rutherford's model C'ytl* He treated persons'life- 
times explicitly. 
III. The above models are open to criticism on two grounds: 
First, income is not very suitable as a state variable 
for a Markov process. It does not embody the "influence