Full text: The Personal Distribution of Income

Th^ose few units which survive for good continue to grow; on the 
other end of. the scale new entrants/enlarge the total sample 
of firms or wealthy' dynasties. The continuance of the steady am 
state with unchanged distribution is accompanied by a steadily 
growing size of the sample whidh produces ever larger firms, 
wealth holdings etc. These large units always existed potentially 
but could not be realised a± as long as the sample was too small; 
with the growth of the economy such potential sizes become actual 
and in consequence the largest units represent a greater and greater 
shaa*e of the total although the theoretical distribution is 
unchanged. With the finite life and the stable population 
of Champernowne 1 s model this peculiar form of growing inequality 
would not arise. 
Further developments 
We may consider the following stages in the treatment of the 
income distribution: 
I. Champernowne 1 s Model. 
II. Rutherford^ model /I9/. He treated person’s 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

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