Full text: The Personal Distribution of Income

5 
1 
relates here to the rank in an economic hierarchy linked 
to income.As promotion is assumed to be automatic the 
"age" k of the system ,or "spent life time" is 
geometrically distributed.Since the income is also an 
exponential function of k the Pareto law results from an 
elimination of k from the two exponential functions. 
It is natural to object here that Champernowne's model 
(Champernowne 1953)has been drastically simplified in the 
above argument. In his model there are more 
alternatives:People can either rise one step in the ladder 
or stay in the same state or recess to a lower 
state,although the possibilities of movement are limited 
to a certain range.The steady state solution which 
Champernowne obtains for his model is, however,essentially 
the same as the simplified case treated above. 
Champernowne assumes that the probability of transitions 
from state k-v to state k is independent of k and depends 
only on v.That means that the transitions depend on the 
size of the jump but not on where it starts from or where 
it ends. On this basis the following equation for the 
steady state is established: 
1 
X k = S p v X k _ v . (5) 
-n 
In terms of generating function the equation becomes
	        

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