Full text: The Personal Distribution of Income

u Q = 1 - p. P < 1. (2) 
The result is,of course, identical with the distribution 
of the spent waiting time derived above. 
So far we have described the process without mentioning 
income,and have identified the states with a kind of age 
(seniority). We have now to define the income in relation 
to the class intervals of the matrix. Note that income is 
to be measured logarithmically. The lower limit of class 1 
is to be taken as the minimum income. We may choose the 
income units in such a way as to make the minimum income 
equal to unity, i.e.on the logarithmic scale it will be 
zero. The income y k at the lower limit of successive 
income classes k is defined by 
or In y k = kh (3) 
where h is the size of the class interval on the 
logarithmic scale. 1 To find the tail of the steady state 
distribution P(y k ) we sum (2) from k to <» and obtain 
p k .Thus 
In P(y k ) = In p (1/h) In y k 
• — 1 
and, putting -h In p = a , we have 
In P(y k ) = - a In y R . (4) 
Evidently the crucial feature of the model is the 
geometric distribution of the recurrence time. This

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