# Full text: The Personal Distribution of Income

```4
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
``` ### Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.