Jr
to the tail of the recurrence time distribution, : .e. to p .
More directly, the vector of steady state probabilities
can be derived from the following two conditions:
U K = pu K-1
u Q * qu,_ + + <a u o + • • • O)
The first condition ensures the invariance of the steady
state; the second ensures that entries to and exits from
the income population balance.
It follows that
u£ * p*Si Q (2)
u Q »1-p p<1
The result is, of course, identical with the distribution
of the spent waiting tine.derived above.
\—•
We have now to define the income in relation to the class
intervals of the matrix: The lower limit of class 1 is
taken to be the minimum income. We may choose the income
units such that the minimum income is unity, i.e. on the
logarithmic scale it is zero. The income y^ at the lower
limit of successive income classes k is defined by
fc.h
H * e
or In y^ • kh
where h is the size of the class interval on the log scale '.
The difficulties arising from the discrete representation of
a continuous income variable in the matrix do not concern
us here. See fgl/ p. 62.