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The transitim probabilities will also reflect long run develop
ments: Growth, organisational changes and innovations etc.
After the explicit introduction of time (age, and also "historical"
time) the model could also be made more realistic by making the
span of control as well as the income relation b into random variable.
The pattern of the explanation could then, X think, be extended
from the managers to other groups of income earners.
So far we have only refered to the separate groups (like managers
etc) each of which is represented by a dimension in the hierarchy
space. The relation between these dimensions remains open, and
therefore also the question how these separate distributions
combine into a total income distribution which still shows the
familiar Pareto pattern. Prima facie the relation between the various
hierarchy dimensions is undetermined; our society does not definitly
rank business managers, doctors, officers etc. The only common
denominator is income. There is, however, some sort of vague
hierarchy of the hierarchies themselves, indicated by the mean
income and by the inequality as measured by the Pareto coefficient.
On both counts wealth is at the top of the hierarchies; the stars,
the managers and some professions follow in a rather uncertain order.
By and large, however, you will find the groups with lower mean
income also have higher Pareto coefficient and are larger groups.
1 should insist on the greatly irrational (or "traditional")