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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 variables. 
The pattern of the explanation could then, I 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. Prlma 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. 
I should insist on the greatly irrational (or "traditional")