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An Attempted Generalisation
In dealing with income of property owners we have chosen as a
state variable wealth which evolves slowly in a stochastic process?
unearned income can be derived from it by means of another random
variable/ the rate of return. Can we generalise this two-step expla
nation to include also earned income?
In a somewhat formal way we could speak of the rank which an
individual occupies in one or several hierarchies. Examples
of such hierarchies are wealth/ education/ status, grade (level)
of an official or manager, rank of officers, ability, degree of
specialisation, grading by popularity of stars etc. Each of these
would represent a dimension in what might be called hierarchical
space. An individual would occupy a certain point in that space,
corresponding to its rank in the various hierarchies, and it
would have certain probabilities of transition within a certain
time to another point in that space. In other words, an indi
viduals* hierarchical position in society (a vector) would be the
state variable of a stochastic process.
To each point in the hierarchical space corresponds a certain probabil
lity distribution of income? the basic rule is that the higher
rank means expectation of a higher Income.