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;
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 hierarchises. Examples
of such hierarchies are wealth, education, status, grade (level)
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of an official or manager, rank of officers, ^obility, degreSe of
specialisation, grading by popularity of stars etc. Each of these
would represent a dimension in what might be called hierarchical
ey
spe'ce. An individual would occupy a certain point in that space,
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corresponding to its r0nk in the various hierarchies, and it
would h&ar€; certain probabilities of transition with ip 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.
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To each point in the hierchical space corresponds a certain probability
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distribution of income; the basic rule that the higher rank means
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expectation of a higher income.
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