20
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 probabi
lity distribution of income; the basic rule is that the higher
rank means expectation of a higher income.