3
Thus it could be expected that the income of the various
counties in England would be Pareto distributed because
it results in each case from the addition of individual
incomes which are Pareto distributed.
Champernowne's pioneering work (1953) in essence goes back
to his fellowship dissertation of 1936, published 1973.
He builds on a tradition which explains the normal distribution
as the result of the addition of random unit steps
(left or right ) on the line over a long time ( random walk;
for the terms and concepts relating to random processes
refer to Feller Vol I ).If the random walk takes place on
the logarithmic scale the distribution of the sum of steps
will tend to log normality. This does not give, however,
a stable distribution, because the dispersion will go on
increasing all the time. Champernowne chooses the technique
of the Markov chain: Each yearjs income depends only on the
previous year's income/plus a random increment proportionate
/
to last year's income; the probability of various increments
remains constant from one year to the other. This feature
is called the law of proportionate effect. Thus the required
data will be embodied in a matrix which contains the
probabilities of transition from one income in one year to
another income in the following year. The number of
income receivers remains stable in Champernowne's model
because‘each exit is assumed to be automatically compensated
by a new entry. To guaratee that the system reaches a
steady state it is assumed that on the average the change of
income is downwards; this is necessary to compensate the
tendency of the system to diffusion which is characteristic
of the unrestrained random walk. The assumption reflects