Rich-poor gap measure

[huy.duong@ctsu.ox.ac.uk]

Dear anh Zung,

>No, a good measurement of the gap is not the difference of the income
>numbers
>as you wrote, but the difference of their logarithms.

The difference of logs, as the ratio of incomes, would be constant in
the scenario I mentioned and would therefore be a good, or better, measure.

However, economic books use what they call Lorenz curves (LC).
An LC plots the percentage of wealth owned on the y axis
against the percentage of popuplation on the x axis (after
suitable ordering of course). If wealth is equally distributed
then the LC id a straight line with gradient 1. Deviations from this 
straightline mean inequality. (Imagine that the LC hangs like
a hamock at 45%. This would mean that the first 50% of the
population have less than 50% of the nation's wealth and the 2nd
50% have more than 50%. The lower the hamock, the less the first
50% have and the more unequal the wealth distribution). This 
graphical representation facilitates the seeing of the difference
in wealth, not the ratio, as the rich-poor gap.

Also, what are most often published are not differences of logs
but the proportions of wealth owned by the poorest x percent of
the population and by the richest x percent of the population.
It is most natural to see the difference between these figures, 
not the ratio.

But all of this is just convention. What is the reality?
Is the gap between me and my friend bigger when I earn 200$
and he earns 500$, or when I earn 400$ and he earns 1000$.
I would say that it's the latter. The ratio is academic.
Before he has 300$ more than me and now he has 600$ more
and that's what counts. So I would say that the gap has grown.

Huy