The Corner

Re: Income Inequality

I can’t resist the opportunity to explain the Gini coefficient, which is the

usual measure of equality of income (or any other individual attribute) in a

population. Ready? Here goes. Take the entire population and make them

stand in a line, equally spaced apart. They must stand by increasing order

of income (or whatever), with those persons having least at the far left,

those having the most at far right. Now take a walk along the line from

left to right, carrying a clipboard, pencil, and pocket calculator. Keep

adding up the income of the people you pass. When you have traveled

one-hundredth of the way along the line, write down the total so far.

Repeat at two one-hundredths, three one-hundredths,… all the way to the

end. The last number you write, at 100 one-hundredths (i.e. the rightmost

end of the line) will be the grand total income for the population. Now

plot an x-y graph, with the x’s being 1/100, 2/100, 3/100,… and the y’s

being the corresponding totals from your clipboard AS A PERCENTAGE OF THE

GRAND TOTAL. If there is perfect income equality, the graph will be a

straight line going from bottom left to top right. Halfway along the line,

you would have tallied half the grand total income, and so on. Perfect

INequality–the situation where one person has all the income and no-one

else has anything–will be a flat horizontal line along the x-axis doing an

instantaneous vertical rise at the far right. The area between these two

extremes is an isosceles right-angled triangle. Any actual graph will be a

concave-downward curve inside this triangle, moored at bottom left and top

right. The area between this curve and the hypoteneuse, as a percentage of

the total area of the triangle, measures inequality. Total equality: zero.

Total inequality: 100. The USA was running a Gini of about 40 on income

distribution last time I looked, which is highish for OECD countries. The

Scandinvians are down in the 20s, places like Brazil up in the 60s.

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