What you are actually watching
Inequality statistics get quoted constantly and explained rarely. The Lorenz curve is worth
twenty minutes because once you can read it, most of the argument becomes legible.
How to read the curve
Line everybody up from poorest to richest. Walk along the horizontal axis to any point, say
40%, and you have the poorest 40% of people. Read up to the curve and you have the share of
all income those people hold between them.
The dashed diagonal is perfect equality: 40% of people would hold 40% of
income, and so on for every point. The real curve always sags below it, because the poorest
40% always hold less than 40%. How far it sags is what the Gini turns into a number.
Drag the spread slider and watch the sag deepen. Nothing else about the economy is changing,
only how widely incomes are dispersed.
Where the Gini comes from
The Gini coefficient is the shaded gap between the diagonal and the curve,
divided by the entire triangle beneath the diagonal. That is all it is: a measure of how far
the distribution has moved away from equality, scaled so the answer always sits between zero
and one.
Zero means everyone earns identically and the curve lies on the diagonal. One means a single
person holds everything and the curve runs flat along the bottom before leaping up at the
very end. Real economies sit well inside those extremes, and the presets here are
illustrative shapes rather than any particular country.
The limitation that matters most
Switch to "Same Gini, different shape". Both curves score identically on the Gini, to three
decimal places, and they describe completely different societies.
One is a smooth ladder: incomes spread continuously, with people at every rung and a
plausible path from one to the next. The other is two rigid blocks, where everyone inside a
class earns precisely the same and there is nothing in between. Same coefficient. Nothing
else alike.
This is not a flaw to be fixed, it is what summarizing a distribution in one number
necessarily costs. The standard correction is to read the quintile shares
alongside the headline figure, which is why serious statistical agencies publish both, and
why a debate conducted entirely in Gini points is usually missing something.
Why the Gini is least sensitive where the argument is loudest
The Gini responds most strongly to changes around the middle of the distribution and least
strongly to changes at the very top and very bottom. That is an awkward property, because
the middle is where shares tend to be most stable across countries and decades, while the
tails are where the political argument actually happens.
The Palma ratio exists for exactly this reason. It divides the income share
of the richest 10% by that of the poorest 40%, ignoring the middle entirely on the grounds
that it barely moves. It is cruder and it is more responsive to the thing people are usually
arguing about.
What redistribution does to the picture
Switch back to redistribution and drag the tax slider. Every point on the curve lifts toward
the diagonal, and the Gini falls by exactly the tax rate. Set 30% on a Gini of 0.5
and it lands on 0.35, precisely.
That exactness comes from the simplicity of the scheme modeled here: a flat tax on all
income, paid straight back out as an identical amount to everyone. It moves each person the
same proportion of the way toward the mean, so it moves the entire curve the same proportion
of the way toward the diagonal.
Real systems are progressive, taking a rising share as income rises, which reaches any given
reduction at a lower average rate. The direction and mechanism are the same, but no real
country's tax code reduces to one number this cleanly.
What this model leaves out
A great deal, and some of it changes the interpretation rather than the arithmetic.
This is income, not wealth, and wealth is distributed far more unequally
almost everywhere. It is a snapshot, so it cannot see mobility: two societies with identical
curves feel very different if one has people moving between quintiles across their lives and
the other does not. It ignores age entirely, and since earnings rise and then fall over a
career, some measured inequality is simply people being at different stages. Households are
treated as individuals, and there is no adjustment for household size, which real statistics
handle with equivalence scales.
Most importantly, the Gini says nothing about the level of income. A poor country
where everyone has very little can score better than a rich one. A recession that hits high
earners hardest improves the number while leaving everyone worse off. It answers a question
about spread, and it is silent on whether people are doing well.
Things to try
Each takes a few seconds and lands something the headline figure will not.
1Prove the redistribution rule
Note the Gini, then set the tax to 50%. The new figure is exactly half the old one.
Try 20% and 30% and confirm it holds every time.
2Find the identical twins
Switch to the shape comparison and drag the lower class size. Every setting produces a
different society with the same Gini as the smooth one.
3Watch the middle refuse to move
Change the spread and follow the middle fifth's share. It moves far less than the top
and bottom, which is exactly the Gini's blind spot.
4Compare the two measures
Track the Gini and the Palma ratio as you raise the spread. The Palma climbs much
faster, because it is reading only the tails.
5Approach both extremes
Drag the spread to its minimum and the curve meets the diagonal. Drag it to the
maximum and watch the poorest 40% share collapse toward nothing.
6Break the comparison
In shape mode, shrink the lower class below the Gini value. The two-class economy
becomes impossible to build, and the page explains why.
Common questions about inequality measurement
What is a Lorenz curve?
A graph of cumulative income share against cumulative population share, with people ordered from poorest to richest. Read along to 40% on the horizontal axis and up to the curve, and you have the share of all income going to the poorest 40% of people. A perfectly equal society would trace the diagonal, because any given share of people would hold exactly that share of income.
What does the Gini coefficient actually measure?
The gap between the Lorenz curve and the line of perfect equality, expressed as a fraction of the whole triangle beneath that line. Zero means everyone has an identical income and one means a single person holds everything. It is a summary of how far a distribution sits from equality. It is not a measure of poverty, and it says nothing about how well anyone is actually doing.
Can two countries have the same Gini and look completely different?
Yes, and this is the most important limitation of the measure. The same coefficient can be produced by a smooth ladder of incomes or by two rigid classes with nothing in between, and those are very different places to live. Compressing an entire distribution into one number necessarily discards the shape. Reading the quintile shares alongside the headline figure is the standard correction, which is why statistical agencies publish both.
How much does redistribution change the Gini?
For a proportional tax funding an equal transfer, the Gini falls by exactly the tax rate, so a 30% tax on a Gini of 0.5 leaves 0.35. That is an exact result rather than an approximation, because the scheme moves every point on the Lorenz curve the same fraction of the way toward the diagonal. Real progressive systems reach a given reduction at lower average rates, since they concentrate the burden higher up.
What is the Palma ratio and why use it?
The income share of the richest 10% divided by that of the poorest 40%. It exists because the Gini is least sensitive exactly where most political argument happens, at the very top and the very bottom, and most sensitive around the middle where shares tend to be comparatively stable. The Palma looks only at the two ends, so it responds when the tails move and ignores the part that mostly does not.
Does a lower Gini mean people are better off?
Not on its own. The Gini describes only how income is spread, not how much of it there is. A poor country where almost everyone has very little can score better than a rich one with a broad middle class. A recession that hits high earners hardest can improve the figure while leaving everybody worse off in absolute terms. It answers a question about distribution and is silent on the level.
Should this be measured before or after taxes and transfers?
Both, and the gap between them is itself the interesting number. Market income inequality measures what the economy produces before government acts, while disposable income inequality measures what households actually have to spend. Countries with similar market inequality can end up far apart after redistribution, so quoting one without saying which is being used makes comparisons close to meaningless.