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Gini Coefficient and Lorenz Curve - YouTube
Channel: Khan Academy
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in this video we're going to discuss
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income inequality which is something
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that is often debated thinking about
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comparing countries thinking about
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whether it's an issue or not and how to
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address it and to appreciate what income
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inequality is let's imagine two
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different countries let's imagine first
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country a and there's two people in
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country a so you have person one here
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who makes $1000 a year that's their
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income and then there's person two in
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country a that makes 99 thousand dollars
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a year so what is going to be the
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average income in country a if these are
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the only two people you could think of
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it as the per capita national income
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well the average income here average
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income to figure that out you would just
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have to average the 1000 and the 99
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thousand so you have a total income of
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one plus ninety-nine a hundred thousand
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and divided by two folks we're going to
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have an average income of $50,000 per
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year now let me construct another
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country that has the same average income
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but the distribution is very different
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so in country B let's say the first
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citizen of country B they make $50,000 a
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year and let's say there's a second
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person in country B and they also make
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$50,000 per year per year well what's
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the average income now well this is even
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easier to compute 50 plus 50 divided by
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2 your average income is $50,000 per
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year so what you see here is two
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countries that if you just looked at the
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average income they seemed similarly
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wealthy but that doesn't give you they
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seem to have similar average income so
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you say oh maybe they're similarly
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prosperous but when you go a step deeper
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you see that they are very different
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country a is a lot more unequal than
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country B when it comes
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to income so question is is above and
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beyond looking at things like average
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income or average GDP or per capita GDP
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how do you measure inequality and this
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is something that this Italian
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statistician Corrado Gini tried to
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address and he comes up with something
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called a Gini coefficient to measure
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income inequality for a nation and the
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way he approached it is actually pretty
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intuitive what he did is he sets up two
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axes so this axis right over here is
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going to be the cumulative percentage of
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the population so you start at 0% and
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then you get all the way to hundred
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percent of the population so this is the
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cumulative percent of the population in
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a country and then on this axis on this
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axis you have the cumulative percentage
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of the income in a country so this would
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be zero down here and then this would be
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hundred up here and so this is
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cumulative percent of income in a
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country and then he said well what would
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a perfectly equal society look like when
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a perfectly equal society as you add a
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percentage on your cumulative percentage
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of population you should add that exact
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same percentage to your cumulative
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percentage of income so as you go up you
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really should just have a slope of 1
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going up like this so one way to think
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about it is when you're at 0 percent of
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the population you should have 0 percent
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of the income if you have a total of 10
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percent of the population they should
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have 10 percent of the national income
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if you were to go to 50 percent of the
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population which looks like it's around
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there if it was perfectly distributed
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the income well then that should be 50
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percent of the national income but no
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nation is actually there and so then we
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have to think compare that to the
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reality so let's say you look at a
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country and and what you do is when
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you're looking at the cumulative
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percentage of the population you start
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at the left with the lowest income and
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as you add percentage of the population
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you get to higher
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in higher income folks so let's say
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we're looking at a country that for the
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poorest folks as you add percentages to
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the cumulative population you're not
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adding the same percent to the
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cumulative income and so it might you
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might have a curve that looks like this
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and then as you add percentages in the
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wealthier population for every 1% you
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add you're adding more than 1% of
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national income and so this curve
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variety over here which you could view
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is describing the reality for certain
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nation this is known as a Lorenz curve
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Lorenz curve and what Jeany said is well
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the difference between the Lorenz curve
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and this line right over here that that
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would be a measure of income inequality
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and so he would look at this area right
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over here and say what percentage is
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this area between this line and the
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Lorenz curve what percentage is this of
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this total area under the line and this
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percentage is called the Gini
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coefficient and it's typically quoted as
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being a value from 0 to 1 or sometimes
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you might see the scale as being from 0
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to 100 so what would a Gini coefficient
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of 0 represent well if you have a Gini
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coefficient of 0 that means that this
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area right over here between the Lorenz
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curve and this line is 0 so that means
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that we are dealing with a perfectly
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equal income distribution so at the 0
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end this is perfect equality perfect
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income equality and then what is one or
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a hundred mean that means that the area
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between the line and the Lawrence curve
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is a hundred percent of the area under
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this line so that would look like
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something like this a country whose
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Lorenz curve looks like something like
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this where all of these people I keep
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adding more and more and more population
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but I'm not adding more and more income
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and then all of a sudden you get to the
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very last person and then that
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and as all of the income so that person
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has all of the income well in that case
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the Gini coefficient would be the
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percentage of this area which would be
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100% which we could view as a one or a
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hundred and so an interesting thing to
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do is is look at Gini coefficients for
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various countries and compare them and
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that's exactly what we have here on this
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map and you can see that the the
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countries that are shaded red these are
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countries that have high Gini
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coefficients so this is where you have
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more income inequality and the ones that
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are shaded green are the ones where you
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have relatively low Gini indices or Gini
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coefficients and so that would be
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indicative of reasonably low income
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inequality now it's important to point
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out you might think that red is always
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bad and green is always good but this
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just tells you inequality it does not
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tell you on average how prosperous folks
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are what average income is in that
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country and so this is an indication
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that in places like Latin America and
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sub-saharan Africa you definitely have
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very high inequality and places like
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Canada and Europe you seem to have a
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very low inequality but it doesn't tell
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you that people for sure are better off
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in Canada than say the United States for
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example you could have a higher average
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income in the United States than you
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have in Canada and one can have a very
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spirited debate which one you would
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rather be would you rather be in a
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country that has higher inequality and
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higher average income or one that has
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lower income and lower inequality
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