The Gini Coefficient

We’ve now seen how we can use a Lorenz Curve to look at a country’s income inequality:

First of all, we need to label our axes – on the vertical axis we put “cumulative percentage of income”, and on the horizontal axis we put “cumulative share of population”.

Second, we need to draw our 45° line of perfect equality, which starts in the bottom left corner and ends up in the top right corner.

Third, we need to sketch the Lorenz Curve for our country. The more income inequality a country has, the further the curve will be from the 45° line of perfect equality!

But, to get a more exact measure of income inequality, economists look at a Lorenz curve, and then use it to find the Gini coefficient.

First, economists will label this area, “A”. Second, they label this other area, “B”! Finally, they find the Gini coefficient, which is given by…

G = A / (A + B)…where A is the size of our first area, B is the size of our second area, and G is our Gini coefficient!

Let’s look at a country with fairly low income inequality, like this. If the area of section A was 0.1, and the area of B was 0.4, what would the Gini coefficient be? [need a pretty equal Lorenz curve]

If the area of section A was 0.1, and the area of B was 0.4, the Gini coefficient be 0.1 divided by (0.1 + 0.4) – which is 0.2!

Now let’s look at a country with more income inequality. If the area of section A was 0.3, and the area of B was 0.2, the Gini coefficient would be… [new less equal Lorenz curve]

If the area of section A was 0.3, and the area of B was 0.2, the Gini coefficient be 0.3 divided by (0.3 + 0.2) – which is 0.6!

Finally, let’s look at a country with loads of income inequality. If the area of section A was 0.45, and the area of B was 0.05, the Gini coefficient would be… [new less equal Lorenz curve]

If the area of section A was 0.45, and the area of B was 0.05, the Gini coefficient be 0.45 divided by (0.45 + 0.05) – which is 0.9!

So, as the Gini coefficient increases…

As the Gini coefficient increases, income inequality increases!

But, the Gini coefficient will always be between 0 and 1. That means that….

The Gini coefficient will always be between 0 and 1, meaning 0 is perfect income equality, and 1 is total income inequality, where one person earns an entire country’s income!

So, in summary, the Gini coefficient is given by…

The Gini coefficient is given by G = A / (A + B)…whereas A is the size of this first area on the Lorenz Curve, B is the size of our second area, and G is our Gini coefficient!

The Gini coefficient will always be between 0 and 1, where…

The Gini coefficient will always be between 0 and 1, where 0 is perfect income equality, and 1 is total income inequality, where one person earns an entire country’s income!