Using the Lorenz Curve

We’ve now seen how the Lorenz Curve could be used to measure income inequality in the way that Lenin and King Zhou pay their staff.

But normally, we don’t use to Lorenz Curve to look at how rulers pay their staff – we use it to measure income inequality across entire countries!

So, on this horizontal axis, we normally look at an entire population – meaning the horizontal axis becomes the ‘cumulative percentage of population’.

At this point we’re looking at the lowest earning 10% of the population, at this point we’re looking at the lowest earning 50% of a country’s population, and at this point we’re looking at the lowest earning 80%!

And like before, we have the cumulative income on this axis. But seeing as the total income in a country is normally a really big, unneat number – like 2.169 trillion, for instance – we just use percentages of income instead.

So, this axis becomes cumulative percentage of income, the percentage of total income that a portion of a population earns!

So, on the horizontal axis we write ‘cumulative percentage of population’, and on the vertical axis we write ‘cumulative percentage of income’!

To measure how bad a country’s levels of income equality are, we simply plot that country’s Lorenz curve – like we plotted King Zhou’s Lorenz Curve – and then compare it to our 45° line of perfect equality, which we must also plot for comparison!

The closer a country’s Lorenz Curve is to our 45° line of perfect equality, the more equal its incomes are!

So, which of the following countries has less income inequality?

Norway has less income inequality than America, as their Lorenz curve is closer to our 45° line of perfect equality!

Which of the following countries has more income inequality?

Israel has more income inequality than the UK, as their Lorenz curve is further away from our 45° line of perfect equality!

So, in summary, we can use our Lorenz Curve to look at income equality in entire countries:

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, which has some income inequality. If a country only has a bit of income inequality, like Norway, the curve will be closer to the 45° line of perfect equality – like this. If a country has lots of income inequality, like America, the curve will be further away from the 45° line of perfect equality – like this!