The Lorenz curve and Gini coefficient - YouTube

In this video we’ll learn about the Lorenz curve and how it is used to measure inequality.

From there we will calculate the Gini coefficient and understand what its value tells us.

Suppose we had a country of 100 people and each of them earned 1 percent of the nation’s

income.

Each individual represents 1% of the population.

If the first person earns 1% of the income and the second person earns 1% of the nation’s

income, then together they earn 2% of the nation’s income.

Since they each have an equal share, we say that income is equally distributed.

Continuing this through the hundredth household, we would have perfect equality as each person

in society is earning the same amount of income.

The 1st household earns as much as the 100th household.

That would look something like this, the line of perfect equality.

Now suppose that only the 100th household had all of the country’s income.

The other 99% in this case have none of the income and this 1% of the population accounts

for all of the income in the country.

This is represented by the red line which represents absolute inequality.

Thankfully, most societies don’t operate like this either.

Most economies operate along a curve that looks something like this, called the Lorenz

Curve.

Like the previous two lines, it represents the distribution of income across the population.

In this case there is some inequality of the distribution that has been introduced.

We use the Lorenz curve to calculate the Gini coefficient.

If the Gini coefficient is equal to zero, then we have perfect equality in society.

However, as the Gini coefficient approaches the value of 1, inequality is higher.

The area above the Lorenz curve but below the line of perfect equality is called A.

The remaining area is called B.

We divide A by (A+B) to determine the Gini coefficient.

Let me demonstrate how we do this.

Let’s use the case of the Lorenz curve in increasingly unequal societies to demonstrate

how the Gini coefficient is calculated.

The line of perfect equality does not represent this economy’s distribution of income.

Instead, it is represented by the purple Lorenz curve.

The area above the Lorenz curve is measured by area A, whereas below is measured as area

B.

We divide the area of A by the total area under the line of perfect equality to arrive

at our Gini coefficient, which in this case will be greater than 0.

The situation here indicates that some inequality exists.

Next let’s consider the example of a society with even greater inequality than this one.

The length of the red arrow will allow you to make a relative comparison of inequality

between the diagrams we’re going to analyse.

You’ll notice that in this more unequal society, the area of A is larger than before.

The larger A gets, the more inequality that exists.

Of the three diagrams, this will be the most unequal society in which most of the country’s

income belongs to a smaller percentage of households.

According to the CIA World Factbook the most unequal countries are (1) Lesotho, (2) South

Africa and (3) Micronesia.

The most equal are (157) Jersey,  (156) The Faroe Islands and (155) Kosovo.

The United States is ranked 39th, United Kingdom 116th, India 95th and Pakistan 130th.

By now you should feel much better about your understanding of the Lorenz curve and Gini

coefficient.

If you have any questions or comments, leave them below.

That’s us done for now and I will see you in the next one!