Relationship Between the Lorenz Curve and the Gini Index

To understand the relationship between the Gini index and the Lorenz curve, we must first understand these two concepts.

To see the relationship between these two concepts, let's define them first:

• Gini index: It is a measure of inequality in the distribution of income.
• Lorenz curve: It is a graphical representation of inequality in the distribution of income

From the above, we can conclude that the Lorenz curve is a representation and the Gini index a number. Now, what is the relationship that unites them?

Calculate the Gini index with the Lorenz curve

Through the Lorenz curve we could calculate the Gini index. If we divide the area that remains between the curve and the line of equality by the total area that remains under the curve, we will obtain our coefficient times 1 (multiplied by 100 it would remain in %). The formula is:

Gini= A/(A+B)

Where:

A = Area above the curve

B = Area under the curve

With which A+B gives as a result the total area of ​​the square in which the graph is represented.

In short, both the Gini Index and the Lorenz Curve are methods to identify income inequalities in a given country or population. Therefore, we must mention that the more developed a country is, the more equity it usually has. That is, the Gini index is closer to 0 and the Lorenz Curve is closer to the line of perfect equality.