Relationship between the Lorenz curve and the Gini index

To understand the relationship between the Gini index and the Lorenz curve we must first know 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 income distribution.
  • Lorenz Curve:It is a graphical representation of inequality in income distribution

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 between the curve and the line of equality by the total area under the curve, we will obtain our coefficient by 1 (multiplied by 100 would be%). The formula is:

Gini = A / (A + B)

Where:

A = Area above the curve

B = Area below 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 there is usually in it. That is, the Gini index is closer to 0 and the Lorenz Curve is closer to the line of perfect equality.

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