Gini coefficient lorenz curve

By: Prof. Dr. Fazal Rehman Shamil | Last updated: February 3, 2025

Question 1:

\[
\text{The Gini Coefficient is a measure of income or wealth inequality, represented by the ratio of the area between the Lorenz curve and the line of perfect equality to the total area under the line of perfect equality.}
\]
\[
\text{It is calculated using the formula:}
\]
\[
G = \frac{A}{A + B}
\]
\[
\text{Where: }
\]
\[
A \text{ is the area between the Lorenz curve and the line of perfect equality, and }
\]
\[
B \text{ is the area under the Lorenz curve.}
\]

Lorenz Curve:

\[
\text{The Lorenz curve is a graphical representation of the distribution of income or wealth. The line of perfect equality represents an equal distribution of income.}
\]
\[
\text{The Lorenz curve lies below this line, with more curvature indicating greater inequality.}
\]
\[
\text{The Gini Coefficient is the ratio of the area between the Lorenz curve and the line of perfect equality (A) to the total area under the line of perfect equality (A + B).}
\]

Example:

\[
\text{Consider a society with a population of 5 people, where the incomes are:}
\]
\[
\{10, 20, 30, 40, 50\}
\]
\[
\text{Plot the Lorenz curve, and then calculate the area (A) between the curve and the line of perfect equality. The area under the Lorenz curve is (B).}
\]
\[
\text{Finally, the Gini coefficient is calculated as: }
\]
\[
G = \frac{A}{A + B}
\]

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