How can the Gini coefficient be computed?

The Gini coefficient is a measure of income inequality within a population, and it is calculated using the areas that represent income distribution on a Lorenz curve. The Gini coefficient quantifies the extent to which the distribution of income deviates from a perfectly equal distribution.

To compute the Gini coefficient, we take the area between the line of perfect equality (which is a 45-degree line) and the Lorenz curve, and divide this by the total area under the line of perfect equality. In this formula, Area X typically represents the area between the Lorenz curve and the line of perfect equality, while Area Y represents the area under the Lorenz curve.

The correct computation is represented as Area X divided by the total area, which is the sum of Area X and Area Y, represented as Area X / (Area X + Area Y). This results in a value between 0 and 1, where 0 indicates perfect equality and 1 indicates perfect inequality.

Understanding this helps to grasp why dividing Area X by the total area (Area X + Area Y) is the appropriate method for calculating the Gini coefficient, reflecting how far the income distribution strays from perfect equality.