Measuring Inequality
How unequal is a society? The Gini coefficient, introduced by Corrado Gini in 1912, provides a single number answer on a scale from 0 (perfect equality) to 1 (perfect inequality). It is derived from the Lorenz curve, first proposed by Max O. Lorenz in 1905, which plots the cumulative share of income against the cumulative share of population ranked from poorest to richest.
The Lorenz Curve
The 45-degree diagonal represents perfect equality — each percentage of the population holds the same percentage of total income. The actual income distribution creates a curve that bows below this line. The area between the equality line and the Lorenz curve (shaded red in the visualization) is the basis for the Gini coefficient: Gini = 2 times this area. A deeper bow means more inequality.
Pareto's Power Law
Italian economist Vilfredo Pareto observed in 1896 that income distributions follow a power law — now called the Pareto distribution. The shape parameter alpha (α) controls inequality: when α = 2, the Gini coefficient is 1/(2·2-1) = 0.33 (moderate inequality). When α approaches 1, inequality becomes extreme; as α increases, the distribution becomes more equal. This mathematical relationship connects a fundamental distributional assumption to measurable inequality.
The Effect of Redistribution
The redistribution slider models a simplified tax-and-transfer system: a fraction of total income is collected and redistributed equally to all citizens. Even modest redistribution significantly compresses the Lorenz curve toward equality. In practice, countries use progressive income taxes, wealth taxes, and social transfers (healthcare, education, pensions) to redistribute. The Nordic countries achieve Gini coefficients around 0.25 through redistribution rates of roughly 25-30% of GDP.
Wealth by Quintile
The bar chart on the right breaks the population into five equal groups (quintiles). In highly unequal societies, the top 20% may hold 60% or more of total income, while the bottom 20% holds less than 5%. Thomas Piketty's landmark work Capital in the Twenty-First Century (2014) documented how inequality has been rising in most developed nations since the 1980s, with the top 1% share of income reaching levels not seen since the Gilded Age.