Economic Policy
Lorenz curves help policymakers evaluate the effectiveness of economic policies in reducing income inequality.
Lorenz Curve Analysis: Understanding Income Inequality
A comprehensive tool for analyzing and visualizing income distribution through Lorenz curves and Gini coefficients.
Understanding Lorenz Curves
The Lorenz curve is a graphical representation of income distribution, developed by Max Lorenz in 1905. It shows the relationship between the cumulative percentage of income and the cumulative percentage of the population.
Mathematical Foundation
The curve plots the cumulative proportion of income against the cumulative proportion of the population, ordered from lowest to highest income.
Perfect Equality
A 45-degree line represents perfect equality, where everyone has the same income. The greater the deviation from this line, the greater the inequality.
Interactive Lorenz Curve Calculator
Income Distribution Data
Gini Coefficient
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Income Quintile Ratio
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Mathematical Foundation
Gini Coefficient Calculation
G = 1 - ∑(X[k] - X[k-1])(Y[k] + Y[k-1])
Where:
- X[k] is the cumulative proportion of the population
- Y[k] is the cumulative proportion of income
- k represents each point on the Lorenz curve
Real-World Applications
Wealth Distribution
Analysis of wealth concentration and its changes over time in different economies.
Tax Analysis
Evaluation of tax systems and their impact on income redistribution.