∿ExploreSims
ExploreSims / Economics / Inequality / Lorenz Curve & Gini Coefficient
Premium experiment • distribution geometry

ECONOMICS • INEQUALITY

Lorenz Curve & Gini Coefficient

Change representative incomes across five equal population groups and watch the Lorenz curve and Gini coefficient respond.

● INCOME DISTRIBUTIONEquality line ↔ Lorenz curve
Gini coefficient
Bottom share
Top share
Top/bottom ratio

Reasoning inspector

live model state
Gini—
Bottom quintile share—
Top quintile share—
Top/bottom ratio—
Bottom 60% share—
Mean income—

Experiment with the mechanism

The Lorenz curve converts a distribution into cumulative population and income shares. The Gini coefficient summarizes the area between that curve and perfect equality.

LEARN WITH THE SIMULATION

Understand Lorenz Curve & Gini Coefficient by experimenting.

START HERE

A Lorenz curve orders incomes from lowest to highest and plots cumulative income share against cumulative population share. The farther the curve bows below the equality line, the larger the area associated with inequality and the higher the Gini coefficient.

BUILD THE IDEA

What you should understand first

  • Construct cumulative income shares from an ordered distribution.
  • Connect the Lorenz curve's bow to the Gini coefficient.
  • Distinguish a summary inequality measure from the underlying distribution that produced it.

TRY IT YOURSELF

Can two visibly different income distributions produce similar Gini coefficients?

  1. Create a moderately unequal baseline and record the Gini coefficient.
  2. Raise the top income while also lifting one of the middle incomes.
  3. Search for another visibly different pattern with a similar Gini.
  4. Compare bottom-share and top/bottom-ratio metrics.
Read the visual:

The Gini compresses the whole distribution into one number. Different shapes can therefore produce similar coefficients even when specific groups have different shares.

WHY IT WORKS 01

Geometry turns distribution into one number

The 45-degree line represents perfect equality. The Gini coefficient is proportional to the area between that line and the Lorenz curve, so greater bowing generally means greater measured inequality.

WHY IT WORKS 02

One number cannot describe every distributional detail

Because the Gini aggregates many pairwise income differences, distinct distributions can share similar values. Group shares and ratios remain useful companions when interpreting the coefficient.

DO NOT MIX THESE UP

Common misconception

A Gini coefficient does not reveal who is rich or poor, does not measure absolute living standards, and does not uniquely determine an income distribution. This five-representative-income model is illustrative rather than a population estimator.

PRACTICE CHALLENGE

Can you reduce the Gini without changing the highest income?

  • Record the baseline Gini and top income.
  • Raise one or more lower incomes while keeping the top value fixed.
  • Watch the Lorenz curve move toward equality.
  • Explain why the coefficient falls.
Reveal the reasoning

Yes. Raising lower incomes increases their cumulative income shares, moving the Lorenz curve upward toward the equality line. The area gap shrinks even though the top income itself is unchanged.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Five representative incomes stand in for equal-sized population groups and are sorted before calculation.
  • The Lorenz curve is approximated by straight segments between cumulative quintile points.
  • The Gini coefficient is computed from the area under that piecewise-linear Lorenz curve.

Model limitations

  • Five representative values cannot reproduce the detail of an actual household income distribution.
  • Taxes, transfers, household size, wealth, negative incomes and sampling uncertainty are not modeled.

CONNECT IT

Where this matters

  • Income inequality education
  • Distributional comparisons
  • Lorenz-curve interpretation
  • Understanding limits of summary statistics

WORDS THAT MATTER

Key vocabulary

Lorenz curve
Cumulative income share plotted against cumulative population share after sorting from lowest to highest income.
Gini coefficient
A normalized measure of the gap between the Lorenz curve and perfect equality.
Perfect equality
A distribution where each cumulative population share receives the same cumulative income share.
Quintile
One fifth of a population after ranking by the variable of interest.