How Do Lorenz Curves and Gini Coefficients Work?
Inequality and poverty
What you will learn
- A Lorenz curve shows cumulative income shares from poorest to richest.
- Apply the model to an original scenario and justify its limits.
Essential definitions
- Lorenz curve
- A graph relating cumulative population shares, ranked poorest first, to cumulative income or wealth shares.
- Gini coefficient
- An inequality index from zero for complete equality towards one for extreme concentration.
Build the meaning of a point
A Lorenz curve shows how total income is distributed. Rank people from poorest to richest. Put cumulative population percentage horizontally and cumulative income percentage vertically, both from 0 to 100. Cumulative means including everyone up to that point in the ranking.
The point (40, 15) means the poorest 40% receive 15% of all income. It does not refer to the richest 40%. The curve starts at (0, 0) and ends at (100, 100). The diagonal equality line joins those endpoints: with equal incomes, the poorest 40% would receive 40%.
Compare curves and read the Gini
For conventional non-negative incomes, a curve farther below the equality line generally shows more inequality. Compare income shares at the same population percentage. If two curves cross, different parts of the distribution move in different directions, so a simple visual ranking becomes ambiguous.
The Gini coefficient is the area between the equality line and Lorenz curve divided by the whole area below the equality line. Zero represents equality and values closer to one greater concentration. Some tables use a 0–100 scale instead; check the convention. A fall from 0.42 to 0.35 indicates less measured inequality with consistent data, not a seven-percent fall in poverty.
Connect redistribution to evidence
Taxes and transfers can move the disposable-income curve closer to equality than the market-income curve. That shows redistribution during the measured period. It does not alone reveal effects on incentives, future growth or wealth.
Two economies with the same Gini can have very different average incomes and public services. Household adjustment, missing informal income and survey coverage also matter. Pair the diagram with poverty and income evidence. Shared SL/HL study focuses on interpreting curves and the coefficient; the next HL lesson constructs coordinates from quintile data.
Lorenz curves and income distribution
Initial grouped Gini ≈ 0.32; selected distribution ≈ 0.19. Cumulative income shares at 0, 20, 40, 60, 80, 100% of people: 0%, 8.94%, 25.3%, 46.48%, 71.55%, 100%. HL construction: add successive quintile shares; do not plot individual shares as cumulative values.
Rank households from poorest to richest. A Lorenz point shows the cumulative income share held by the corresponding cumulative population share. A curve closer to equality generally indicates less inequality when curves do not cross.
How to draw it and model assumptions
- Both axes run 0–100%; population share horizontally, income share vertically.
- Draw the equality line from (0,0) to (100,100).
- Add cumulative quintile shares, beginning (0,0) and ending (100,100).
Hypothetical income shares for equal-sized quintiles. Curve interpretation is shared; constructing from quintile data is HL. The displayed grouped Gini is an approximation from straight segments, not a required guide calculation.
Apply and evaluate
- Compare like-for-like income concepts and dates; crossing curves need more evidence than a simple visual ranking.
Common misconceptions
- A lower Gini describes greater equality, not necessarily higher incomes or lower absolute poverty.
Knowledge check
What does (60, 30) mean on a Lorenz curve?
Real-world application
Poverty lines depend on a PPP vintage
5 June 2025: The World Bank’s June 2025 update set the international extreme-poverty line at $3.00 per person per day in 2021 PPP international dollars, replacing $2.15 in 2017 PPP dollars.
The change is not an ordinary market-exchange-rate conversion. PPP data and the national poverty lines underlying the benchmark changed. Comparing poverty counts across releases requires a consistent method; a statistical revision is not itself proof that living conditions suddenly worsened.
World Bank, June 2025 update to global poverty lines ↗Historical evidence checked 9 October 2026. The model interpretation is an original teaching application.
What to remember
A Lorenz curve shows cumulative income shares from poorest to richest. The Gini summarises concentration, but neither measure alone reveals poverty or average living standards.
Completion is your own reflection on learning, not a test score. Syllabus references: 3.4.03.
Sources and applications
Lessons in this section
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