Preview
Constructing a Lorenz Curve and Estimating the Gini Coefficient from Data
IB DP Economics — Unit 3: Macroeconomics | HL | 3.4 Economics of Inequality and Poverty
📋 What You Will Learn
- Identify what a Lorenz curve represents and how it is constructed from income distribution data
- Explain the relationship between the Lorenz curve and the line of perfect equality
- Construct a Lorenz curve by converting raw income share data into cumulative percentages
- Estimate the Gini coefficient using the approximation formula and interpret the result
- Analyse how changes in the Lorenz curve and Gini coefficient reflect changes in income inequality
- Evaluate the strengths and limitations of the Gini coefficient as a measure of inequality
🔍 Guiding Question Can a single number — the Gini coefficient — meaningfully capture the degree of inequality in a society, and what are the consequences of relying on it to guide economic policy?
🌍 Why This Matters In 2023, South Africa recorded a Gini coefficient of approximately 0.63 — the highest of any country with reliable data — meaning its Lorenz curve bows dramatically away from the line of perfect equality. Meanwhile, Slovakia's Gini sits near 0.23. Both are market economies, yet the lived experience of inequality is radically different. The Lorenz curve and Gini coefficient give economists a precise, comparable way to measure this difference — and to track whether policy is making things better or worse.
What Does Income Inequality Mean — and Why Measure It?
In any economy, income is not distributed equally across households. Some households earn far more than others due to differences in wages, capital ownership, inheritance, and access to education. Measuring the extent of this inequality is essential for evaluating the fairness of an economy and the effectiveness of redistributive policies.
Two tools dominate this measurement at the IB HL level: the Lorenz curve (a graphical representation) and the Gini coefficient (a numerical summary). Understanding how to construct and interpret both from raw data is a core HL quantitative skill tested in Paper 3.
📖 Definition — Income Distribution Income distribution refers to how total national income is divided among individuals or households in an economy, typically expressed as the share of income received by each quintile (fifth) or decile (tenth) of the population when ranked from lowest to highest income.
The Lorenz Curve
The Lorenz curve was developed by American economist Max Lorenz in 1905. It is the most widely used graphical tool for visualising income inequality. Before defining it formally, consider what it is trying to show: if we line up every household in an economy from poorest to richest, what cumulative share of total income does the bottom X% of households receive?
📖 Definition — Lorenz Curve A Lorenz curve is a graph that plots the cumulative percentage of total income received against the cumulative percentage of the population (ranked from lowest to highest income). The further the Lorenz curve bows below the diagonal line of perfect equality, the greater the degree of income inequality.
Key Features of the Lorenz Curve
- Axes: horizontal axis = cumulative % of population (0–100%); vertical axis = cumulative % of income (0–100%)
- Line of perfect equality: a 45° diagonal from origin (0,0) to (100,100) — represents a hypothetical situation where every person earns the same income (bottom 20% earn 20% of income, bottom 40% earn 40%, etc.)
- Actual Lorenz curve: always lies below or on the line of perfect equality; the