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 the Lorenz curve represents and how to construct one from income distribution data
- Explain the relationship between the Lorenz curve and the line of perfect equality
- Calculate an approximation of the Gini coefficient using the area method from tabular data
- Analyse what different Gini coefficient values reveal about the degree of income inequality in an economy
- Apply Lorenz curve and Gini analysis to compare inequality across countries and over time
- Evaluate the limitations of the Gini coefficient as a measure of inequality
🔍 Guiding Question How accurately does a single number — the Gini coefficient — capture the reality of income inequality in an economy, and what are the consequences of relying on it for policy decisions?
🌍 Why This Matters In 2023, South Africa recorded a Gini coefficient of approximately 0.63 — among the highest in the world — while Denmark's stood at around 0.29. Both countries have functioning market economies, yet the lived experience of inequality is radically different. The Lorenz curve and Gini coefficient are the tools economists use to make these comparisons precise, comparable, and policy-relevant.
1. Income Distribution and Why We Measure It
Markets distribute income unequally — some households earn far more than others. To design effective redistribution policy, governments need a way to measure how unequal that distribution is. A simple average income figure tells us nothing about distribution. We need a tool that captures the shape of the entire distribution.
📖 Definition — Income Distribution Income distribution refers to how total national income is divided among individuals or households in an economy. It is typically expressed by ranking households from lowest to highest income and examining what share of total income each group receives.
📖 Definition — Lorenz Curve A Lorenz curve is a graphical representation of income (or wealth) distribution. It 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 away from the diagonal line of perfect equality, the greater the degree of inequality.
📖 Definition — Line of Perfect Equality The line of perfect equality (also called the 45-degree line) is the diagonal reference line on a Lorenz curve diagram. It represents a hypothetical situation in which every person receives an equal share of income — the bottom 20% earn 20% of income, the bottom 40% earn 40%, and so on.
2. Constructing the Lorenz Curve: Step-by-Step
The Lorenz curve is built from a frequency distribution table showing what share of income each quintile (or decile) of the population receives. The key operation is converting these shares into cumulative percentages — this is what allows the curve to be plotted.
Step 1 — Rank the population from lowest to highest income
- Divide the population into equal groups — usually quintiles (fifths: 20% each) or deciles (tenths: 10% each)
- The first quintile = the poorest 20% of households; the fifth quintile = the richest 20%
Step 2 — Record each