Inequality: income, wealth, the Lorenz curve and Gini coefficient

Income and wealth

• Income is a flow: wages, profits, interest, rent and benefits received over a period.
• Wealth is a stock: the value of assets owned at a point in time (property, shares, savings, pensions).

Wealth is usually far more unequal than income, because it accumulates and is inherited, and wealth itself generates income (rent, dividends).

The Lorenz curve in words

Horizontal axis: cumulative percentage of households, ranked from poorest to richest (0 to 100%). Vertical axis: cumulative percentage of income (0 to 100%).

• The 45-degree line of perfect equality: the poorest 20% get 20% of income, and so on.
• The Lorenz curve sags below the line. The further it bows away, the greater the inequality.

If one country's Lorenz curve lies entirely inside another's (closer to the diagonal), it is more equal.

The Gini coefficient

Let A be the area between the line of equality and the Lorenz curve and B the area under the Lorenz curve. Then Gini = A / (A + B).

• 0 = perfect equality; 1 = perfect inequality (one household has everything). It is often reported as an index from 0 to 100.
• Because A + B = 0.5 (half of the unit square), Gini = 1 - 2B.

The World Bank's estimate of South Africa's Gini index was 54.1 in 2022 (59.6 in 2014), one of the highest of any country with data.

A hypothetical country's income distribution

Calculating B from quintiles

Each quintile is a strip 0.2 wide. Its area is a trapezium: 0.2 x (cumulative share at the start + cumulative share at the end) / 2. Add the five strips to get B, then Gini = 1 - 2B.

Limitations: the Gini does not show where inequality is (two different Lorenz curves can give the same Gini); it ignores benefits in kind (free health care, education); and data quality varies between countries.

Worked example

Find the Gini coefficient for the hypothetical country in the table.

1. Cumulative shares: 0, 0.05, 0.15, 0.30, 0.50, 1.00
2. B = 0.2 x [(0 + 0.05) + (0.05 + 0.15) + (0.15 + 0.30) + (0.30 + 0.50) + (0.50 + 1.00)] / 2
3. B = 0.1 x 3.00 = 0.30
4. Gini = 1 - 2 x 0.30 = 0.40

Answer: Gini = 0.40 (an index of 40)

Check yourself

1. On a Lorenz diagram, area A = 0.18 and area B = 0.32. Calculate the Gini coefficient.
   Show answer

   0.36. 0.18 / 0.50 = 0.36.

2. The area under a Lorenz curve (B) is 0.31. Calculate the Gini coefficient.
   Show answer

   0.38. A + B = 0.5, so Gini = 1 - 2 x 0.31 = 0.38.

3. Quintile income shares are 8%, 12%, 16%, 22% and 42%. Calculate the Gini coefficient to 2 decimal places.
   Show answer

   0.31. Cumulative: 0.08, 0.20, 0.36, 0.58, 1.00. B = 0.1 x (0.08 + 0.28 + 0.56 + 0.94 + 1.58) = 0.344; Gini = 1 - 2B = 0.312.

4. In the lesson's hypothetical country, what percentage of income do the poorest 60% of households receive?
   Show answer

   30 %. 5 + 10 + 15 = 30%.

5. Which statement about wealth and income is correct?
   • Wealth is a stock of assets; income is a flow over time
   • Income is a stock; wealth is a flow
   • Wealth is usually more equally distributed than income
   • Income includes the value of a house you own
   Show answer

   Wealth is a stock of assets; income is a flow over time. Stock versus flow is the key distinction.

6. Country X's Lorenz curve lies closer to the line of equality than Country Y's at every point. Therefore
   • X has a higher Gini coefficient than Y
   • X has a lower average income
   • X has a lower Gini coefficient than Y
   • Y has less poverty
   Show answer

   X has a lower Gini coefficient than Y. Closer to the diagonal means smaller area A and a lower Gini.

7. Explain one limitation of the Gini coefficient.
   Show answer

   Different Lorenz curves can give the same Gini, so it does not show where in the distribution inequality occurs (for example the poorest or the richest), and it ignores benefits in kind such as free health care.. A single number hides the shape of the distribution.

8. According to World Bank data (via FRED), what was South Africa's Gini index in 2022?
   • 25.0
   • 54.1
   • 35.0
   • 90.0
   Show answer

   54.1. The World Bank estimate for 2022 was 54.1, very high by world standards.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Level in Economics specification (issue 2)
• FRED: GINI index for South Africa (World Bank, World Development Indicators)

Last updated 8 November 2026. Spotted a mistake? Tell us.