Measuring Income and Wealth Inequality: The Lorenz Curve and Gini Coefficient
Income is a flow, the money a person or household receives over a period of time, while wealth is a stock, the value of assets someone owns at a point in time minus any debts, so income and wealth inequality are related but distinct measures.
Before you start
Make sure you're comfortable with these topics first:
Method
- Distinguish income, a flow received over a period of time, e.g. per year, from wealth, a stock, the value of assets held at a point in time minus debts, and give an example of each.
- Describe how a Lorenz curve is constructed: rank the population from poorest to richest, then plot the cumulative percentage of the population on the horizontal axis against the cumulative percentage of total income or wealth they hold on the vertical axis.
- Interpret the diagram: the 45-degree diagonal line represents perfect equality; the further the actual Lorenz curve sags below this line, the greater the inequality it represents.
- Define the Gini coefficient as the area between the Lorenz curve and the line of perfect equality, divided by the whole area under the line of perfect equality, a value from 0 to 1, or 0 to 100 if expressed as a percentage.
- Interpret a change in the Gini coefficient over time or a comparison between countries: a rising Gini coefficient means inequality has increased, and a falling one means inequality has decreased.
- Recognise the limitations of the Gini coefficient as a single summary statistic: it cannot show where in the distribution inequality has changed, does not adjust for household size or cost of living differences, and different countries may measure income differently.
- When given cumulative percentage data, be able to read off, from a Lorenz curve or table, the share of income or wealth held by a specified bottom or top percentage of the population and compare it with what perfect equality would predict.
Worked example
In Country X, the poorest 50% of the population hold 20% of total income, and in Country Y, the poorest 50% hold 35% of total income. State which country's Lorenz curve sags further from the line of perfect equality, and explain what this means for the two countries' Gini coefficients.
- Recall that under perfect equality, the poorest 50% of the population would hold exactly 50% of total income, the 45-degree line.
- Compare Country X: the poorest 50% hold only 20% of income, a gap of 50% - 20% = 30 percentage points below perfect equality.
- Compare Country Y: the poorest 50% hold 35% of income, a smaller gap of 50% - 35% = 15 percentage points below perfect equality.
- Since Country X's Lorenz curve sags further below the line of perfect equality at this point, Country X shows greater income inequality at this point.
- Conclude that, other things being equal, Country X is likely to have a higher Gini coefficient, closer to 1, than Country Y, since a Lorenz curve that sags further from the diagonal encloses a larger area between the curve and the line of perfect equality.
Practice questions
Try each question, then tap to reveal the answer.
Q1Define income.Show answer
Answer: The money a person or household receives over a period of time, e.g. from wages, benefits, interest, dividends and rent, a flow measure.
Q2Define wealth.Show answer
Answer: The value of the assets a person or household owns at a point in time, e.g. property, savings, shares, pensions, minus any debts, a stock measure.
Q3What does the 45-degree diagonal line represent on a Lorenz curve diagram?Show answer
Answer: The line of perfect equality, where every cumulative percentage of the population holds exactly the same cumulative percentage of income or wealth.
Q4What does it mean if one country's Lorenz curve sags further from the line of perfect equality than another's?Show answer
Answer: That the first country has a more unequal distribution of income (or wealth) than the second.
Q5What range of values can the Gini coefficient take, and what do the two extremes represent?Show answer
Answer: Between 0 and 1, or 0 to 100 as a percentage: 0 represents perfect equality, and 1, or 100, represents perfect inequality, where one person holds all the income or wealth.
Q6State one limitation of using the Gini coefficient to compare inequality between two countries.Show answer
Answer: For example, it does not show where in the income distribution the inequality lies, or countries may measure income differently, making direct comparison less reliable.
Q7If a government policy increases the share of total income held by the poorest 20% of the population, what would happen to the Lorenz curve and the Gini coefficient?Show answer
Answer: The Lorenz curve would move closer to the line of perfect equality, and the Gini coefficient would fall, indicating reduced income inequality.
Exam-style questions
Written in the style of a A Level Economics exam paper, with a full mark scheme.
Explain, using the concepts of the Lorenz curve and the Gini coefficient, how a government could show that income inequality has fallen in its country over a ten-year period.
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Evaluate the usefulness of the Gini coefficient as a measure of inequality for informing government policy.
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Free printable worksheet
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