AQA Specification focus:
‘The Lorenz curve and Gini coefficient. Students will be expected to interpret measures of inequality such as the Gini coefficient but they will not be expected to calculate the Gini coefficient.’
Understanding how economists measure inequality is crucial for analysing the distribution of income and wealth. The Lorenz curve and Gini coefficient are the key tools used.
The Lorenz Curve
Definition and Purpose
The Lorenz curve is a graphical representation used to illustrate the distribution of income or wealth within an economy. It compares the cumulative percentage of households with the cumulative percentage of income they receive.
Lorenz Curve: A graphical representation showing the proportion of total income earned by cumulative shares of the population, ranked from the poorest to the richest.
The curve provides a visual comparison between perfect equality and the actual distribution. It helps identify the degree of inequality by showing how far the distribution deviates from equality.
Structure of the Curve
The horizontal axis shows the cumulative percentage of the population.
The vertical axis shows the cumulative percentage of income received.
The line of perfect equality is a 45° diagonal, indicating that, for example, 20% of the population receives 20% of the income.
The actual Lorenz curve typically bows below the line of equality, reflecting that lower-income households receive a smaller share of total income.
The larger the gap between the Lorenz curve and the line of equality, the greater the level of inequality.
Key Insights
The Lorenz curve highlights:
Proportional distribution of income.
Relative inequality between population groups.
Whether income is concentrated heavily among a small proportion of households.
It does not provide a single numerical measure but forms the basis for calculating the Gini coefficient.
The Gini Coefficient
Definition and Use
The Gini coefficient is a numerical measure of income inequality derived from the Lorenz curve. It quantifies inequality on a scale between 0 and 1.
Gini Coefficient: A statistical measure of inequality ranging from 0 (perfect equality) to 1 (perfect inequality), calculated as the ratio of the area between the Lorenz curve and the line of equality to the total area under the line of equality.
Although AQA students are not expected to calculate the Gini coefficient, they must be able to interpret its meaning and understand its implications for inequality.
Interpretation of the Gini Coefficient
0 = perfect equality: everyone has the same income.
1 = perfect inequality: one individual has all the income, while everyone else has none.
Real-world values typically range between 0.25 and 0.6, depending on the country.
Higher Gini coefficients indicate greater inequality, while lower coefficients suggest a more equal distribution of income or wealth.
Advantages of the Gini Coefficient
Provides a single, comparable statistic to track inequality.
Useful for international comparisons of inequality levels.
Allows measurement of changes in inequality over time within a country.
Limitations of the Gini Coefficient
While useful, the Gini coefficient has limitations that AQA students should understand:
It does not show where in the distribution inequality lies (e.g., whether among the poorest or the middle classes).
It can be affected by population size and structure.
Countries with different income distributions can have the same Gini coefficient.
It does not consider non-monetary welfare factors such as public services or informal economies.
Using Lorenz Curves and Gini Coefficients Together
Complementary Insights
The Lorenz curve and Gini coefficient complement each other:
The Lorenz curve provides a visual picture of inequality.
The Gini coefficient gives a numerical summary.
When combined, they offer a fuller understanding of how income and wealth are distributed.
Policy Relevance
These measures are vital for governments and economists because:
They help assess the fairness of income distribution.
They guide decisions on taxation, welfare, and redistribution policies.
They allow policymakers to track whether inequality is worsening or improving.
For example, if the Gini coefficient rises, it suggests inequality is increasing, prompting debate over whether government intervention is necessary.
Interpreting Graphs and Data
Graphical Interpretation
Students must be able to read and interpret Lorenz curves presented in exam questions or data sets. Key points include:
Comparing two Lorenz curves for different years to see if inequality has increased or decreased.
Relating shifts in the curve to changes in economic conditions or policies.
Linking a “closer to equality” Lorenz curve with a lower Gini coefficient.
Data Analysis
When interpreting data:
Look for trends in the Gini coefficient over time.
Consider what might have caused changes (e.g., tax reforms, globalisation, or technological change).
Relate these shifts to broader themes of economic performance and welfare distribution.
Summary Points for AQA Students
The Lorenz curve illustrates income distribution visually, comparing actual distribution with perfect equality.
The Gini coefficient is a numerical measure between 0 and 1 showing the extent of inequality.
AQA requires interpretation, not calculation, of the Gini coefficient.
Both tools are widely used in economic analysis, policy debates, and evaluation of fairness in income and wealth distribution.
FAQ
The Lorenz curve was first developed by Max O. Lorenz in 1905 as a way of representing wealth distribution. It was originally used in the United States to study income disparities.
Since then, it has become a standard tool in economics for visualising inequality, providing the foundation for the Gini coefficient, which was introduced later by Corrado Gini in 1912.
The Lorenz curve gives a visual understanding of inequality, showing how far the distribution of income deviates from equality.
The Gini coefficient summarises this visually represented inequality into a single number, making it easier for comparison across time periods or countries.
Used together, they balance clarity and precision: the curve shows where inequality lies, while the coefficient shows how much.
Yes, the Gini coefficient can measure inequality in both income and wealth distribution.
Wealth inequality tends to be much greater than income inequality, as assets like property and shares are more concentrated in a small proportion of the population.
Comparing income and wealth Gini values can highlight the different dimensions of inequality in an economy.
Redistributive policies shift the Lorenz curve closer to the line of equality. Examples include:
Progressive taxation
Welfare benefits
Subsidised public services
Policies favouring the wealthy or reducing redistribution tend to pull the Lorenz curve further away from equality, showing greater disparity.
International comparisons can be misleading because:
Countries may have similar Gini values but very different income levels.
The coefficient does not capture differences in living costs, welfare provision, or informal economic activity.
As a result, two nations with the same Gini coefficient may not experience inequality in the same way.
Practice Questions
Define the Lorenz curve and explain what it shows about income distribution. (2 marks)
1 mark for correctly defining the Lorenz curve as a graphical representation of income or wealth distribution.
1 mark for explaining that it shows the proportion of income received by cumulative percentages of the population.
Using the Gini coefficient, explain how economists measure income inequality and outline two limitations of this measure. (6 marks)
Up to 2 marks for stating that the Gini coefficient is a numerical measure ranging from 0 (perfect equality) to 1 (perfect inequality).
1 mark for noting that it is derived from the Lorenz curve.
1 mark for correctly identifying one limitation (e.g., does not show where in the distribution inequality lies).
1 mark for identifying a second limitation (e.g., countries with different income distributions can have the same Gini coefficient).
1 mark for any further valid limitation or clear development of an identified point (e.g., it does not account for non-monetary welfare factors).
