Lorenz Curve

How do we calculate inequality in society? How do we know if inequality is improving or worsening in a specific country? This article helps answer those questions by explaining the Lorenz curve.

Interpreting the Lorenz curve graph

To interpret the Lorenz curve, we need to first understand how it is represented on the diagram. There are two curves in Figure 1 below.

We first have the 45° straight line, known as the line of equality. It has a slope of 1 which illustrates perfect equality in income or wealth.

The Lorenz curve lies beneath the 45° line of equality. The further away the curve is from the 45° line, the greater the income or wealth inequality in an economy. We can see that in the diagram below.

The x axis shows the percentage of the total population. The y axis shows the percentage of total income or wealth. The word ‘cumulative’ in both axes means up and including.

Fig. 1 - The Lorenz Curve

Interpreting the data from the Lorenz curve is quite simple. Pick a point from the x axis and read off the y axis. For example, reading off the diagram, 50% of the population has access up to and including 5% of the country's national income. In this example, income is distributed very unequally as half of the population has a very small share of the country’s national income.

Shifts of the Lorenz curve

The Lorenz curve can shift closer or further away from the 45° line of equality. In the diagram below, the Lorenz curve has moved closer to the line of equality. This means that inequality in this economy has decreased.

Fig. 2 - Lorenz curve shifts

According to the diagram above, initially, only 90% of the population had access to 45% of the country’s national income. After the curve shifted, 90% of the population has access to 50% of the country’s national income.

The Lorenz curve and the Gini coefficient

The Lorenz curve is linked to the Gini coefficient. You can calculate the Gini coefficient using this curve.

Graphically, the Gini coefficient measures how far the Lorenz curve is from the line of equality. It quantifies the level of economic inequality in an economy.

Fig. 3 - Gini coefficient calculated from Lorenz Curve

In the diagram above, the shaded area is Area A. The remaining white space is Area B. Plugging the values for each area into the formula gives us the Gini Coefficient.

The Gini coefficient is calculated with the following formula:

$Ginicoefficient=\frac{AreaA}{AreaA+AreaB}$

A coefficient of 0 means that there is perfect equality. This means that every 1% of a population has access to 1% of national income, which is unrealistic.

A coefficient of 1 means that there is perfect inequality. This means that 1 individual has access to the entire country’s national income.

A lower coefficient indicates that income or wealth is distributed more equally across the population. A higher coefficient indicates that there is severe income or wealth inequality and is mainly due to political and/or social disruption.

Why is the Lorenz curve important?

The Lorenz curve is important because it helps economists measure and understand income or wealth inequality.

Economists are interested in how income and wealth inequality changes over time in an economy. It also allows them to compare the level of economic inequality between different countries.

Limitations of the Lorenz curve

While the Lorenz curve is helpful for economists to make comparisons on the level of income and wealth distribution, it does have some limitations. Most of these limitations lie with the data.

For example, the Lorenz curve doesn't take into account:

• Wealth effects. A household may have a low income compared to the rest of the population, thus lying in the bottom 10%. However, they may be ‘asset rich’ and possess assets that are appreciating in value.
• Non-market activities. Activities such as education and healthcare make a difference to a household’s standard of living. In theory, a country could have a Lorenz curve close to the line of equality, but have poor education and healthcare standards.
• Lifecycle stages. An individual’s income changes throughout their lifetime. A student may be poor due to the early stages of their career, but may later earn more than the average person in that country. This variation in income is not considered when analysing inequality with the Lorenz curve.

Lorenz curve example

The Lorenz curve below has been plotted to fit the data describing England’s income distribution.

Fig. 4 - England's Lorenz Curve

Thanks to the curve, we can see that wealth is unequally distributed across England. The top 10% hold 42.6% of the country’s total net wealth. Those in the bottom 10% hold 0.1% of England’s total net wealth.

To find the Gini coefficient, divide the area between the line of equality by the sum of the total area under the line of equality. In 2020, England’s Gini coefficient reached 0.34 (34%), a slight decrease from the previous year.

Now you have seen how economists show graphically how income and wealth are distributed in an economy with the Lorenz Curve. Go to 'Equitable Distributions of Income' to learn how income can be distributed equitably.