Lorenz Curve

  • Definition: The Lorenz curve is a way of showing the distribution of income (or wealth) within an economy. It was developed by Max O. Lorenz in 1905 for representing wealth distribution.
  • The Lorenz curve shows the cumulative share of income from different sections of the population.
  • If there was perfect equality – if everyone had the same salary – the poorest 20% of the population would gain 20% of the total income. The poorest 60% of the population would get 60% of the income.

Diagram of Lorenz curve

In this Lorenz curve, the poorest 20% of households have 5% of the nation’s total income.

The poorest 90% of the population holds 55% of the total income. That means the richest 10% of income earners gain 45% of total income.

Shift in the Lorenz Curve

In this example, there has been a reduction in inequality – the Lorenz curve has moved closer to the line of equality.

  • The poorest 20% of the population now gain 9% of total income
  • The richest 10% of the population used to gain 45% of total income but now only get 25% of total income.

The Lorenz Curve and the Gini Coefficient

The Lorenz Curve can be used to calculate the Gini coefficient – another measure of inequality.

The Gini coefficient is area A/A+B

lorenz-curve-a-b

The closer the Lorenz curve is to the line of equality, the smaller area A is. And the Gini coefficient will be low.

If there is a high degree of inequality, then area A will be a bigger percentage of the total area.

A rise in the Gini coefficient shows a rise in inequality – it shows the Lorenz curve is further away from the line of equality.

Lorenz Curve and wealth

Wealth Inequality and Lorenz curve

wealth-components

The Lorenz curve shows the cumulative wealth of each wealth decile. It shows that the lowest 38% of individuals have zero property wealth. The top 10% own nearly 50% of property wealth.

With financial wealth, inequality is even greater with 60% of the population in debt and negative wealth. The top 10% have 80% of the nations financial wealth.

Source:

Gini Coefficient in the UK

income inequality giniThis shows that since 1979, the UK has seen a rise in inequality – especially during the 1980s.

The original Lorenz Curve

original-lorenz-curve

American Statistical Association June 1905 JSTOR

Interestingly, the original Lorenz curve had percents of total income and percents of the population on different axis.

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