# Lorenz Curve

- 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.In this Lorenz curve, the poorest 20% of households have 5% of the population.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.
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 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

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 in Great Britain ONS, published July 2012

#### Gini Coefficient in the UK

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