The Lorenz curve

The extent of inequality can be indicated through Lorenz curves (after American economist, Max Lorenz).

Inequality refers to differences in the distribution of income or wealth (or other factors, such as access to doctors, opportunities to work etc.) between different socio-economic groups.

Achieving a more equitable distribution of income is seen as an important objective of macroeconomic policy.

If the distribution of income is perfectly equal, any given percentage of the population (for example, 40%) will gain the same percentage of income (at 40%).

However, when income is distributed unequally, a given percentage of the population (say 40%) do not gain the same percentage of income (at 15% in the graph).

The Lorenz curve

Lorenz curve 2 has a less equal distribution than curve 1, given that 40% of income earners only get 5% of the economy’s income.

Lorenz curves can be used in three fundamental ways:

  1. To look at inequality in a single country over a period of time.
  2. To compare inequality in two counties.
  3. To consider the effect of a policy change on inequality.

Video on the Lorenz curve

The Gini co-efficient

The Gini co-efficient is also a device for measuring inequality, and can be understood in terms of comparing areas in a Lorenz curve diagram.

The Lorenz curve

The Gini co-efficient (G) is calculated as area A/A+B, as shown in the graph.

If the Lorenz curve goes all the way to the edges, the area B disappears, so the result must be G = A/A which equals 1. Hence, when absolute inequality occurs the Gini-co-efficient will equal 1. Conversely, when the Lorenz curve is on the line of perfect equality, A disappears, hence G = zero. Gini co-efficients for 5 selected countries confirms that as inequality rises, G moves towards 1.

Norway 0.27
UK 0.34
USA 0.41
Ecuador 0.45
Angola 0.53

Other indices

There are several other indices that attempt to measure inequality, including:

The Robin Hood index

The Robin Hood index (also known as the Hoover index, and Schutz index) shows the proportion of all income that would have to be redistributed to achieve a state of perfect equality. This means that it measures the amount of income that would need to be transferred from those higher income earners to the lower income earners to achieve equality. The higher the value, the more redistribution is required.

The Lorenz curve

Graphically, it is the maximum vertical distance between the 45 degree line and the Lorenz curve.

The Palma ratio

The Palma ratio is the ratio of the national income shares going to the top 10 per cent of households compared with the bottom 40 per cent. It is based on the observation that changes in income differences at the extremes (the top and bottom) gives a better clue of changes in the overall level of inequality, given that the ‘middle’ groups are more stable over time.

The 20/20 ratio

Similarly, the 20/20 ratio compares the ratio of the average income of the richest 20 per cent of the population to the average income of the poorest 20 per cent.

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