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The Gini coefficient

The Gini coefficient is a number between zero and one providing an indication of the degree of inequality in the distribution of income.  It can be defined by referring to the Lorenz curve, where the area between the actual Lorenz curve and the line of absolute equality (Area A) is divided by the total area under the line of absolute equality (Area A + B).  

This is highlighted in the three diagrams below.  The first diagram uses the actual Lorenz curve for Australia (2009-10).  As Area A is smaller than Area B, it results in a Gini coefficient somewhat less than .05.  [If Area A were the same size as Area B, it would yield a Gini coefficient of 0.5. ] The ABS computed the Gini coefficient to be 0.328 for this period.

It should be apparent that as inequality worsens in an economy, the Lorenz curve moves further away from the 45 degree line and the size of the Area A increases relative to Area B.  This means that the Gini coefficient moves away from zero and approaches 1.   The next two diagrams cover the two extreme (hypothetical) positions.  Figure B shows that, at the extreme, total inequality (one person earning all income) would mean that Area A covers the entire space and Area B disappears.  This means that the Gini  coefficient = A/A = 1.  As inequality lessens (or equality improves), the Lorenz curve moves closer to the 45 degree line and the size of Area A decreases relative to Area B.  This means that the ratio A/(A+B) moves closer to zero.  At the extreme, total equality (everyone earning exactly the same income) would mean that Area B covers the entire space, and Area A disappears.  This means that the GC = 0/0+B = 0 as shown in Figure c.

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