The Gini Coefficient

The Gini Coefficient is often used an indicator of inequality in a country. Additionally, one can also use the Gini Coefficient as an indicator of economic development. The Gini Coefficient is based on the Lorenz Curve and measures the degree of income or wealth inequality in an economy. The coefficient is bound between zero and one. This means that the coefficient can take on values between zero and one. A Gini Coefficient of one states complete inequality. That is, one single person receives all the income or holds all the wealth of the economy, while all others receive or own nothing. A Gini Coefficient of zero implies perfect equality. That is, all individuals obtain the same income. See the discussion of the Lorenz Curve for a clear illustration of the concept. 

The following expression defines the Gini Coefficient mathematically:

Gini = \frac{1}{2 \mu} \sum^{n}_{i=1}\sum^{n}_{j=1}f(y_{i})f(y_{j})|y_{i}-y_{j}|

where \mu = sum^{n}_{i=1}f(y_{i})

The Gini Index is equal to the area between the actual income distribution curve and the line of perfect income equality. As it is an Index it is scaled to a number between 0 and 100.  The Gini Coefficient is the Gini Index mapped to a number between 0 and 1. That is, the Gini Coefficient is the Gini Index divided by 100.


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