Lorenz Curve was developed by Max O. Lorenz in order to describe the extent of social inequality in a society. Imagine a graph (Lorenz Curve) in which the cummulated income (expressed as a percentage) is placed on the vertical axis and the cumulated number of households (expressed as a percentage) is placed on the horizontal axis. If there was perfect equality (so that the first 10 per cent of the households received 10% of the income and 20% of the households received 20% of the income, etc.) a diagonal line (Lorenz Curve) would be drawn across the graph. When actual income distributions are depicted on this graph the line (a 'Lorenz' curve) departs from the line of perfect equality. For example, the bottom 20 per cent of households may receive only 4.5% of the total income. This line is the Lorenz curve and can be expressed mathematically.
The Gini coefficient is an expression of the ratio of the amount of the graph located between the line of perfect inequality and the Lorenz curve to the total area of the graph below the line of equality. The Lorenz curve is a graphical representation of the proportionality of a distribution (the cumulative percentage of the values). To build the Lorenz curve, all the elements of a distribution must be ordered from the most important to the least important. Then, each element is plotted according to their cumulative percentage of X and Y, X being the cumulative percentage of elements.
For instance, out of a distribution of 10 elements (N), the first element would represent 10% of X and whatever percentage of Y it represents (this percentage must be the highest in the distribution). The second element would cumulatively represent 20% of X (its 10% plus the 10% of the first element) and its percentage of Y plus the percentage of Y of the first element.
The Lorenz curve is compared with the perfect equality line, which is a linear relationships that plots a distribution where each element has an equal value in its shares of X and Y. For instance, in a distribution of 10 elements, if there is perfect equality, the 5th element would have a cumulative percentage of 50% for X and Y. The perfect equality line forms an angle of 45 degrees with a slope of 100/N. The perfect inequality line represents a distribution where one element has the total cumulative percentage of Y while the others have none.
Lorenz curve provides a fuller grasp of how the gini coefficient is determined.