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# Lorenz Curve and GINI-Coefficient/GINI-Concentration Ratio:

## Definition:

An American statistician Conard Lorenz (1905) used a diagram to show the relationship between the population groups and their respective shares. The same diagram (Lorenz Curve) is used to show the relative inequality in the distribution of income at the world level.

Whereas the GINI-Coefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level.

## Explanation with Diagram and Example:

Figure 1, on the horizontal axis the numbers of income recipients are plotted, not in absolute terms but in cumulative percentages. For example, at point B we have the lowest (poorest) 20% of the population; at point F there is bottom 60% population; and at the end of the axis there is all 100% of the population which are the recipients of income. The vertical axis, as shown below:

The share of total income that is earned or received by each % of population. It is also cumulative up to 100% so that both axis are equally long and the entire figure is then enclosed in a square. A diagonal line is drawn from the left hand corner (the origin of the square to the upper right hand corner).

At every point on this diagonal the percentage of income received is exactly equal to the percentage of income recipients. For example, the point "P" on this diagonal which is half way along the length of the diagonal, represents 50% of the income being distributed to exactly 50% of the population. While point "Q" (the three quarter point) shows that 75% of the income is going over to the 75% of the population. Thus, this diagonal line is the representative of perfect equality in respect of distribution of income. Each percentage group of income recipients is receiving that same percentage the total income. As the bottom 40% receives 40% of income, while the top 5% receive only 5% of the total income.

Whereas the Lorenz Curve shows the quantitative relationship between the percentage of income recipients and the percentage of the total income which they actually received, say during a year. The horizontal and vertical axis have been divided into ten equal segments corresponding to each of the 10 deciles groups. Point A (in the Fig. 1) show that 10% of the population receives only 1.8% of total income. Point B shows that the bottom 20% is receiving 5% of income and 80% of the population is receiving 48% of the income.

The more the Lorenz curves away from the diagonal (perfect equality), the greater will be the inequality. The extreme case of perfect inequality is a situation where one person receives all the national income, while every body else receives nothing.

In Fig. 2, we have Lorenz Curve which shows relatively greater equality in the distribution of income. In such case the Lorenz Curve is away from horizontal axis.

While in Fig. 3, we have Lorenz Curve which has greater curvature and it is closer to the bottom horizontal axis shows greater inequality in the distribution of income. The Gini-Co-efficient is employed to measure the aggregate inequality.

## Degree of Inequality in a Country:

The degree of inequality in a country can be obtained by calculating the ratio of the "area between the diagonal and the Lorenz Curve as compared to the total, area of the half square in which the curve lies".

Thus in Fig. 4:

"The ratio of the shaded area EA to the total area of the triangle BCD".

This ratio is known as, GINI-Concentration Ratio or GINI-Coefficient.

This ratio is attributed to Italian statistician C. Gini who formulated it in 1912. The Gini-Coefficients are aggregate inequality measures and they can vary any where from zero to one. When the value of such ratio is zero, it represents perfect equality regarding the distribution of income. On the other extreme, if the value of this ratio is 1 it shows perfect inequality. The countries which are furnished with unequal income distributions the value of such ratio ranges in between 0.5 and 0.7. On the other hand, the countries having relative equality in their distributions of income the value of such coefficient ranges in between 0.2 to 0.35.

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## Lorenz Curve and GINI-Coefficient

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