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.
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
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.