# What�s �Gini Index

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```							What’s “Gini Index?”
What’s “Gini coefficient (or Gini index) ?”
Gini coefficient is an indicator of inequality in a society. It ranges
from 0 to 1. While “0” means perfect equality where everyone’s income or
wealth is of same amount, “1” shows “perfect inequality” where only one
person has all of the wealth or income in the whole society and everyone
other than him has nothing.
Then, how is Gini index calculated?
To understand it, we should know the “Lorenz curve.”
Then, what is the “Lorenz Curve?”
Let’s suppose that there are 5 people in a small economy. Assume
that the income of person A is \$1, B’s income is \$2, C’s \$3, D’s \$4, and E’s
\$10. The total income of the 5 people is \$20. Thus, person A’s share of the
total income of the economy is .05 (5%), B’s share is 10%, etc.
Let’s list those 5 guys from the poorest to the richest. Since the
whole population of our imaginary economy is only 5, person A is the poorest
20%, and the cumulative income of from A to B represents the cumulative
income of the poorest 40%, etc.
<Table 1>
Person A     B           C            D            E
The Poorest    20%          40%         60%          80%          the
Richest
Income         1            2           3            4            10
Income         1            3           6            10           20
(cumulative)
Share(%) in    5            10          15           20           50
the economy
Cumulative % 5              15          30           50           100

As seen in the table, the poorest 20% of the population earns 5% of
the total income of the economy, the poorest 40% earns 15%, the poorest
60%, the poorest 80 percent 50%. The rest 50% of the total income of the
economy goes to the richest 20%.

Let’s transform this table into a graph. The vertical axis denotes the
cumulative share of income, and the horizontal axis lists the whole population
of this economy from the poorest to the richest.

<Figure 1>
Cumulative % of Total Income

100%

80%

60%

40%

20%

20%       40%         60%   80%   The   Richest

You can see a curve that links the points which denotes the cumulative
share of the total income of the poorest 20, 40, 60, 80% and the richest.
That curve is the “Lorenz curve!”

Above our Lorenz curve, there is a diagonal line, the slope of which is
45 degree.
If everyone has the same amount, thus same share of income in the
economy, the Lorenz curve will coincide with the diagonal line, because the
cumulative percentage of income will increase at the same rate as the
percentage of population, as shown in <table 2>.

<Table 2>
Person A        B           C           D         E
The Poorest      20%             40%         60%         80%       the
Richest
Income           4               4           4           4         4
Income           4               8           12          16        20
(cumulative)
Share(%) in      20              20          20          20        20
the economy
Cumulative % 20                  40             60               80    100

On the contrary, if the income distribution is perfectly unequal, that’s
to say, only one person (“person E” in our model) has all of the income in the
economy and others nothing, as shown in <table 3>, the shape of Lorenz
curve will be “reversed L” as the bold curve in the <figure 2>.

<Table 3>
Person A      B              C                D     E
The Poorest        20%           40%            60%              80%   the
Richest
Income             0             0              0                0     20
Income             0             0              0                0     20
(cumulative)
Share(%) in        0             0              0                0     100
the economy
Cumulative % 0                   0              0                0     100

<Figure 2>
Cumulative % of Total Income

100%

80
%

60
%

40
%

20
%

20        40        60   80        The   Richest

%        %         %    %
Then, what’s the relationship between Lorenz curve and Gini index?
Let’s go back to <Figure 2>.
Gini index is the share of the area between the diagonal line and the
Lorenz curve in the whole area under the diagonal line. In <Figure 3>, the
share of area ‘B’ in the triangle is the Gini index, which is….. “A / (A+B).”
Thus, under the condition of “perfect equality,” since the Lorenz curve
precisely coincides with the diagonal line, the square measure of area A will
be “0,” thus the Gini index will also be “0.”
On the contrary, under the condition of “perfect inequality,” the area A
will take the whole triangle, thus the square measure of area “B” will be zero.
Thus, the Gini index is “A / (A+B) = A / (A+0) = A / A = 1.”
<Figure 3>

A

B

-Reference: Lee, Joon-koo. 1998. Microeconomics. Seoul (Korea):
Bummoonsa.
(in Korean language)

```
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