Gini Index

Index to see the degree of income inequality in a society.
Algebraically, it is defined as "Expected value of the ratio of the difference of two arbitrary specimens to the mean value of all specimens".

However, it is understood generally by the geometry definition "Area enclosed by the Lorenz curve and the diagonal", which has an equal meaning of the algebraical definition.
If you take the horizontal axis as the cumulative share of people from lower income and draw the cumulative share of income earned, then the curve becomes Lorenz curve, and the area between the Lorenz curve and the straight line (diagonal = even distribution line) becomes Gini Index (the triangular area composed of the axis and the diagonal is assumed to be 1).

We cannot understand the value of the Gini Index as the real degree of income inequality, easily.
However, when the Gini Index is g, and the society can be divided into the rich layer and the poor layer by r : 1-r, the share of the rich layer income becomes r+g, and it makes us know the degree of inequality.
For instance, if the Gini Index is 0.3 and the share of rich layer is 20% then the income share of the rich layer becomes 50 percent of the whole income.
( Refer to a right picture.)

AP:QP=1-g:g

Xp=1-r

Xq=1-r/(1-g)=(1-g-r)/(1-g)

Yq=Xq=(1-g-r)/(1-g)

Yp=1-g-r

Gini Index	Share of Upper layer (%)	Gap between two layers (times)
0.2	40	2.3
0.3	35	3.4
0.4	30	5.4
0.5	25	9
0.6	20	16
0.7	15	32
0.8	10	81
0.9	5	361

Though it isn't easy to understand the meaning of the Gini Index, in this analysis, we assume that the society is devided into two layers and the group of A% of total people earns 100-A% for easy understanding.
For instance, the Gini Index of 0.7 means the rich layer of 15% earns 85% of total income and the gap of two layers becomes about 32times ((85/15)/(15/85)=32.1).
As for the Gini Index of 0.7068 as the income of the world, the rich layer of 14.7% earns 85.3% of total income and the gap of two layers becomes 33.9 times even if the income inequality within each country is neglected.
This Gini Index is decided by the area, and is not related to the shape of the Lorenz curve. Therefore, even if the ratio of a rich layer to the poor layer is different, the Gini Index becomes the same in some cases.
The Gini Index is 0.3 in "the society where one king owns 30 percent of the whole income and the other people have others" and also in "the society where the citizen layer of 70% gets all income and the slave layer of 30% gets nothing". There is no clear definition of the difference in this case.

Standard of Gini Index
-0.1	There is an artificial background for leveling.
0.1-0.2	Though considerably equal, there is an anxiety to obstruct the effort to the improvement.
0.2-0.3	Usual distribution type that exists in general in society
0.3-0.4	Though there are some differences, there is also a desirable respect in the improvement throug competition.
0.4-0.5	The difference is serious.
0.5-	The improvement is required except under special circumstances.

A right table is one standard, and we have to examine it on individual real cases.
For instance, if there are some people who positively select rented houses, the asset differential concerning the house and land doesn't become a problem just because the Gini Index is large.
On the other hand, it is necessary to note that there is a possibility that the difference of the Gini Index only shows the difference of the attribute of the constituent members in each region in the comparison of the Gini Index between two regions.
For instance, the Gini Index of the city of schools with many students must be lower than that of the new house city where people live with their families.