It is the most representative income distribution indicator of the degree of income inequality. The Gini coefficient is expressed as a number between 0 and 1, where the distribution of income is completely equal and 1 is completely unequal.
eople as 100. And the line connecting the cumulative population ratio and the cumulative income ratio is defined as the Lorentz curve.
In the figure, the diagonal line in the square shows that the cumulative population ratio and the cumulative income ratio match, that is, all populations have the same income, showing a completely equal income distribution. In reality, however, a Lorentz curve such as curve A or B is created because there is no completely equal distribution of income. Comparing Lorenz curves A and B, 50% of the population accounts for 30% of total income for curve A, whereas curve B accounts for 25% of total income, indicating that the degree of income inequality in B is worse than in A. In other words, the further away from the diagonal, the greater the degree of inequality in income distribution.
The Gini coefficient is calculated using the Lorenz curve because it is equal to the value obtained by dividing the area between the diagonal and the Lorenz curve by the area of the entire triangle below the diagonal. If the distribution of income is completely equal, that is, if everyone's income is the same, the area between the diagonal and the Lorenz curve becomes zero, so the Gini coefficient is also zero. Conversely, if the distribution of income is completely unequal, the Lorenz curve will have a right angle. In this case, the area between the diagonal and Lorentz curves matches the area of the entire triangle below the diagonal, so the Gini coefficient is 1.
Gini Coefficient
The Gini coefficient can be calculated using the Lorentz curve. To draw the Lorenz curve, the total population is set to 100 by listing the total population in order of low-income to high-income, the horizontal axis is set to the population accumulation ratio, and the vertical axis is set to the total income accumulated by these people as 100. And the line connecting the cumulative population ratio and the cumulative income ratio is defined as the Lorentz curve.
In the figure, the diagonal line in the square shows that the cumulative population ratio and the cumulative income ratio match, that is, all populations have the same income, showing a completely equal income distribution. In reality, however, a Lorentz curve such as curve A or B is created because there is no completely equal distribution of income. Comparing Lorenz curves A and B, 50% of the population accounts for 30% of total income for curve A, whereas curve B accounts for 25% of total income, indicating that the degree of income inequality in B is worse than in A. In other words, the further away from the diagonal, the greater the degree of inequality in income distribution.
The Gini coefficient is calculated using the Lorenz curve because it is equal to the value obtained by dividing the area between the diagonal and the Lorenz curve by the area of the entire triangle below the diagonal. If the distribution of income is completely equal, that is, if everyone's income is the same, the area between the diagonal and the Lorenz curve becomes zero, so the Gini coefficient is also zero. Conversely, if the distribution of income is completely unequal, the Lorenz curve will have a right angle. In this case, the area between the diagonal and Lorentz curves matches the area of the entire triangle below the diagonal, so the Gini coefficient is 1.
