Flow algorithm
According to Lorenz curve, Hirschman put forward an index to judge the equality of distribution. Let the area between the actual income distribution curve and the absolute equality curve of income distribution be a, and the area at the lower right of the actual income distribution curve be B. The degree of inequality is expressed by the quotient of a divided by (A+B). This value is called Gini coefficient or Lorenz coefficient. If a is zero and Gini coefficient is zero, it means that income distribution is completely equal; If b is zero, the coefficient is 1, and the income distribution is absolutely unequal. The more equal the income distribution, the smaller the curvature of Lorenz curve and the smaller the Gini coefficient. On the contrary, the more income distribution tends to be unequal, the greater the curvature of Lorenz curve and the greater the Gini coefficient. In addition, you can refer to Pareto index (an index to measure the degree of uneven income distribution).
Many domestic scholars have explored the specific calculation method of Gini coefficient and put forward more than ten different calculation formulas. Zhang Jianhua, a teacher from the School of Economics and Business of Shanxi Agricultural University, put forward a simple and easy-to-use formula: suppose a certain number of people line up in the order of income from low to high, and divide them into n equal groups, and the cumulative income from group 1 to group I accounts for wi of the total population income, which shows that the formula is obtained by dividing the integral (area b) of Lorenz curve by the sum of the areas of n equal trapeziums by the definition of definite integral.
economic meaning
Gini coefficient is an index to judge the fairness of income distribution defined by Italian scholar corrado Gini according to Lorenz curve in the early 20th century. It is an important analytical index used to comprehensively examine the income distribution differences of residents in various countries in the world.
Its specific meaning refers to the proportion of all residents' income used for uneven distribution. The maximum value of Gini coefficient is "1" and the minimum value is "0". The former means that the income distribution among residents is absolutely unbalanced, that is, 100% of the income is occupied by the owner of a unit; The latter means that the income distribution among residents is absolutely average, that is, the income between people is completely equal, without any difference. But these two situations are only absolute forms in theory, and generally do not appear in real life. So the actual value of Gini coefficient can only be between 0 and 1. The smaller the Gini coefficient, the more average the income distribution, and the larger the Gini coefficient, the more uneven the income distribution. 0.4 is usually regarded as a warning line for the gap between the rich and the poor in the world. If it is greater than this value, social unrest will easily occur.