What Is the Lorenz Curve?

Lorenz curve, also translated as "Lorentz curve". That is, within a population (country, region), a curve consisting of the percentages of the percentage of the poorest population to the richest population corresponding to the income percentage of each population percentage. In order to study the distribution of national income among nationals, American statistician (or Austrian statistician) MO Lorenz (1876- 1959) proposed the famous Luo Lenz curve.

Lorentz curve

The Lorentz curve is used to compare and analyze a country in different times or different countries in the same era.

Although distributable according to income

The Lorentz curve has the following properties:

(1) P (0) = 0, Q (0) = 0, that is, 0% of the population's income accounts for 0% of total income; and P () = 1, Q () = 1, that is, 100% of the population Revenue accounts for 100% of total revenue.

(2) When the Lorentz curve is a 0A line at a 45 ° angle, the proportion of the population increases by one unit, and the corresponding proportion of income also increases by one unit, which indicates that everyone has the same income, that is, the income distribution is absolutely average. Straight 0A Become an absolute average.

(3) When the Lorentz curve is a 0BA polyline, the proportion of the population remains unchanged before it increases to 100%. When the proportion of the population reaches 100%, the proportion of income immediately reaches 100%, which indicates that all income is concentrated in One person's hands, while others' incomes are zero, that is, the social income distribution is absolutely uneven. The 0BA polyline is called the absolute uneven line.

(4) The Lorentz curve is actually a distribution curve, and the Lorentz function Q = Q (P) is a distribution function.

Obviously, in real life, the two extreme phenomena of absolute equalization or absolute inequality in the distribution of capital among various economic sectors do not exist; on the contrary, inequality, differences are common and normal, and generally The situation is somewhere in between. That is, the Lorentz curve is a curve between the absolute average and the absolute inequality.

Generally speaking, when a country is poor, the gap between the rich and the poor is larger, and when it is rich, the gap between the rich and the poor is smaller. However, there are exceptions. This exception is China. The reason is that the improvement of China's welfare system can't keep up with the speed of development. If the system is not perfect, there are loopholes and opportunities are available. Another reason is China's special situation. China is a planned economic system. It's a long time. Unfortunately, we are now in this process period and will be in this process period for a long time. Therefore, the gap between the rich and the poor when China was poor was small, but now that the economy is improving, the gap between the rich and the poor is getting wider.