The "inverted U-shaped curve", that is, Kuznets curve, was first put forward by simon Kuznets, a famous American economist and Nobel laureate in economics, at 197 1. Because it is a curve that bends upward first and then the graph bends downward, it looks like an inverted U-shape, so people call it an inverted U-shape curve. From 65438 to 0955, in the article Economic Growth and Income Inequality, Kuznets put forward the relationship between per capita wealth growth (efficiency and development) and per capita wealth distribution (fairness) from the perspective of development economics. After analyzing the empirical data of economic growth and income gap in 18 countries, Kuznets concluded that the long-term change track of income distribution is "deterioration first, then improvement". Or in his own words, "the long-term trend of income distribution inequality can be assumed as: rapid expansion in the initial stage of economic growth from pre-industrial civilization to industrial civilization, then temporary stability, and then gradual contraction in the later stage of growth." He also came to the conclusion that "the income inequality of developing countries in the early stage of development is higher than that of developed countries in the later stage of development". Kuznets believes that in the early stage of economic development, the growth of per capita wealth will lead to the expansion of income gap; After a short period of stability, with the growth of per capita wealth, the income gap will gradually narrow. But this proposition is only a guess, and the data obtained from the economic development history of European and American countries are not absolutely correct. On the one hand, the "inverted U-shaped curve" is not inevitable, that is, economic growth does not necessarily lead to widening income gap. For example, in the process of economic development, the four little dragons in Asia did not have an obvious "inverted U-shaped curve" phenomenon because they properly handled the relationship between economic growth and income gap. On the other hand, the inflection point of the "inverted U-shaped curve" does not necessarily appear automatically, that is, after the income gap expands, there is no human action and it will not automatically narrow. Most economists regard Kuznets curve as a specific historical phenomenon, not an economic law. In western countries, the downward trend of Kuznets curve is due to the corresponding measures taken by the government to narrow the income gap, such as political reform and institutional adjustment. Kuznets curve is a hypothesis, and the shape of the curve is determined by a series of mathematical methods, but there are also various problems in this series of mathematical methods, which are controversial in academic circles. Among them, the serious problem lies in the mathematical method used by Kuznets, which narrows the real income gap between people in high-income countries. The practical significance of this theory is that China is facing the problems of widening income gap and frequent social injustice. Whether the relationship between economic growth and income gap can be successfully handled determines whether China can successfully complete its economic transformation and step into a well-off society in an all-round way. (Semimonthly Talk, Issue 1 1, Issue 12, Cai Wenquan Root)