in p>1857, Ernst Engel, a world-famous German statistician, expounded a law: with the increase of household and individual income, the proportion of expenditure on food in income will gradually decrease. This law is called Engel's law, and the coefficient reflecting this law is called Engel's coefficient. The formula is:

Engel's coefficient (%) = total food expenditure/total household or individual consumption expenditure ×111%

Engel's law mainly expresses a certain trend that the proportion of food expenditure to total consumption expenditure changes with the change of income. This paper reveals the correlation between residents' income and food expenditure, and illustrates the influence of economic development and income increase on living consumption with the proportion of food expenditure to total consumption expenditure. As we all know, eating is the first need of human survival. When the income level is low, it will inevitably occupy an important position in consumption expenditure. With the increase of income, when the food demand is basically met, the focus of consumption will begin to shift to other aspects such as clothing and use. Therefore, the poorer a country or family life, the greater the Engel coefficient; On the contrary, the richer the life, the smaller the Engel's coefficient.

once Engel's law and Engel's coefficient were put forward, they were widely accepted and confirmed by western economists, and they thought that they had universal applicability. In China, it was also used in statistical work earlier. The Engel coefficient is generally calculated by using the survey data of urban and rural households in various places. For example, according to the survey data of urban households in Beijing in 1998, the per capita consumption expenditure of residents is 6971.8 yuan, of which the per capita food expenditure is 2865.7 yuan, and the Engel coefficient is 41.1%.

Engel's coefficient is often used internationally to measure the living standards of people in a country or region. According to the standards put forward by FAO, the Engel coefficient is above 59% for poverty, 51-59% for food and clothing, 41-51% for well-off, 31-41% for wealth, and below 31% for the richest. When using this standard to compare international and urban and rural areas in China, we should take into account those incomparable factors, such as the difference in the price of consumer goods, the difference in residents' living habits, and the special factors caused by different social and economic systems. For the incomparable problems in the comparison of these cross sections, corresponding elimination should be made in the analysis and comparison. In addition, when observing the historical changes, it should be noted that Engel's coefficient reflects a long-term trend, rather than an absolute tendency to decline year by year. It is to seek a long-term trend by ironing out short-term fluctuations.