2. There is a lower limit to the means of subsistence necessary for personal survival (taking grain as an example). It is a quantitative and accurate expression of Malthus' theory that "food is necessary for human survival". It is also rooted in human biological attributes. This lower limit is expressed by S, which means the basic ration level (kg/person) to ensure survival.
3. There is an upper limit on the output per unit of land, which is the "boundary law of land productivity". It is also rooted in the biological characteristics of agriculture. Mr. Pei pointed out that the "land productivity boundary" is different in different times and under different technical conditions. Generally speaking, it increases with the improvement of technical level. From this perspective, the "land productivity boundary" is relative; However, in any relatively stable period, there is often no technological progress in society, and the stable (or stagnant) technological situation determines that the "land productivity boundary" at that time is unbreakable. From this perspective, it is absolute. Mr. Pei uses y to indicate the maximum yield per mu (kg/mu).
4. The land (area) that society can use is limited. It is rooted in geographical conditions that human beings cannot change. Mr. Pei uses A for land (mu).
We assume that the initial state of society is vast and sparsely populated, with relatively abundant land. In a relatively independent society, the natural growth of population will inevitably require more food to support it. Because the output of unit land is limited, it is necessary to expand the planting area, so the wasteland around the village is reclaimed as cultivated land. When there is no wasteland between villages for reclamation, the surplus population will choose to move to remote areas for reclamation until the remote areas are gradually reclaimed.
But the population did not stop growing because of the lack of arable land. In order to solve the survival problem of the new population, people have to use the original land more intensively, increase labor input on the original land to obtain higher output, and push the land output close to or reach the local "land productivity limit" at that time (the land quality is also different). The closer the land output is to the "land productivity limit", the less the marginal return per unit of labor input, which is the principle of "diminishing marginal return" that people often say. Because the population growth rate exceeds the growth rate of grain output, the per capita grain is getting less and less until the survival bottom line S, then Malthus will suppress the population's grain. At this time, the total grain output reaches the maximum, and the per capita grain is ay/n, which is equal to the minimum demand of individuals for grain, that is, s=ay/n, and can also be converted into ns=ay. At this time, the grain yield per unit area has reached the limit y, and it can't be increased any more; The cultivated land area is also limited by geographical conditions and can only be maintained at a, so the total output ay has reached the limit. Because s is necessary for individual survival, there is no possibility of reduction, so there is no real room for population n to increase, and then society converges to ns=ay state. The author calls the population state n at this time a saturated state (this population is called "environmental population capacity" in geography). If there are no exogenous variables, society will operate according to this principle, and finally there will be a state of population saturation. At this time, four
All factors are deadlocked, and society itself is limited to stagnation (no economic growth). Social scientists call this situation "population trap" and "population balance" and so on.
Teacher Pei concluded that the social situation at any time is nothing more than three situations: ns < ay, ns=ay and ns > ay. The first situation is that the total demand is less than the total output, the society still has surplus, the land output has not reached the limit, and the total output still has room to continue to increase. According to Malthus principle, this society must be able to support more people. Because the population has a natural growth trend, and the population growth is faster than the grain growth, the society will eventually reach the state of ns=ay, which will become the second situation. The third situation is that the demand is greater than the total output. At this time, it is difficult for society to feed the existing population, so it will starve people and force the population to return to the level of ns=ay.
It should be pointed out that Mr. Pei also realized that the situation in Nanjing was the root cause of social unrest and peasant uprising. Although Mr. Pei also mentioned natural disasters, he did not deeply analyze why NS > AY appeared in society. In fact, natural disasters are important "exogenous variables" that cause social changes. When we incorporate natural disasters into Malthus model, we will get the following reasoning:
When the society converges to the state of ns=ay, if a large-scale natural disaster suddenly occurs, the grain output per unit area will be greatly reduced (Y value will be reduced), or even no harvest (y=0). At this time, the overall situation of NS > AY will appear, and the social situation will become very severe. Since s is the bottom line of survival, we can only reduce the population n to achieve balance. Malthus believed that wars, plagues and natural disasters would all lead to a "real" decrease in population. From the perspective of population model, the mechanisms of war, plague and natural disasters are not the same. Plague often occurs when the population is saturated. When the society converges to the state of ns=ay, the population generally falls into poverty, people are malnourished and their health level declines. Even without natural disasters, they are vulnerable to plague. As we all know, the Black Death in Western Europe once caused a large population decline. There is not much information about plague in China's historical records, but this does not mean that there are few large-scale plagues in China, but only a few people have systematically recorded and studied them. There are many records about social wars in the history of China, among which large-scale peasant uprisings and peasant wars are mostly closely related to natural disasters. Natural disasters force farmers to survive, and participating in the uprising is the only possible way out. Peasant uprisings and social wars destroyed a large number of people (two-thirds of the population were destroyed by many wars in China's history), the conflict between man and land tended to ease, natural disasters passed repeatedly, and the surviving population longed to live and work in peace and contentment, so a new ruling dynasty (provider of public goods) came into being and society began a new dynasty cycle. With the improved Malthusian model, the state of NS < AY starts again, and after ns=ay converges, the state of NS > AY is finally triggered by natural disasters, leading to the next round of social collapse. In short, natural disasters indirectly destroyed the population, and wars and plagues directly destroyed the population, both of which caused Malthus to suppress the population.
It is easy to see that Mr. Pei's generalization of Malthusian model that four elements converge in a state of equilibrium is indeed more scientific than Malthusian theory. In particular, the four elements are rooted in the "laws of nature" which are beyond human control and cannot be explained by the theoretical model of social economy, and indeed fall to the "lowest level of non-economy", which can be regarded as the basic "axiom" of the theoretical framework of social science. The author believes that Mr. Pei has indeed made important theoretical contributions to social science.