A dynamic comprehensive mathematical model for Malthusian principles

Abstract The Malthusian Trap is a mechanism that describes how population growth suppresses the average income in the pre-industrial human history. Studies of the pre-industrial world demonstrated the staggering effect of the average income worldwide. From the original Malthusian literature,"The perpetual tendency in the race of man to increase beyond the means of subsistence is one of the general laws of animated nature which we can have no reason to expect will change.", the tendency to "increase beyond the means of subsistence" is an axiom of the Malthusian Trap mechanism. The the tendency to "increase beyond the means of subsistence" can also be understand as increase the birth rate as high as possible. On the other hand, the birth rate is observed to be decreasing drastically in modern society. The Demographic transition theory demonstrate this transition from high-birth-high-death to low-birth-low-death over economical development. This paper developed a comprehensive mathematical model that tries explain the high-birth tendency and the transition from high-birth-high-death states to low-birth-low-death states. In the model, 3 fundamental elimination processes are demonstrated. 1) The High-Birth-Elimination explains the tendency to increasing birth rate; 2) the Low-Average-Elimination forces decreasing living condition; and 3) the High-Quota-Elimination based on extra resource force gain access to extra resources for creatures or economical developments for human being. The elimination process demonstrated two drastically different situation. Under Malthusian trap, the average income decreased as low as possible while birth rate is pushed as high as possible. Out of Malthusian trap, the average income growth rate is pushed high by decreasing birth rate. The model draws a necessary and sufficient condition between the Malthusian trap and the elimination processes, thus explained the transition from high-birth-high-death to low-birth-low-death based on escaping Malthusian trap.