The Power Law Population Growth Model

Abstract

The classical logistic equation is generalized to a model with power law growth parameter. It is shown that though the growth of human population was influenced by many factors, but the power law model can be successfully applied to give the distribution of population by seeking a suitable power law growth parameter. The verifications are made with the population of provinces of China, the mainland of China, and the American. Some interesting values of power law growth parameters are determined. The power law parameter is a decreasing function of population. For provinces of China are: Ji-Lin 0.6, Liao-Ning 0.5825, Fu-Jian 0.595, Zhe-Jiang 0.58, Nei-Meng 0.615, Wu-Gong County 0.8, respectively. For the mainland of China, the parameter is 0.474, and for American the parameter is 0.5.

Keywords: Logistic equation, growth of the population, differential equation, power law exponent

JEL Classification: N30