Optimal Global Population Analysis Based on Solow Growth Model

Over the past century, the global population has increased dramatically, reaching around eight billion people. There has been a decrease in population growth rates in both developed and developing countries in recent years. Scholars have worked hard to calculate the optimal proportion of the global population, but the results vary widely among different scholars. This paper examines the global optimal population using a Lagrange Multiplier Optimization model based on the Solow exogenous growth model and utility maximization theory. Finally, the results showed that as opportunity costs of using capital and consumption prices decrease, marginal costs of living increase, thereby limiting population growth. When exogenous resources and autonomous growth factors increase, marginal benefits increase, thereby stimulating population growth. This essay aims to provide new perspectives for estimating the global population using the Lagrange Multiplier method and to determine the factors that affect population change. It is shown in this paper that, in the long run, society tends to have a rate of zero population growth until the improvements in technology and production exceed the carrying capacity of the environment.