蛛网模型的数学研究

Mathematical study on the Cobweb model

针对传统蛛网模型假设条件局限性问题,从经济学定义出发,运用生产者考虑前两期的价格来决定自己本期产量的条件,构建了二阶线性非齐次差分方程的蛛网数学模型。对改进后的蛛网模型进行了动态和稳定性分析,得到了均衡价格存在的稳定性条件。在理论上对蛛网模型做了进一步的延伸;在实践中有助于生产者更加理性的生产,最终达到利润最大化,实现社会资源的最优配置。

In the light of limitations of the traditional cobweb model,based on its definition in economics,the use of the producer price of the first two periods is considered to determine their current conditions of production.The mathematical model of cobweb is constructed for non-homogeneous second order linear differential equation.The dynamic and stability of improved cobweb are analyzed to get the stability condition of the existence of equilibrium price.The tradition cobweb model is further extended in theory.In practice,it will help the producers with a more rational production to maximize profits and achieve optimal allocation of social resources.