差分方程形式下不同预期的蛛网模型及其稳定性研究——以中国猪肉市场为例

Different Expected Cobweb Models in the Form of Difference Equations and their Stability

蛛网模型是一类典型的具有时滞效应的经济学模型,与无时滞的系统相比具有更复杂的动态特性,具有非常重要的理论意义与实际价值。传统的蛛网模型由于过于简化,并且将变量视为连续出现,不能够很好的贴合实际,而且目前对不同预期形式的蛛网模型的研究还不够完善。基于此,本文将预期理论引入到传统的蛛网模型中,使用差分方程构建供需系统,将时间视为离散变量,而非连续变量,更符合数学与经济的双重意义。在完成理论分析之后,以近二十年国内猪肉市场为对象进行实证研究,对2020年猪肉市场的供需进行理性预测。这些成果可以有效的扩展蛛网模型在实际生活中的应用,也为宏观调控决策提供强有力的理论依据。

Cobweb model is a typical economic model with time-delay effect.In contrast with the system without time delay,cobweb model has more complex dynamic characteristics and has very important theoretical significance and practical value.The traditional cobweb model is too simplified and takes the variables as continuous occurrence,which cannot fit the reality well.Moreover,the research on different expected forms of cobweb model is not perfect.Accordingly,the paper introduces the expectation theory into the traditional cobweb model,uses the difference equations to construct the supply-demand system,and regards time as a discrete variable rather than a continuous variable,which is more in line with the dual significance of mathematics and economy.After completing the theoretical analysis,the paper takes the domestic pork market in the past 20 years as an example to make a rational prediction on the output and price of pork market in 2020.These results can effectively expand the application of cobweb model in real life,and also provide a strong theoretical basis for macro-control decision-making.