Analysis of 3D Cobweb Economic Differential Dynamic System Based on Supply-Demand and Price Relationships

Abstract

When the supply and demand of commodities are out of equilibrium, the dynamic changes in supply and demand are mainly manifested in the dynamic fluctuation of commodity prices and the change of price will drive the change of supply and demand. This paper proposes a method for constructing a three-dimensional cobweb economic model using the “predator-prey” theory. Firstly, based on the intrinsic driving relationships among supply, price, and demand, a differential dynamic model of the commodity and a pulse differential model when productivity increases are established. Secondly, the differential dynamics theory is used to analyze the existence of the model’s positive equilibrium and to prove its global asymptotic stability, uniform boundedness, persistence, and existence of the periodic solution. Finally, the correctness of the conclusions of the model is verified by numerical simulation. The relevant conclusions of model (1) reveal the evolution laws of supply, price, and demand that fluctuate around the positive equilibrium and tend to balance. Model (32) reveals that with the continuous improvement of production technology, supply quantity, price, and demand will fluctuate, but all three will change periodically. These conclusions can provide valuable help for people in the production, sale, and purchase of goods.