A Study On Nonlinear Cobweb Theory And Application

Cobweb model is the classical model in dynamic economy analysis, applied todiscribe the trend of supply,demand and price. In the assumption of linearity, thetraditional cobweb model can only discribe convergence,divergence and two-periodsimple behaviors, can not detail complex dynamic behaviors. In the assumption ofequilibrium, the behaviors of price series is determined with supply function anddemand function, can not make sure that prices series converge to equilibrium price,so that this sorts of perfect efficient price adjustment is not sure the best one. Themain problem of solving the practice and stability for cobweb model, is that proposinga nonlinear and disequilibrium cobweb model, and selecting the adaptive priceadjustment methods, in order to making the model system can arrive an equilibriumfrom disequilibrium with great rapidity of the convergent speed, and realizing thestability of economic system.In this paper, we analyses the classical consumption model and production model,and give an improvement to the models and its equilibrium conditions. To thegenenrial nonlinear and disequilibrium cobweb model, detail the dynamic behaviors,the convergence conditions and convergent speed, select the best price adjustmentmethod. To a sort of cobweb model with the special supply curve, research thedynamic behaviors of price systems of the equilibrium cobweb model anddisequilibrium cobweb model, and analyses their convergence conditions andconvergent speed, select the best price adjustment method. The resuits demonstratethat the disequilibrium cobweb model can discribe more complex dynamic behaviorsthan equilibrium cobweb model, and in the condition of selecting the adaptive priceadjustment methods, can make the model system can arrive an equilibrium fromdisequilibrium with great rapidity of the convergent speed. So the disequilibriumcobweb model is not only suitable to practice economics, but also beneficial to thestability of economic system.