Nonlinear Dynamics and Multistability in a Cobweb Model

Abstract

This paper studies the dynamic characteristics of an economic cobweb model whose producers adopt a gradient-based mechanism. The model’s producers are taken to be boundedly rational, and then the model is studied as a 1D and 2D discrete time dynamical system. Due to the lack of information in the market regarding the function of demand, the producers depend on the estimation of the marginal profit variations so as to update their prices next period. The equilibrium price point is calculated, and its local stability conditions are discussed through analytical and numerical investigations. In the 2D model, where the memory factor is introduced, the equilibrium price is obtained, and it is shown that it can be destabilized through chaotic behaviors, which are formed due to period doubling and Neimark-Sacker bifurcation. Furthermore, we study the symmetric case when the producers update their prices based on the marginal profit in the past two time periods, and therefore, we investigate the influence of the speed of adjustment parameter on the stability of equilibrium price.