On the stability of an adjustment process for spatial price equilibrium modeled as a projected dynamical system

This paper presents a stability study for the continuous-time adjustment process proposed for the perfectly competitive spatial price equilibrium problem modeled as a projected dynamical system by Nagurney, Takayama, and Zhang (1995). Two distinct approaches are adopted here for establishing the stability of the spatial price equilibrium under such an adjustment process. One approach utilizes the monotonicity condition on the supply prices, demand prices, and transaction costs to develop various stability properties. The other utilizes the regularity concept, adapted from Zhang and Nagurney (1995), which enables us to explore the stability of the adjustment process - a nonstandard dynamical system, via its minimal face flow - a standard dynamical system.