Set Valued Dynamical Systems and Economic Flow

The purpose of this monograph is to illuminate the central issues of dynamic analysis applied to economic models, using a generally accepted language of the study of dynamical systems at a level of sophistication likely to be understood by an economist versed in elementary topology. Whether an economic system is governed by a first order difference equation or several simultaneous multivalued partial differential equations, its solution is a flow that determines the state of the system given an initial condition and elapsed time. Thus the flow of a system is the central concept from which the theory here expounded develops. The explicit examples and applications herein are discrete time models, but the theoretical re- sults hold for continuous time models as well. The supplementary bibliography in- cludes several papers at the frontier of set-valued dynamics which may be viewed using the basic concepts defined in this text; all of these works involve demon- strating that (almost) all possible trajectories that a system may follow converge to some set of equilibria. The application of set valued dynamical analysis to economic models is pro vided to engender in the reader an appreciation for the relevance of these con- cepts to economic theory.