Asymptotic Behavior of Trajectories in Some Models of Ecnomic Dynamics

Abstract

Asymptotic behavior of trajectories in Neumann type models of economic dynamics with average growth rate is studied. Index set is introduced and the sequence of cones generated by the cone Z of the Neumann-Gale model is considered. The concept of quasi rate of the model z_i is introduced. The relationship between the concepts of average growth rate and quasi rate is found. The relationship between the turnpikes M_α for different values of х and the set A_z of conic hulls of the sets of all angular distance limit points is examined. Upper and lower estimates for a non-empty turnpike are obtained. Under some additional conditions, more accurate lower estimate is obtained which allows to conclude that in most cases the set M_α is a subset of the set A_z. Algorithm is proposed for constructing a trajectory X_i , which has the point x among its angular distance limit points. Theorem on the existence of a turnpike which has the point х among its angular distance limit points is proved.