Behavior of optimal trajectories in the neighbourhood of an equilibrium point (Q794545)

It is known that under certain assumptions optimal trajectories of dynamical economic models are globally stable, i.e., they can be approximated at an equilibrium point independently of the initial state. \textit{M. J. P. Magill} [Int. Econ. Rev. 20, 577-597 (1979; Zbl 0497.90012) and Disc. Paper No.296, Northwestern Univ. at Evanston (1977)] studied the behavior of an optimal trajectory more precisely in the neighborhood of an equilibrium point. In a model with continuous time he clarified the conditions which characterize the cyclic or monotonic behavior of optimal trajectories near equilibrium. In the present paper we shall study the qualitative behavior of optimal trajectories in a dynamical economic model with discrete time. We shall prove a theorem giving sufficient conditions for monotonic behavior of optimal trajectories and a theorem on cyclic behavior of trajectors. We shall analyze two-dimensional models in more detail. For such models we derive inequalities which characterize the behavior of optimal trajectories.