TURNPIKE-THEORY - SOME NEW RESULTS ON THE SADDLE-POINT PROPERTY OF EQUILIBRIA AND ON THE EXISTENCE OF ENDOGENOUS CYCLES

This paper discusses the saddle point stability of equilibria and the existence of endogenous cycles in a general optimal growth model defin ed as a variational problem. We shall give new proofs of several turnp ike theorems and generalize a condition on the indirect utility functi on suggested by Brock, Scheinkman, and Magill to the analysis of stabi lity and bifurcation. Furthermore, we shall provide a characterization of the bound delta beyond which the steady state may be unstable and prove that under some conventional assumptions delta is the discount rate value for which a bifurcation of periodic orbits may be obtained by means of the Hopf theorem.