ESSAY II – On Optimal Steady States of n-Sector Growth Models when Utility is Discounted *

Publisher Summary This chapter presents results on local and global stability of n-sector growth models when utility is discounted mostly for small rates of discount. It is well known that when future utility is not discounted, precise results about optimal steady states (OSSs) can be proven under fairly general assumptions. In particular, existence, uniqueness, and turnpike properties have been established by several authors. The counter examples presented by Kurz, Sutherland, and Weitzman, however, show that when utility is discounted, additional assumptions are required to obtain turnpike results. In general, it would be interesting to know how the sub manifolds of stability change as δ changes. The proof that the turnpike theorem holds for discount factors near one is divided in two parts. It shows that optimal paths visit neighborhoods of the modified OSSs. Local stability holds for such neighborhoods. The chapter discusses other problems such as uniqueness and continuity of OSSs. It also discusses the relation between the saddle-point property and the local stability of infinite horizon optimal growth paths.