Discounting and long-run behavior: Global bifurcation analysis of a familyof dynamical systems

This paper is concerned with the relationship between the discount rate and the nature of long-run behavior in dynamic optimization models. The theory is developed under two conditions. The first is history independence, whic h rules out multiple limit sets. The second is a condition that avoids the reversion to a stable steady state, as the discount factor is lowered, once cycles have emerged. These conditions appear to be the minimal restriction s that would allow analysis by a bifurcation diagram. The results are illus trated by two well-known examples in this literature, due to Sutherland and Weitzman-Samuelson. Journal Economic Literature Classification Numbers. C6 1, D90, O41. (C) 2001 Academic Press.