Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems

Abstract 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, which 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 restrictions that would allow analysis by a bifurcation diagram. The results are illustrated by two well-known examples in this literature, due to Sutherland and Weitzman–Samuelson. Journal of Economic Literature Classification Numbers: C61, D90, 041.

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