Limit cycles in intertemporal adjustment models: Theory and applications

This paper starts from well-behaved (i.e., concave) one-state-variable optimal control models. The crucial feature is that indigenous growth is present. The replacement of the control by an adjustment process and presumably penalizing these adjustments may convert stable (and only stable) fixed point equilibria into limit cycles. Indeed, given positive growth and proper externalities (such that discounting exceeds growth), one can generate stable limit cycles with ease, e.g., for a separable framework. Examples from such diverse fields as renewable resources, optimal saving and public choice highlight the economic applicability.

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