Impatience and dynamic optimal behavior: A bifurcation analysis of the Robinson–Solow–Srinivasan model

This paper provides a study of optimal economic growth under discounting in discrete time in a two-sector version of the Robinson–Solow–Srinivasan model. It examines how dynamic optimal behavior changes in response to increasing impatience. The optimal policy function is a pan map for high discount factors and a check map for low discount factors. It is shown that the transformation from the pan map to the check map, for the intermediate range of discount factors, can be quite intricate. This is demonstrated by proving the existence of two bifurcation values of the discount factor in the borderline case of the model, which establishes the possibility of reswitching of optimal actions as the discount factor varies.