Optimal growth under discounting in the two-sector Robinson-Solow-Srinivasan model: a dynamic programming approach

摘要

We use a version of a two-sector model to provide a strong form of a "folk-theorem" on the existence of a threshold discount factor such that: (i) for discount factors above this threshold value, optimal behavior is qualitatively similar to that in the corresponding undiscounted optimization problem, (ii) for discount factors below this threshold value, optimal behavior is qualitatively different from that in the undiscounted case. In the process, we provide an explicit solution of a non-linear optimal policy function for all discount factors above the threshold value. Our bifurcation analysis is conducted by using the dynamic programming approach, and we exploit the convex structure of our model to develop a variation of the standard method in dynamic programming used to identify the optimal policy correspondence.