Skiba Points for Small Discount Rates

The present article uses perturbation techniques to approximate the value function of an economic minimization problem for small values of the discount rate. This can be used to obtain the approximate location of the Skiba states in the problem; these are states for which there are two distinct optimal state trajectories, converging to different optimal steady states. It is shown that the sets of these indifference thresholds are locally smooth manifolds. For a simple example, all relevant quantities are computed explicitly. Moreover, the approximation can be used to obtain parameter-dependent approximations to the indifference manifolds.