A numerically computed DNS-curve in a two state capital accumulation model.

In this paper we study a capital accumulation model in an optimal control theoretic framework, where the capital stock and the investment rate are modeled as state variables and the change in the investment rate as control. Adjustment costs are introduced for both investment rate and the change in the investment rate. Moreover, we model network externalities by a convex segment in the revenue function, which implies the existence of two long-run optimal steady states, one with a low level and the another with a high level capital stock. It depends on the initial capital endowment and initial investment rate to which steady state it is optimal to converge. We numerically compute a curve in the state plane, starting from which the decision-maker is indifferent between converging to one of these steady states, and identify this curve by DNS-curve; its negative slope shows that there is a trade-off between initial capital endowment and initial investment rate.