A DNS-curve in a two-state capital accumulation model: a numerical analysis

In this paper we study a capital accumulation model in an optimal control theoretic framework, where the capital stock and the investment rate are modelled as state variables and the change in the investment rate as control. Adjustment costs are introduced for investment rate and its change. 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 other 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, for which it holds that, when starting from a point on this curve, the decision maker is indifferent between going to either one of these steady-states, and identify this curve as the DNS-curve. The negative slope of the DNS-curve indicates that there is a trade-off between the initial capital endowment and initial investment rate. (C) 2002 Elsevier Science B.V. All rights reserved.