A DNS-curve in a two-state capital accumulation model: A numerical analysis
type: Item
instance of: scholarly article
title: A DNS-curve in a two-state capital accumulation model: A numerical analysis
zbMATH Open document ID: 1029.91029
DOI: 10.1016/S0165-1889(01)00070-7
author: Josef L. Haunschmied
author: Peter M. Kort
author: Richard F. Hartl
author: Gustav Feichtinger
publication date: 2003-01-21T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 1856538
zbMATH Keywords: capital accumulation
zbMATH Keywords: optimal control
zbMATH Keywords: network externalities
zbMATH Keywords: optimal steady-states
zbMATH Keywords: DNS-curve
Wikidata QID: Q59389823
MaRDI profile type: Publication
cites work: Non-Convexities in Continuous-Time Investment Theory
cites work: A complete characterization of optimal growth paths in an aggregated model with a non-concave production function
cites work: Limit cycles in intertemporal adjustment models
cites work: Adjustment Costs in the Theory of Investment of the Firm
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Optimal dynamic investment policies under concave-convex adjustment costs
cites work: A Two-Sector Model of Endogenous Growth with Leisure
cites work: On the Transversality Condition in Infinite Horizon Optimal Problems
cites work: Optimal Growth with a Convex-Concave Production Function
published in: Journal of Economic Dynamics and Control
description: scientific article; zbMATH DE number 1856538