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

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  • Haunschmied, J.L., Kort, P.M., Hartl, R.F., Feichtinger, G.

Abstract

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.

Suggested Citation

  • Haunschmied, J.L., Kort, P.M., Hartl, R.F., Feichtinger, G., 2001. "A numerically computed DNS-curve in a two state capital accumulation model," Computing in Economics and Finance 2001 103, Society for Computational Economics.
    • Handle: RePEc:sce:scecf1:103
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    More about this item

    Keywords

    multiple equilibria; invariant stable manifolds; discontinous feedback rule; capital accumulation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing

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