The present value of resources with large discount rates

The present value of resources with large discount rates This paper describes a method to detect limit cycles for optimal control problems in the plain. The procedure includes two steps. First, the solution paths are analytically studied for large discount rates. Second, we demonstrate by means of computer simulations how the dynamics found can be traced back to small discount rates. We apply this method to two specific examples from resource management: a taxation problem and an exploited system of predator-prey interaction which show that the limit cycles may grow as the discount rates decrease. The principle that small discount rates are more conservative than large ones is therefore questionable. The relation of our results to theorems in optimal growth theory is also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

The present value of resources with large discount rates

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683332
Publisher site
See Article on Publisher Site

Abstract

This paper describes a method to detect limit cycles for optimal control problems in the plain. The procedure includes two steps. First, the solution paths are analytically studied for large discount rates. Second, we demonstrate by means of computer simulations how the dynamics found can be traced back to small discount rates. We apply this method to two specific examples from resource management: a taxation problem and an exploited system of predator-prey interaction which show that the limit cycles may grow as the discount rates decrease. The principle that small discount rates are more conservative than large ones is therefore questionable. The relation of our results to theorems in optimal growth theory is also discussed.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: May 1, 1997

References

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