The present value of resources with large discount rates
- 62 Downloads
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.
Key WordsOptimal control Variation of discount rates Limit cycles Resource management Conservation of resources
Unable to display preview. Download preview PDF.
- 6.C.W. Clark (1976), Mathematical Bioeconomics; The Optimal Management of Renewable Resources, New York: Wiley.Google Scholar
- 7.C.W. Clark (1985), Bioeconomic Modelling and Fishery Management, New York: Wiley-Interscience.Google Scholar
- 8.C.W. Clark (1990), Mathematical Bioeconomics; The Optimal Management of Renewable Resources, second edition, New York: Wiley.Google Scholar
- 9.F. Clarke (1983), Optimization and Non-Smooth Analysis, New York: Wiley-Interscience.Google Scholar
- 12.G. Feichtinger, V. Kaitala, A. Novak (1991), Stable Resource Employment and Limit Cycles in an Optimally Regulated Fishery, University of Technology, Vienna.Google Scholar
- 16.M. Rauscher (1990), Environmental Resources by an Indebted Country, Journal of Institutional and Theoretical Economics, 146:500–517.Google Scholar
- 20.M. Sieveking (1991), Stability of Limit Cycles, Preprint, University of Frankfurt.Google Scholar