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Optimal Exploitation of Renewable Resources: Lessons in Sustainability from an Optimal Growth Model of Natural Resource Consumption
- Source :
- Lecture Notes in Economics and Mathematical Systems ISBN: 9783319751689
- Publication Year :
- 2018
- Publisher :
- Springer International Publishing, 2018.
-
Abstract
- We study an optimal growth model for a single resource based economy. The resource is governed by the standard model of logistic growth, and is related to the output of the economy through a Cobb-Douglas type production function with exogenously driven knowledge stock. The model is formulated as an infinite-horizon optimal control problem with unbounded set of control constraints and non-concave Hamiltonian. We transform the original problem to an equivalent one with simplified dynamics and prove the existence of an optimal admissible control. Then we characterize the optimal paths for all possible parameter values and initial states by applying the appropriate version of the Pontryagin maximum principle. Our main finding is that only two qualitatively different types of behavior of sustainable optimal paths are possible depending on whether the resource growth rate is higher than the social discount rate or not. An analysis of these behaviors yields general criterions for sustainable and strongly sustainable optimal growth (w.r.t. the corresponding notions of sustainability defined herein).
- Subjects :
- Mathematical optimization
010102 general mathematics
Optimal control
01 natural sciences
Natural resource
0103 physical sciences
Sustainability
010307 mathematical physics
Social discount rate
0101 mathematics
Logistic function
Resource-based economy
Hamiltonian (control theory)
Mathematics
Renewable resource
Subjects
Details
- ISBN :
- 978-3-319-75168-9
- ISBNs :
- 9783319751689
- Database :
- OpenAIRE
- Journal :
- Lecture Notes in Economics and Mathematical Systems ISBN: 9783319751689
- Accession number :
- edsair.doi...........9e1032cad4b2c866af476976c5b8d7c7