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Optimal Exploitation of Renewable Resources: Lessons in Sustainability from an Optimal Growth Model of Natural Resource Consumption

In: Control Systems and Mathematical Methods in Economics

Author

Listed:
  • Sergey Aseev

    (Steklov Mathematical Institute of Russian Academy of Sciences
    International Institute for Applied Systems Analysis
    Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences)

  • Talha Manzoor

    (Lahore University of Management Sciences)

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).

Suggested Citation

  • Sergey Aseev & Talha Manzoor, 2018. "Optimal Exploitation of Renewable Resources: Lessons in Sustainability from an Optimal Growth Model of Natural Resource Consumption," Lecture Notes in Economics and Mathematical Systems, in: Gustav Feichtinger & Raimund M. Kovacevic & Gernot Tragler (ed.), Control Systems and Mathematical Methods in Economics, pages 221-245, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-75169-6_11
    DOI: 10.1007/978-3-319-75169-6_11
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