Abstract
We study optimal research and extraction policies in an endogenous growth model in which both production and research require an exhaustible resource. It is shown that optimal growth is not sustainable if the accumulation of knowledge depends on the resource as an input, or if the returns to scale in research are decreasing, or the economy is too small. The model is stated as an infinite-horizon optimal control problem with an integral constraint on the control variables. We consider the main mathematical aspects of the problem, establish an existence theorem and derive an appropriate version of the Pontryagin maximum principle. A complete characterization of the optimal transitional dynamics is given.
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Notes
- 1.
Of course, the upper bound for ε that guarantees the validity of this statement depends on x 0, but x 0 is fixed from the onset.
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Acknowledgements
The research was supported by the Austrian National Bank (OeNB) (Jubiläumsfonds project no. 13585) and the Russian Foundation for Basic Research (projects nos. 10-01-91004-ASF-a and 11-01-12112-ofi-m-2011). The authors would like to thank Arkady Kryazhimskiy, Tapio Palokangas, Gerald Silverberg, and the participants of the Green Growth and Sustainable Development symposium at IIASA for valuable comments and suggestions.
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Aseev, S., Besov, K., Kaniovski, S. (2013). The Problem of Optimal Endogenous Growth with Exhaustible Resources Revisited. In: Crespo Cuaresma, J., Palokangas, T., Tarasyev, A. (eds) Green Growth and Sustainable Development. Dynamic Modeling and Econometrics in Economics and Finance, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34354-4_1
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