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Stochastic technical change, non-renewable resource and optimal sustainable growth

Author

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  • Gilles Lafforgue

    (LERNA - Economie des Ressources Naturelles - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

Abstract

We develop a stochastic endogenous growth model involving a non-renewable resource, in which innovation arrivals are governed by a non-stationary Poisson process. Using a CRRA analytical example, we characterize the optimal trajectories of the model and analyze the effects of uncertainty in the sense of Rothschild and Stiglitz by computing a mean-preserving spread. We show that increased variability in the innovation process always implies a smaller optimal R&D effort, since this leads to a reduced marginal rate of return. Effects on the other variables of the model may also be unambiguously identified depending upon the relative risk aversion of agents, the social discount rate and the marginal arrival rate of innovations. Finally, we investigate the conditions under which, on average, the economy reaches a sustainable growth path.

Suggested Citation

  • Gilles Lafforgue, 2008. "Stochastic technical change, non-renewable resource and optimal sustainable growth," Post-Print hal-02667561, HAL.
    • Handle: RePEc:hal:journl:hal-02667561
    DOI: 10.1016/j.reseneeco.2008.07.001
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    Cited by:

    1. Elettra Agliardi, 2011. "Sustainability in Uncertain Economies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(1), pages 71-82, January.
    2. Le, Thanh & Le Van, Cuong, 2016. "Transitional dynamics in an R&D-based growth model with natural resources," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 1-17.
    3. Junhe Chen & Matt Davison, 2021. "Deterministic Asymmetric-cost Differential Games for Energy Production with Production Bounds," SN Operations Research Forum, Springer, vol. 2(4), pages 1-38, December.
    4. Voosholz, Frauke, 2014. "The influence of different production functions on modeling resource extraction and economic growth," CAWM Discussion Papers 72, University of Münster, Münster Center for Economic Policy (MEP).
    5. Bikourne, Mariem & Akdim, Khadija & Ez-Zetouni, Adil, 2025. "Stochastic analysis of an economic growth model incorporating Itô–Lévy driven investment, optimal control and numerical simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    6. Carretero-Gómez, Anselmo & Piedra-Muñoz, Laura, 2021. "Sustainability of non-renewable resources: the case of marble in Macael (Spain)," MPRA Paper 119917, University Library of Munich, Germany.
    7. Thanh Le & Cuong Le Van, 2014. "Natural Resources, R&D and Economic Growth," Working Papers 2014-112, Department of Research, Ipag Business School.
    8. Le, Thanh & Le Van, Cuong, 2018. "Research and development and sustainable growth over alternative types of natural resources," Economic Modelling, Elsevier, vol. 70(C), pages 215-229.
    9. Hooper, Emma, 2019. "Sustainable growth and financial markets in a natural resource-rich country," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 341-348.
    10. Julen Gonzalez-Redin & J Gareth Polhill & Terence P Dawson & Rosemary Hill & Iain J Gordon, 2018. "It's not the 'what', but the 'how': Exploring the role of debt in natural resource (un)sustainability," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-19, July.
    11. Figueroa, Adolfo, 2013. "Economic growth and the environment," Revista CEPAL, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL), April.
    12. Julen Gonzalez-Redin & Iain J. Gordon & J. Gareth Polhill & Terence P. Dawson & Rosemary Hill, 2024. "Navigating Sustainability: Revealing Hidden Forces in Social–Ecological Systems," Sustainability, MDPI, vol. 16(3), pages 1-23, January.
    13. Ludkovski, Michael & Sircar, Ronnie, 2016. "Technology ladders and R&D in dynamic Cournot markets," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 127-151.

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