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Optimal Investment in Heterogeneous Capital and Technology Under Restricted Natural Resource

Author

Listed:
  • Raouf Boucekkine

    (School of Economics, CNRS and EHESS
    UCLouvain)

  • Natali Hritonenko

    (Prairie View A&M University)

  • Yuri Yatsenko

    (Houston Baptist University)

Abstract

We consider the optimal control of nonlinear integral equations with endogenous delay and state constraints, which describe a developing economy subjected to resource constraints. The economy invests in new resource-efficient technologies, invests in new capital, and scraps obsolete capital. We derive the optimality condition and determine long-term asymptotically exponential trajectories that optimally combine scrapping the dirtiest capital and developing new clean technologies. Next, we study the short-term dynamics of the model and show that it leads to a sustainable growth with active resource constraint.

Suggested Citation

  • Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, 2014. "Optimal Investment in Heterogeneous Capital and Technology Under Restricted Natural Resource," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 310-331, October.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:1:d:10.1007_s10957-013-0453-y
    DOI: 10.1007/s10957-013-0453-y
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Hritonenko, Natali & Yatsenko, Yuri, 2011. "Scarcity, regulation and endogenous technical progress," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 186-199, March.
    2. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    3. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 1998. "Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-384, December.
    4. Segerstrom, Paul S, 2000. "The Long-Run Growth Effects of R&D Subsidies," Journal of Economic Growth, Springer, vol. 5(3), pages 277-305, September.
    5. R. M. Solow & J. Tobin & C. C. Weizsäcker & M. Yaari, 1971. "Neoclassical Growth with Fixed Factor Proportions," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 9, pages 68-102, Palgrave Macmillan.
    6. Hart, Rob, 2004. "Growth, environment and innovation--a model with production vintages and environmentally oriented research," Journal of Environmental Economics and Management, Elsevier, vol. 48(3), pages 1078-1098, November.
    7. Daniel J. Wilson, 2002. "Is Embodied Technology the Result of Upstream R&D? Industry-Level Evidence," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 5(2), pages 285-317, April.
    8. Boyan Jovanovic, 2009. "The Technology Cycle and Inequality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(2), pages 707-729.
    9. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 71-102, October.
    10. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    11. YATSENKO, Yuri & BOUCEKKINE, Raouf & HRITONENKO, Natali, 2009. "On explosive dynamics in R&D-based models of endogenous growth," LIDAM Reprints CORE 2205, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Citations

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    Cited by:

    1. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, 2017. "Technological Progress, Employment and the Lifetime of Capital," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 305-337, Springer.
    2. Natali Hritonenko & Nobuyuki Kato & Yuri Yatsenko, 2017. "Optimal Control of Investments in Old and New Capital Under Improving Technology," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 247-266, January.
    3. Raouf Boucekkine & Blanca Martinez & Ramon Ruiz-Tamarit, 2013. "Optimal Sustainable Policies under Pollution Ceiling: The Demographic Side," AMSE Working Papers 1354, Aix-Marseille School of Economics, France, revised 04 Nov 2013.
    4. Yatsenko, Yuri & Hritonenko, Natali, 2020. "Optimal asset replacement: Profit maximization under varying technology," International Journal of Production Economics, Elsevier, vol. 228(C).
    5. Aznar-Márquez, J. & Ruiz-Tamarit, J.R., 2017. "Sustainable growth and environmental catastrophes," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 83-91.
    6. Raouf Boucekkine & Fouad Ouardighi & Konstantin Kogan, 2025. "Recycling of Multi-source Waste in an Aggregate Circular Economy," Lecture Notes in Operations Research,, Springer.
    7. Natali Hritonenko & Yuri Yatsenko, 2024. "Analysis of optimal lockdown in integral economic–epidemic model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 235-259, February.

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