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.
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Acknowledgements
The authors are grateful to Associate Editor Prof. David G. Luenberger and to three anonymous reviewers for valuable comments. This paper was partially written when N. Hritonenko and Y. Yatsenko visited Aix-Marseille Université, and the authors are grateful to AMSE for the financial support of this visit. R. Boucekkine acknowledges the financial support of the Belgian research programme ARC grant 09/14-08. N. Hritonenko appreciates the support of NSF DMS 1009197.
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Communicated by David G. Luenberger.
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Boucekkine, R., Hritonenko, N. & Yatsenko, Y. Optimal Investment in Heterogeneous Capital and Technology Under Restricted Natural Resource. J Optim Theory Appl 163, 310–331 (2014). https://doi.org/10.1007/s10957-013-0453-y
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DOI: https://doi.org/10.1007/s10957-013-0453-y