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Tr. Mat. Inst. Steklova, 2019, Volume 304, Pages 83–122 (Mi tm3985)  

Optimal Policies in the Dasgupta–Heal–Solow–Stiglitz Model under Nonconstant Returns to Scale

S. M. Aseevab, K. O. Besova, S. Yu. Kaniovskic

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria
c Austrian Institute of Economic Research (WIFO), Arsenal, Objekt 20, 1030 Vienna, Austria

Abstract: The paper offers a complete mathematically rigorous analysis of the welfare-maximizing capital investment and resource depletion policies in the Dasgupta–Heal–Solow–Stiglitz model with capital depreciation and any returns to scale. We establish a general existence result and show that an optimal admissible policy may not exist if the output elasticity of the resource equals one. We characterize the optimal policies by applying an appropriate version of the Pontryagin maximum principle for infinite-horizon optimal control problems. We also discuss general methodological pitfalls arising in infinite-horizon optimal control problems for economic growth models, which are not paid due attention in the economic literature so that the results presented there often seem not to be rigorously justified. We finish the paper with an economic interpretation and a discussion of the welfare-maximizing policies.

DOI: https://doi.org/10.4213/tm3985

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 304, 74–109

Bibliographic databases:

Document Type: Article
UDC: 517.977.5
MSC: 49K15, 49K45, 91B62
Received: December 20, 2018
Revised: March 3, 2019
Accepted: March 3, 2019

Citation: S. M. Aseev, K. O. Besov, S. Yu. Kaniovski, “Optimal Policies in the Dasgupta–Heal–Solow–Stiglitz Model under Nonconstant Returns to Scale”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 83–122; Proc. Steklov Inst. Math., 304 (2019), 74–109

Citation in format AMSBIB
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\by S.~M.~Aseev, K.~O.~Besov, S.~Yu.~Kaniovski
\paper Optimal Policies in the Dasgupta--Heal--Solow--Stiglitz Model under Nonconstant Returns to Scale
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 83--122
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3985}
\crossref{https://doi.org/10.4213/tm3985}
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\jour Proc. Steklov Inst. Math.
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\vol 304
\pages 74--109
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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