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

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 adm...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 304; no. 1; pp. 74 - 109
Main Authors Aseev, Sergey M., Besov, Konstantin O., Kaniovski, Serguei Yu
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 2019
Springer Nature B.V
Subjects
Capital depreciation
Control theory
Depletion
Depreciation
Economic development
Economic models
Elasticity
Growth models
Horizon
Mathematics
Mathematics and Statistics
Maximization
Maximum principle
Optimal control
Optimization
Policies
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Summary: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543819010061