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We prove that if the total factor productivity A of an aggregative economy is right at the barrier $ \sigma +\lambda $ σ + λ , with σ being the growth rate of labor force and λ the real interest rate, then the unique policy to optimally control the economy is the same as the one for optimally controlling weak economies, where $ A \lt \sigma +\lambda $ A < σ + λ. This result gives a complete answer for the interesting open question raised by Vu Thi Huong in her recent paper [Optimal economic growth problems with high values of total factor productivity. Appl Anal. 2022;101:1315–1329]. [ABSTRACT FROM AUTHOR]

The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control problems from the monograph of Cesari L. [Optimization theory and applications. New York: Springer-Verlag; 1983]. Our results are obtained not only for general problems but also for typical ones, where the production function is given by either the AK function or the Cobb–Douglas one, while the utility function can be in a linear or power form. Some open questions and conjectures about the regularity of global solutions of finite horizon optimal economic growth problems are formulated in this paper. [ABSTRACT FROM AUTHOR]

This paper solves a question raised in the paper of Huong, Yao, and Yen [Optimal processes in a parametric optimal economic growth model. Taiwanese J Math. 2020. Available from: ] about optimal economic growth problems with production functions and utility functions being all in the form of AK functions. By using a solution existence theorem from the paper of Huong [Solution existence theorems for finite horizon optimal economic growth problems. Preprint arXiv:2001.03298v2. Submitted] and a maximum principle from the book of Vinter [Optimal control. Boston (MA): Birkhäuser; 2000], we prove that the problem in question has a unique solution and give a comprehensive synthesis of the optimal processes. Our results show that if the value of total factor productivity is enough high and the planning time is short, then expanding the production facility does not lead to a higher total consumption satisfaction of the society. Meanwhile, if the value of total factor productivity is enough high and the planning time is relatively long, then the highest total consumption satisfaction of the society is attained only if the largest expansion of the production facility is made until a special time. [ABSTRACT FROM AUTHOR]

In this article, a maximum principle for finite horizon state-constrained problems is analyzed via parametric examples. These parametric examples resemble typical optimal growth problems in mathematical economics. Since the maximum principle is only a necessary condition for local optimal processes, a large amount of additional investigations are needed to obtain a comprehensive synthesis of finitely many processes suspected for being local minimizers. Our analysis not only helps to understand the principle in depth, but also serves as a sample of applying it to meaningful prototypes of optimal economic growth models. Problems with unilateral state constraints have been studied in Part 1 of the article. Problems with bilateral state constraints are addressed in this Part 2. [ABSTRACT FROM AUTHOR]