Optimal economic growth problems with high values of total factor productivity

ABSTRACT

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: https://doi.org/10.11650/tjm/200203] 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.

Keywords:

• Optimal economic growth
• optimal control
• maximum principle
• finite horizon
• total factor productivity

2010 Mathematics Subject Classifications:

• 91B62
• 49J15
• 37N40
• 46N10
• 91B55

Acknowledgments

This work was supported by National Foundation for Science $\mathrm{\&}$ Technology Development (Vietnam) under grant number 101.01-2018.308. The author would like to thank Professor Nguyen Dong Yen and the anonymous referee for their insightful comments and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 See, e.g. https://en.wikipedia.org/wiki/Total_factor_productivity.

Additional information

Funding

This work was supported by National Foundation for Science & Technology Development (Vietnam) [grant number 101.01-2018.308].