Solution to an open question about optimal economic growth models

Abstract

We prove that if the total factor productivity A of an aggregative economy is right at the barrier $\sigma +\lambda$, 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 $A<\sigma +\lambda$. 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].

Keywords:

• Economic growth model
• optimal control
• maximum principle
• bang–bang control
• singular control

2010 Mathematics Subject Classifications:

• 49K15
• 49J15

Acknowledgments

The authors would like to thank the two anonymous referees for their valuable comments and suggestions on the earlier version of the present paper. The research of Nguyen Dong Yen was supported by Vietnam Academy of Science and Technology under the project number CTTH00.01/22-23.

Disclosure statement

No potential conflict of interest was reported by the author(s).