A parametric finite horizon optimal economic growth problem is solved by using the maximum principle for optimal control problems with state constraints in the book by R. Vinter [Optimal Control, Birkhäuser, Boston, 2000; Theorem 9.3.1]. From the obtained results it follows that if the total factor productivity is relatively small, then the expansion of the production facility does not lead to a higher total consumption satisfaction of the society.
"Optimal Processes in a Parametric Optimal Economic Growth Model." Taiwanese J. Math. 24 (5) 1283 - 1306, October, 2020. https://doi.org/10.11650/tjm/200203