Optimal Economic Growth Models with Nonlinear Utility Functions

Abstract

We study a class of finite horizon optimal economic growth problems with nonlinear utility functions and linear production functions. By using a maximum principle in the optimal control theory and employing the special structure of the problems, we are able to explicitly describe the unique solution via input parameters. Economic interpretations of the obtained results and an open problem about the case where the total factor productivity falls into a bounded open interval defined by the growth rate of labor force, the real interest rate, and the exponent of the utility function are also expressed.

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Notes

  1. 1.

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

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Acknowledgements

Vu Thi Huong and Nguyen Dong Yen were supported by the project “Some qualitative properties of optimization problems and dynamical systems, and applications” (Code: ICRTM01\(\_\)2020.08) of the International Center for Research and Postgraduate Training in Mathematics (ICRTM) under the auspices of UNESCO of Institute of Mathematics, Vietnam Academy of Science and Technology. Jen-Chih Yao was supported by China Medical University, Taichung, Taiwan. We are grateful to the five anonymous referees, whose detailed comments and significant suggestions have helped us to improve the presentation of the obtained results.

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Correspondence to Nguyen Dong Yen.

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Dedicated to Professor Pham Huu Sach on the occasion of his 80th birthday.

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Huong, V.T., Yao, JC. & Yen, N.D. Optimal Economic Growth Models with Nonlinear Utility Functions. J Optim Theory Appl 188, 571–596 (2021). https://doi.org/10.1007/s10957-020-01797-5

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Keywords

  • Optimal economic growth
  • Optimal control
  • Maximum principle

Mathematics Subject Classification

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