Production functions with given elasticities of output and production

  • Guennadi A. Khatskevich School of Business, Belarusian State University, 7 Špalernaja Street, Minsk 220004, Belarus
  • Andrei F. Pranevich Yanka Kupala State University of Grodno, 22 E. Ažeška Street, Grodno 230023, Belarus

Abstract

In this paper we consider inverse problems of identifying multi­factor production functions from given elasticity of output or from given elasticity of production. The analytical forms of multi­factor production functions with given elasticity of output or with given elasticity of production are indicated. Classes of two­factor production functions that correspond to given (constant, linear, linear­fractional, exponential, etc.) elasticity of output with respect to capital (elasticity of output with respect to labour) are obtained. The set of two­factor production functions with given (constant, linear, linear­fractional, exponential, etc.) elasticity of production is built. The obtained results can be applied in modeling of production processes. 

Author Biographies

Guennadi A. Khatskevich, School of Business, Belarusian State University, 7 Špalernaja Street, Minsk 220004, Belarus

doctor of science (economics), full professor; dean of the faculty of business

Andrei F. Pranevich, Yanka Kupala State University of Grodno, 22 E. Ažeška Street, Grodno 230023, Belarus

PhD (physics and mathematics), docent; associate professor at the department of mathematic and software support for economic systems, faculty of economics and management

References

  1. Humphrey TM. Algebraic production functions and their uses before Cobb – Douglas. Economic Quarterly. 1997;83/1:51– 83.
  2. Shephard RW. Theory of cost and production functions. Princeton: Princeton University Press; 1970.
  3. Kleiner GB. Proizvodstvennye funktsii: teoriya, metody, primenenie [Production functions: theory, methods, application]. Moscow: F inansy i statistika; 1986. 239 p.
  4. Gorbunov VK. Proizvodstvennye funktsii: teoriya i postroenie [Production functions: theory and construction]. Ulyanovsk: Ulyanovsk State University; 2013. 84 p.
  5. Barro RJ, Sala­i­Martin XX. Economic growth. New York: McGraw­Hill; 1995. 539 p.
  6. Cobb CW, Douglas PH. A theory of production. American Economic Review. 1928;18:139 –165.
  7. Douglas PH. The Cobb – Douglas production function once again: its history, its testing, and some new empirical values. Journal of Political Economy. 1976;84(5):903–916.
  8. Arrow KJ, Chenery HB, Minhas BS, Solow RM. Capital­labor substitution and economic eff iciency. The Review of Economics and Statistics. 1961;43(3):225–250. DOI: 10.2307/1927286.
  9. Uzawa H. Production functions with constant elasticities of substitution. The Review of Economic Studies. 1962;29(4):291–299. DOI: 10.2307/2296305.
  10. McFadden D. Constant elasticities of substitution production functions. Review of Economic Studies. 1963;30(2):73– 83. DOI: 10.2307/2295804.
  11. Khatskevich GA. [The change of consumer prices index based on the variable of elasticity of substitution]. Ekonomika i upravlenie [Economics and Management]. 2005;1:32–37. Russian.
  12. Gospodarik CG, Kovalev MM. EAES­2050: global’nye trendy I evraziiskaya ekonomicheskaya politika [EAEU­2050: global trends and the Eurasian economic policies]. Minsk: Belarusian State University; 2015. 152 p.
  13. Mishra SK. A brief history of production functions. IUP Journal of Managerial Economics. 2010;8(4):6 –34.
  14. Losonczi L. Production functions having the CES property. Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis. 2010;26(1):113–125.
  15. Chen B­Y. Classif ication of h­homogeneous production functions with constant elasticity of substitution. Tamkang Journal of Mathematics. 2012;43(2):321–328. DOI: 10.5556/j.tkjm.43.2012.321­328.
  16. Khatskevich GA, Pranevich AF. On quasi­homogeneous production functions with constant elasticity of factors substitution. Journal of the Belarusian State University. Economics. 2017;1:46 –50.
  17. Khatskevich GA, Pranevich AF. [Quasi­homogeneous production functions with unit elasticity of factors substitution by Hicks]. Ekonomika, modelirovanie, prognozirovanie [Economy, Simulation, Forecasting]. 2017;11:135–140. Russian.
  18. Ioan CA, Ioan G. A generalization of a class of production functions. Applied Economics Letters. 2011;18:1777–1784. DOI: 10.1080/13504851.2011.564117.
  19. Vilcu GE. On a generalization of a class of production functions. Applied Economics Letters. 2018;25(2):106–110. 20. Vilcu AD, Vilcu GE. On homogeneous production functions with proportional marginal rate of substitution. Mathematical Problems in Engineering. 2013. Article ID 732643. DOI: 10.1155/2013/732643.
  20. Vilcu AD, Vilcu GE. A survey on the geometry of production models in economics. Arab Journal of Mathematical Sciences. 2017;23(1):18–31.
  21. Il’in VA, Pozniak EG. Osnovy matematicheskogo analiza [Fundamentals of mathematical analysis]. Moscow: Nauka; 2000. 2 parts.
Published
2019-02-09
Keywords: production function, inverse problem, output elasticity, elasticity of production
Supporting Agencies This research was partially supported by Belarusian state program of scientif ic research «Economy and humanitarian development of the Belarusian society» (theme of the project «Development and application of econometric models for investment attractiveness, competitiveness and innovation of regions», No. A65­16).
How to Cite
Khatskevich, G. A., & Pranevich, A. F. (2019). Production functions with given elasticities of output and production. Journal of the Belarusian State University. Economics, 2, 13-21. Retrieved from https://journals.bsu.by/index.php/economy/article/view/2250
Issue
No 2 (2018): Journal of the Belarusian State University. Economics
Section
D. Microeconomics

Copyright (c) 2018 Journal of the Belarusian State University. Economics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The authors who are published in this journal agree to the following:

  1. The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
  2. The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
  3. The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)