Constructing the CES Production Function Based on the Discrete Weibull Distribution
- Autores: Kokov V.V1, Sokolyanskiy V.V1
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Afiliações:
- Bauman Moscow State Technical University
- Edição: Nº 2 (2025)
- Páginas: 50-57
- Seção: Control in Social and Economic Systems
- URL: https://journal-vniispk.ru/1819-3161/article/view/351202
- ID: 351202
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Resumo
This paper considers a probabilistic approach to obtaining the CES production function. It consists in calculating the mean and median of the Leontief function (the quantity of output) as a random variable depending on the capacities of production factors, i.e., the ratios of the factors to their per-unit values. The type of the cumulative distribution function of the minimum from a set of independent random variables is substantiated. Explicit expressions are derived for the mean and median of the quantity of output as CES functions when the factor capacities have (continuous) Weibull distributions. Discretely distributed production factors are considered using the example of a geometric law. An attempt is made to derive the CES function when the factor capacities have discrete Weibull distributions. The difficulties arising in the analytical use of the mean of the Leontief function are described.
Sobre autores
V. Kokov
Bauman Moscow State Technical University
Autor responsável pela correspondência
Email: kokovvsevo@gmail.com
V. Sokolyanskiy
Bauman Moscow State Technical University
Email: sokolyansky63@mail.ru
Bibliografia
- Горбунов В.К. Производственные функции: теория и построение: учебное пособие. – Ульяновск: УлГУ, 2013. – 84 с. – URL: https://ulsu.ru/media/documents/13Горбунов_ПрФунк.pdf [Gorbunov, V.K. Proizvodstvennye funktsii: teoriya i postroenie: uchebnoe posobie. – Ulyanovsk: ULGU, 2013. – 84 s. – URL: https://ulsu.ru/media/documents/13Горбунов_ПрФунк.pdf (In Russian)]
- Jones, C.I. The Shape of Aggregate Production Functions and the Direction of Technical Change // Quarterly Journal of Economics. – 2005. – Vol. 120, no. 2. – P. 517–549.
- Growiec, J. Production Functions and Distributions of Unit Factor Productivities: Uncovering the Link // Economics Letters. – 2008. – Vol. 101, no. 1. – P. 87–90.
- Growiec, J. A Microfoundation for Normalized CES Production Functions with Factor-augmenting Technical Change // Journal of Economic Dynamics and Control. – 2013. – Vol. 37, no. 11. – P. 2336–2350.
- Матвеенко В.Д. «Анатомия» производственной функции: технологическое меню и выбор наилучшей технологии // Экономика и математические методы. – 2009. – T. 45, № 2. – С. 85–95. [Matveenko, V.D. “Anatomy” of the Production Function: Technological Menu and Selection of the Best Technology // Economics and Mathematical Methods. – 2009. – Vol. 45, no. 2. – P. 85–95. (In Russian)]
- Михеев А.В. Вероятностный подход к определению производственных функций // Вестник Астраханского государственного технического университета. Серия: Управление, вычислительная техника и информатика. – 2021. – № 4. – С. 82–94. [Mikheev, A.V. Probabilistic Approach to Determining Production Functions // Vestnik of Astrakhan State Technical University. Series: Management, Computer Science and Informatics. – 2021. – No. 4. – P. 82–94. (In Russian)]
- Математическая статистика: Учебник для вузов / В.Б. Горяинов, И.В. Павлов, Г.М. Цветкова и др.; под ред. В.С. Зарубина, А.П. Крищенко. – 3-е изд., исправл. – М.: Изд-во МГТУ им. Н.Э. Баумана, 2008. – 424 с. [Matematicheskaya statistika: Uchebnik dlya vuzov / V.B. Goryainov, I.V. Pavlov, G.M. Tsvetkova i dr.; pod red. V.S. Zarubina, A.P. Krishchenko. – 3-e izd., ispravl. – M.: Izd-vo MGTU im. N.Eh. Baumana, 2008. – 424 s. (In Russian)]
- Теория вероятностей: Учебник для вузов / В.А. Печинкин, О.И. Тескин, Г.М. Цветкова и др.; под ред. В.С. Зарубина, А.П. Крищенко. – М.: Изд-во МГТУ им. Н.Э. Баумана, 1998. – 456 с. [Teoriya veroyatnostei: Uchebnik dlya vuzov / V.A. Pechinkin, O.I. Teskin, G.M. Tsvetkova i dr.; pod red. V.S. Zarubina, A.P. Krishchenko. – M.: Izd-vo MGTU im. N.E. Baumana, 1998. – 456 s. (In Russian)]
- Rinne, H. The Weibull Distribution: A Handbook. – New York: Chapman and Hall/CRC, 2008. – 808 p.
- Barbiero, A. Discrete Weibull Distributions (Type 1 and 3) // The Comprehensive R Archive Network. – 2025. – URL: https://cran.r-project.org/web/packages/DiscreteWeibull/DiscreteWeibull.pdf.
- Woit, P. Fourier Analysis Notes, Spring 2020. – New York: Department of Mathematics, Columbia University, 2020. – 79 p. – URL: https://www.math.columbia.edu/~woit/fourier-analysis/fouriernotes.pdf.
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