The Cobb-Douglas Production Function and the Old Bowley's Law
Bowley's law, also referred to as the law of the constant wage share, was a noteworthy empirical finding in economics, suggesting that a nation's wage share tended to remain stable over time, as observed through most of the 20th century. The wage share represents the proportion of a countr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212262 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Cobb-Douglas Production Function and the Old Bowley's Law. Roman G. Smirnov and Kunpeng Wang. SIGMA 20 (2024), 045, 20 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862697587016990720 |
|---|---|
| author | Smirnov, Roman G. Wang, Kunpeng |
| author_facet | Smirnov, Roman G. Wang, Kunpeng |
| citation_txt | The Cobb-Douglas Production Function and the Old Bowley's Law. Roman G. Smirnov and Kunpeng Wang. SIGMA 20 (2024), 045, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Bowley's law, also referred to as the law of the constant wage share, was a noteworthy empirical finding in economics, suggesting that a nation's wage share tended to remain stable over time, as observed through most of the 20th century. The wage share represents the proportion of a country's economic output that is distributed to employees as compensation for their labor, usually in the form of wages. The term ''Bowley's law'' was coined in 1964 by Paul Samuelson, the first American laureate of the Nobel Memorial Prize in economic sciences. He attributed this principle to Sir Arthur Bowley, an English economist, mathematician, and statistician. In this paper, we introduce a mathematical model derived from data for the American economy, originally employed by Cobb and Douglas in 1928 to validate the renowned Cobb-Douglas production function. We utilize symmetry methods, particularly those developed by Peter Olver, to elucidate the validity of Bowley's law within our model's framework. By employing these advanced mathematical techniques, our objective is to elucidate the factors contributing to the stability of the wage share over time. We demonstrate that the validity of both Bowley's law and the Cobb-Douglas production function arises from the robust growth of an economy, characterized by expansion in capital, labor, and production, which can be approximated by an exponential function. Through our analysis, we aim to offer valuable insights into the underlying mechanisms that support Bowley's law and its implications for comprehending income distribution patterns in economies.
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| first_indexed | 2026-03-18T08:56:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212262 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T08:56:49Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Smirnov, Roman G. Wang, Kunpeng 2026-02-03T07:57:05Z 2024 The Cobb-Douglas Production Function and the Old Bowley's Law. Roman G. Smirnov and Kunpeng Wang. SIGMA 20 (2024), 045, 20 pages 1815-0659 2020 Mathematics Subject Classification: 34C14; 37C79; 62P20; 91B39; 91B55; 91B62 arXiv:2308.02609 https://nasplib.isofts.kiev.ua/handle/123456789/212262 https://doi.org/10.3842/SIGMA.2024.045 Bowley's law, also referred to as the law of the constant wage share, was a noteworthy empirical finding in economics, suggesting that a nation's wage share tended to remain stable over time, as observed through most of the 20th century. The wage share represents the proportion of a country's economic output that is distributed to employees as compensation for their labor, usually in the form of wages. The term ''Bowley's law'' was coined in 1964 by Paul Samuelson, the first American laureate of the Nobel Memorial Prize in economic sciences. He attributed this principle to Sir Arthur Bowley, an English economist, mathematician, and statistician. In this paper, we introduce a mathematical model derived from data for the American economy, originally employed by Cobb and Douglas in 1928 to validate the renowned Cobb-Douglas production function. We utilize symmetry methods, particularly those developed by Peter Olver, to elucidate the validity of Bowley's law within our model's framework. By employing these advanced mathematical techniques, our objective is to elucidate the factors contributing to the stability of the wage share over time. We demonstrate that the validity of both Bowley's law and the Cobb-Douglas production function arises from the robust growth of an economy, characterized by expansion in capital, labor, and production, which can be approximated by an exponential function. Through our analysis, we aim to offer valuable insights into the underlying mechanisms that support Bowley's law and its implications for comprehending income distribution patterns in economies. The authors sincerely appreciate the invaluable mathematical knowledge they have acquired from Peter Olver, which has been instrumental in the development of this and other projects in the past. The first author (RGS) would like to offer special thanks to the organizers of the conference “Symmetry, Invariants, and their Applications: A Celebration of Peter Olver’s 70th Birthday” for extending an invitation to participate and present a talk. The conference provided an exceptional platform for engaging in stimulating discussions with fellow participants. Additionally, the authors express their gratitude to the anonymous referees for their valuable feedback, new references, insightful suggestions, and constructive critiques, all of which have significantly enhanced the quality of the presentation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Cobb-Douglas Production Function and the Old Bowley's Law Article published earlier |
| spellingShingle | The Cobb-Douglas Production Function and the Old Bowley's Law Smirnov, Roman G. Wang, Kunpeng |
| title | The Cobb-Douglas Production Function and the Old Bowley's Law |
| title_full | The Cobb-Douglas Production Function and the Old Bowley's Law |
| title_fullStr | The Cobb-Douglas Production Function and the Old Bowley's Law |
| title_full_unstemmed | The Cobb-Douglas Production Function and the Old Bowley's Law |
| title_short | The Cobb-Douglas Production Function and the Old Bowley's Law |
| title_sort | cobb-douglas production function and the old bowley's law |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212262 |
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