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Reiner Kümmel
Reiner Kümmel in March 2005, photographed by Thomas Obermeier
Born	1939-07-09 Fulda, Germany
Alma mater	TH Darmstadt, Goethe Universität Frankfurt
Known for	LINEX-function for exogenous growth model
Scientific career
Fields	physics & economics
Institutions	Universidad del Valle, University of Würzburg
Thesis	A: Schichtdicken-abhängiger Quantisierungseffekt in Tunnelkontakten : B: Untersuchungen zum Zwischenzustand und gemischten Zustand von Supraleitern 1. und 2. Art (1968)
Doctoral advisor	Peter Fulde
Other academic advisors	John Bardeen

Reiner Kümmel (born 9 July 1939 in Fulda) is a German physicist specialised in solid-state physics, thermodynamics and econophysics.

Scientific career

Reiner Kümmel studied physics and mathematics at TH Darmstadt from 1959 to 1964. He received a scholarship from the Cusanuswerk and completed his doctorate on superconductivity at Frankfurt University in 1968, where he also habilitated in theoretical physics in 1973. During his doctorate and habilitation, he also conducted research abroad, such as from 1965 to 1967 as a research assistant under the two-time Nobel Prize winner in physics John Bardeen at the University of Illinois at Urbana-Champaign. From 1970 to 1972, he worked in Colombia at the Universidad del Valle in Cali, where he helped to set up a master's programme in physics on a DAAD scholarship, which served to develop the next generation of academics. During this time, he focussed on thermodynamics.

In 1974, he took up a professorship for theoretical physics in Würzburg, which was also characterised by numerous research visits abroad. In the 1970s, the time of the first and second oil price shocks, his interest in economics as a second mainstay began to grow. A lively exchange developed with Wolfgang Eichhorn, who worked as an economist (and mathematician) at the Faculty of Economics at the University of Karlsruhe. His research in physics focussed on the theory of inhomogeneous superconductors and mesoscopic heterocontacts. His economic interests focussed on energy use and emission reduction. From 1996 to 1998, Reiner Kümmel chaired the Energy Working Group of the German Physical Society. He retired in October 2004. Nevertheless, he remained associated with the university with a teaching assignment for the lecture Thermodynamics and Economics until the summer semester 2015.

Work

Kümmel's work on economics intends to improve the mathematical structure of macroeconomic growth models, so that they don't contradict the findings of applied physics, in particular the first and second laws of thermodynamics. Also he identified energy as a powerful factor of production and the dominant component of technological progress. To address these issues amongst others, he developed the so called LINEX function, which depends linearly on energy and exponentially on quotients of capital, labor, and energy.

The LINEX production function, that satisfies the Euler condition (constant returns), is constructed through partial integration of simple mathematical forms for the three marginal productivities of capital, labour and energy, based on plausible assumptions about asymptotic behavior. The LINEX function does not imply (as does the Cobb–Douglas function) that the three factors are all strict substitutes for each other in the sense that more of one factor implies less of the other, or conversely. On the contrary, it implies a more complex and more realistic physical substitution–complement relationship among the variables. The function does not rely on the "cost-share theorem" applied in standard economic theory, that assumes the marginal productivity of capital, labour and energy are equal to their cost-share in the national accounts, which implies that capital and labour are the main factors of production. The parameters of the function are fitted using statistical methods and non-constant (time dependent) marginal productivities of capital, labour and energy can be generated from the fit. Kümmel, and collegue Dietmar Lindenberger first fit the LINEX function using electricity as a proxy for the useful work from energy inputs. The resulting fits were able reproduce observed historical economic growth without assumptions of exogenous and unexplained technological progress. In subsequent work, inspired and informed by Kümmel's findings, Robert Ayres and Benjamin Warr replaced electricity in the function with the useful work from exergy inputs to the US economy (for the period 1900 to 2000) to the LINEX production function to similar effect.

With the use of useful work as input factor, the unexplained growth the "Solow Residual" from Solow's growth model, which is often attributed to exogenous technological progress or total factor productivity, is minimised. Consequently, so called technological progress in neoclassical models can be explained, in large part, as the ability of mankind to integrate increasing energy flows into the economic process and to transform it with high efficiency into useful work. It then follows that energy's economic weight is much larger than it's cost share, and that energy is a powerful factor of production and a dominant component of "technological progress". As Kümmel states "we owe a substantial part of our material wealth to energy conversion in the machines of the capital stock".

In his book The Second Law of Economics, he discusses the influence of energy conservation and entropy on prosperity and adds to the production theory of economics the important scientific component of energy, without which a modern economy cannot be understood. He calls for energy taxes to alleviate the pressure to grow, based on the much higher production elasticity of energy than labour.

Publications

• Reiner Kümmel, Dietmar Lindenberger: Energy, Entropy, Constraints, and Creativity in Economic Growth and Crises. In: Entropy. Band 22, Nr. 10, 14. Oktober 2020, ISSN 1099-4300, 1156. 
• Reiner Kümmel, Dietmar Lindenberger, Florian Weiser: The economic power of energy and the need to integrate it with energy policy. In: Energy Policy 86 (2015), 833–843.
• Reiner Kümmel, Dietmar Lindenberger: How energy conversion drives economic growth far from the equilibrium of neoclassical economics. In: New Journal of Physics 16, Dec. 2014, 125008.
• Reiner Kümmel: Why energy's economic weight is much larger than its cost share In: Environmental Innovation and Societal Transitions 9, Dec. 2013.
• Reiner Kümmel: The Second Law of Economics: Energy, Entropy, and the Origins of Wealth. Springer, Berlin 2011, ISBN 978-1-4419-9364-9. 
• Reiner Kümmel, Robert U. Ayres, Dietmar Lindenberger: Thermodynamic laws, economic methods and the productive power of energy. In: Journal of Non-Equilibrium Thermodynamics, Vol. 35, No. 2, 2010, pp. 145–179.
• Arne Jacobs, Reiner Kümmel: Dynamics of conversion of supercurrents into normal currents and vice versa. In: Phys. Rev. B, Vol. 64, No. 10, 2001.

See also

• The Entropy Law and the Economic Process
• Ecological economics
• Robert Ayres

References

1. ^ Kümmel, Reiner (1968). A: Schichtdicken-abhängiger Quantisierungseffekt in Tunnelkontakten – B: Untersuchungen zum Zwischenzustand und gemischten Zustand von Supraleitern 1. und 2. Art [A: Layer thickness dependent quantisation effect in tunnel contacts – B: Investigations on the intermediate state and mixed state of superconductors of the 1st and 2nd kind] (Thesis) (in German). Frankfurt am Main: Goethe-Universität Frankfurt. Retrieved 2025-01-10.
2. ^ "Prof. Dr. Reiner Kümmel". Universität Würzburg. 2013-10-09. Archived from the original on 9 January 2014. Retrieved 2025-01-10.
3. Dash, Kishore C. (2014). "14 Evolution of Econophysics". In Abergel, Frédéric; Aoyama, Hideaki; Chakrabarti, Bikas K.; Chakraborti, Anirban; Ghosh, Asim (eds.). Econophysics of Agent-Based Models. New Economic Windows. Cham: Springer International Publishing. p. 261. doi:10.1007/978-3-319-00023-7. ISBN 978-3-319-00022-0. Retrieved 2025-01-15. Reiner Kümmel
4. Kümmel, Reiner; Landwehr, Gottfried (1991). "In memoriam John Bardeen". Physikalische Blätter. 47 (5). Wiley-VCH: 399–400. doi:10.1002/phbl.19910470512.
5. Kümmel, Reiner; Strassl, Wolfgang; Gossner, Alfred; Eichhorn, Wolfgang (1985). "Technical progress and energy dependent production functions Articles". Journal of Economics. 45. Springer: 285–311. doi:10.1007/BF01282565. Retrieved 2025-01-11.
6. Kümmel, Reiner. "Welcome to the pages of Prof. Dr. Reiner Kümmel". Fakultät für Physik und Astronomie, Universität Würzburg. Retrieved 2025-01-10.
7. "Arbeitskreis Energie (AKE)". www.dpg-physik.de. Bad Honnef: Deutsche Physikalische Gesellschaft. 2024-05-15. Retrieved 2025-01-10. Vorsitzende seit Gründung des Arbeitskreises
8. Kümmel, Reiner (2007-03-24). Energie und Wirtschaftswachstum oder: Wie Arbeitslosigkeit und Umweltbelastungen vermindert werden können [Energy and economic growth or: How unemployment and environmental harm can be reduced] (PDF) (in German). Würzburg: Würzburg University.
9. "Sommersemester 2015 – Thermodynamik und Ökonomie: Energie und Wirtschaftswachstum, Entropieproduktion und Emissionsminderung". Würzburg: Würzburg University, Department of Physics. 2015-04-14. Retrieved 2025-01-10.
10. Hall, Charles; Lindenberger, Dietmar; Kümmel, Reiner; Kroeger, Timm; Eichhorn, Wolfgang (2001-08-01). "The Need to Reintegrate the Natural Sciences with Economics" (PDF). BioScience. 51 (8). Oxford University Press: 663–673. doi:10.1641/0006-3568(2001)051[0663:TNTRTN]2.0.CO;2. Retrieved 2025-01-13. p. 664: Past criticisms of neoclassical economics from the perspective of natural scientists can be summarized as three fundamental arguments: (1) The structure of the basic conceptual neoclassical model is unrealistic because it is not based on the biophysical world and the laws governing it, especially thermodynamics (Figure la); (2) the boundaries of analysis are inappropriate because they do not include the real processes of the biosphere that provide the material and energy inputs, the waste sinks, and the necessary milieu for the economic process (Figure 2); and (3) the basic assumptions underlying the models used have not been put forth as testable hypotheses but rather as givens.
11. ^ Lindenberger, Dietmar; Kümmel, Reiner (2002). "Energy-Dependent Production Functions and the Optimization Model "PRISE" of Price-Induced Sectoral Evolution". International Journal of Thermodynamics. S2CID 67765773.
12. Ayres, Robert U.; Warr, Benjamin (2005-06-01). "Accounting for growth: the role of physical work". Structural Change and Economic Dynamics. Contains the special issue Approaches to Production Theory. 16 (2): 181–209. doi:10.1016/j.strueco.2003.10.003. ISSN 0954-349X.
13. Ayres, Robert U.; van den Bergh, Jeroen C. J. M.; Lindenberger, Dietmar; Warr, Benjamin (2013-12-01). "The underestimated contribution of energy to economic growth". Structural Change and Economic Dynamics. 27: 79–88. doi:10.1016/j.strueco.2013.07.004. ISSN 0954-349X.
14. Rifkin, Jeremy (2014). The Zero Marginal Cost Society – The Internet of Things, the Collaborative Commons, and the Eclipse of Capitalism. New York, NY: Palgrave Macmillan. p. 72. ISBN 978-1137278463. Retrieved 2025-01-14. Over the past 25 years, a number of analysts, including physicist Reiner Kümmel of the University of Würzburg, Germany, and economist Robert Ayres at INSEAD business school in Fontainebleau, France, have gone back and retraced the economic growth of the industrial period using a three-factor analysis of machine capital, labor performance, and thermodynamic efficiency of energy use. In other words, 'energy' is the missing factor.
15. Homer-Dixon, Thomas; Garrison, Nick (2009). "Introduction". In Homer-Dixon, Thomas (ed.). Carbon shift - How the twin crises of oil depletion and climate change will define the future. foreword by Ronald Wright. Canada: Random House. p. 6-7. ISBN 978-0-307-35718-2. Retrieved 2025-01-15. Often overlooked was the role of energy in economic growth. Growth was invariably much higher than he predicted, and the difference – that proportion of output growth that could not be explained by the measured inputs – came to be called the 'Solow residual.' But as economist Reiner Kümmel later pointed out, this residual often explains more than Solow's thery itself. After Solow's work, it had been widely assumed that the 'something else' that combines with labour and capital to produce economic growth must be technology. But by counting energy inputs in terms of joules rather than dollars, Kümmel not only produced results matching real-world growth rates and nearly eliminated the Solow residual, he also clarified the importance of energy to the economy.
16. Kümmel, Reiner (2013-12-01). "Why energy's economic weight is much larger than its cost share". Environmental Innovation and Societal Transitions. Energy, materials and growth: A homage to Robert Ayres. 9: 33–37. doi:10.1016/j.eist.2013.09.003. ISSN 2210-4224.
17. Mimkes, Jürgen (2012). "The Second Law of Economics". Book Review. Physik Journal (in German). 11 (6). Wiley-VCH: 67. ISSN 1617-9439. Retrieved 2025-01-13.

• 1939 births
• German physicists
• Technische Universität Darmstadt alumni
• Academic staff of the University of Würzburg
• Living people