Abstract
Kantorovich was a gifted Soviet mathematician and the intellectual inspiration of the optimal planning school in Soviet economics. The range of his work was unusually wide. He contributed to both pure and applied mathematics; taught, first, students of engineering, then also of mathematics, and later of mathematical economics; managed research projects; helped the Soviet atom bomb project; invented calculating machines; criticised the Soviet systems of planning and price determination; worked out the best method for calculating urban public transport fares; and invented linear programming. He was (jointly) awarded the 1975 Nobel Prize in economics for his work on the optimal allocation of resources. His career combined mathematics with (micro)economics. He influenced mathematical and economic thought throughout the world but was unable to realise his ambition to fundamentally reform Soviet planning and pricing.
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Change history
09 November 2022
In the original version of the book, the term “Leoinid” in the title, running head and TOC of Chapter 20 has been replaced with “Leonid” so that it should read as “Leonid Kantorovich”.
The correction chapter and the book have been updated with the change.
Notes
- 1.
According to Aganbegyan et al. (1987), there were eleven of them. However, in the references to his end-of-life autobiographical notes, ‘only’ eight are listed.
- 2.
Functional analysis developed as a separate branch of mathematics after the publication in 1932 by the Polish mathematician Stefan Banach of his book Théorie des operations linéaires. This led to the establishment in 1934 of a seminar on the subject in Leningrad. One of its participants was the young mathematical prodigy Kantorovich.
- 3.
The linear semi-ordered spaces on which Kantorovich worked are called K spaces in his honour.
- 4.
Linear programming is the mathematical problem of the maximisation (or minimisation) of a linear function of a number of variables subject to linear inequality constraints. In economic language, it is a method for calculating the most efficient allocation of resources under conditions of constant returns to scale. In everyday language, it is about calculating how to use limited resources to achieve the best possible result.
- 5.
Every linear programming problem has a dual problem. What Kantorovich termed ‘resolving multipliers’ (or later ‘objectively determined valuations’) are variables from the dual problem. They are usually understood as prices, and referred to in the Western literature as ‘shadow prices’, but that was at variance with the Soviet Marxist understanding of prices. In 1939, criticism for having ‘anti-Marxist bourgeois views’ could have fatal consequences.
- 6.
‘Aesopian language’ means a text written in such a way as to convey an innocent meaning to an outsider but a hidden meaning to someone who knows how to read between the lines. It was widely used in the Russian Empire and USSR to evade the authorities.
- 7.
According to Bollard (2020, Chapter 5) and Wikipedia (the article on Kantorovich), before he was evacuated to Yaroslavl, Kantorovich was responsible for safety on the Road of Life (the precarious route over iced-up Lake Ladoga that was the only surface link between besieged Leningrad and the rest of the USSR). This allegedly involved calculating the temperatures, wind speeds, and ice thickness necessary to ensure the ice was thick enough to prevent vehicles falling through it. It also allegedly concerned calculating the safe distance between vehicles. However, I have been unable to find any reliable source that confirms this. Neither in his own end-of-life autobiographical notes (about his scientific achievements) nor in the reminiscences of people who knew him (Dmitriev 2019) is this mentioned. If true, it would be a pioneering example of operations research. Kantorovich’s friend and colleague Sergei Golushkevich was indeed involved in calculating safe routes over the Road of Life for tanks (personal communication from Ivan Boldyrev).
- 8.
This seems to have been in 1950. The person he recommended for the post was appointed instead and was already busy at work in November 1950 (Vladimirov and Kublanovskaya 2002, 155).
- 9.
This continued to give him advantages denied to those not involved with the military (Dmitriev 2019, 648). When he lived in Novosibirsk, he had a piano in his flat. He had been able to obtain it despite the fact that pianos could not be freely bought in shops.
- 10.
For an overview of his work in computational mathematics in 1947‒1957, see Daugavet and Romanovsky (2012).
- 11.
Certificates of invention were official recognition of an invention and its inventor/s. Unlike patents in capitalist countries, they did not confer ownership rights on the inventor. The first of these inventions was electro-mechanical and was soon replaced by electronic computers. The second was more successful. Over a period of ten years, about forty thousand of them were manufactured (Kantorovich 1987, 206).
- 12.
This school treated national economic planning as an optimisation problem.
- 13.
- 14.
For example, he gave a course of lectures on probability theory in a military college, using military examples. This was in about 1940‒41. A textbook based on it was later published (Kantorovich 1946).
- 15.
Kantorovich himself gave a slightly different title for this (unpublished) work but added that he later changed its title (Kantorovich 1987, 203).
- 16.
The English translation is Kantorovich (1965).
- 17.
Yaroshenko proposed that Soviet political economy should concern itself with the rational organisation of production and economic planning. This was something for which Kantorovich—quite independently—supplied an instrument (linear programming) that could have enabled Yaroshenko’s proposal to be realised in some cases. Stalin, however, considered that the rational organisation of production and economic planning were matters of economic policy, to be decided by the leadership and not by economists.
- 18.
The article from which this quotation comes uses the term GDP. However, in a personal communication. co-author of the article Ivan Boldyrev has stated that the Russian original is vypusk konechnoi produktsii and that final output is a better translation.
- 19.
On the one hand, he provided the statistical data for Stalin’s speech ‘On the grain front’ (May 1928). On the other hand, he publicly opposed Lysenko’s views on genetics at the notorious August 1948 session of the All-Union Academy of Agricultural Science named after Lenin (for which he lost his main job). Furthermore, in 1950‒55, he struggled against the liquidators in statistics (people who wanted to do away with statistical theory), even taking the risky step of publishing an article entitled ‘Statistics as a science’ in 1952 when Stalin was still alive and inspiring attacks on science.
- 20.
I was affiliated to this Chair as an international exchange student in 1965‒67. As a young resident outsider from the UK, I found the search for optimality bizarre. In view of the difficulties of everyday life, it seemed to me rather obvious that more modest measures, such as attention to providing quality food in shops open to all and without queues, would have been more appropriate.
- 21.
In 1951, Kantorovich co-authored a book with A.Zalgaller on the rational cutting of industrial materials (a revised edition was published in 1971 and a third updated edition in 2012). Their results were applied for many years in a factory building railway freight carriages and saved a considerable amount of metal. However, the reduction of waste meant a reduction in the amount of scrap iron available for steel mills. The steel plants complained and Kantorovich was summoned to the Leningrad Regional Party headquarters and accused of complicity in economic sabotage. However, this did not have adverse consequences for him because of his military work. Nevertheless, co-author Zalgaller was persecuted because he was a Jew, and Kantorovich, whose position was much stronger because of his military work, helped him. He also helped other colleagues who were persecuted for the same reason (Dmitriev 2019, 646 and 696). However, Kantorovich himself occasionally encountered state anti-Semitism. On one occasion he set up a Chair (kafedra) in computational mathematics but, because he was a Jew, he was not permitted to head it and a Russian was appointed instead (Dmitriev 2019, 684‒685).
- 22.
Hicks was a joint winner of the 1972 Nobel Prize.
- 23.
Hicks followed up these remarks with speculation about the role of game theory in analysing social processes.
- 24.
According to prof. A.V.Bukhvalov (Dmitriev 2019, 636), ‘In his last interview he [Kantorovich] said approximately the following: “Maybe I was mistaken in where and when it is possible to apply the mathematical models which I develop. Perhaps they require not the socialist person but the communist person”’. This last sentence means people who put the interests of society above their own personal interests. It is a striking recognition of the fact that it was often difficult to implement linear programming in the USSR because to do so was against the interests of many people. It also draws attention to the difference between technical and social systems.
- 25.
Council for Mutual Economic Assistance (Russian acronym SEV), often referred to in the West as Comecon.
- 26.
- 27.
However, the British Marxist economist Dobb (1967) argued that there was no contradiction between the Marxist theory of value and Kantorovich’s optimal valuations (shadow prices) since the latter corresponded to Marx’s ‘market prices’ (which he only tackled in the incomplete Volume 3 of Capital) and Marshall’s ‘short-period’ prices. They had nothing to do with the analysis of long-period prices in Volume 1 of Capital. Dobb’s argument was welcomed by Novozhilov, as was apparent at a meeting I had with him in Leningrad in 1966.
- 28.
DOSSO entirely ignored Kantorovich but Koopmans did mention him. Already in 1956, Koopmans corresponded with Kantorovich—see Sect. 3.
- 29.
For a popular book on the last two issues, see Case and Deaton (2020) a book co-authored by the 2015 Nobel Prize winner (Angus Deaton) and his wife. That medical care differs fundamentally from ordinary commodities, which can be efficiently produced and distributed through the market system, because of uncertainty and asymmetrical information, was pointed out by Arrow (1963).
- 30.
These result from treating higher education as an ordinary commodity bought be students and sold by universities. This ignores the external effects of education on the economy and society as a whole.
- 31.
The English translation of this book is Kantorovich and Akilov (1982).
References
Ackerman, F. (2002). Still dead after all these years: interpreting the failure of general equilibrium theory, Journal of Economic Methodology 9(2), 119‒139.
Aganbegyan, A. et al. (1987), Leonid Vital’evich Kantorovich, Uspekhi matematicheskikh nauk 42(2), 177‒182. (In Russian).
Arrow, K. (1963). Uncertainty and the welfare economics of medical care, American Economic Review 53(5), 941‒973.
Belykh, A. (1990). O vospriyatii ekonomicheskikh rabot L.V.Kantorovicha na Zapade, Ekonomika i matematicheskie metody 26(2), 238‒247. (On the Reception of Kantorovich's Economic Works in the West. In Russian).
Boldyrev, I. and Düppe, T. (2020). Programming the USSR: Leonid V. Kantorovich in context, British Journal for the History of Science 53(2), 255‒278.
Bollard, A. (2020). Economists at war (Oxford: Oxford University Press). The relevant parts are Chapters 5 and 9 part 3.
Campbell, R.W. (1961). Marx, Kantorovich, Novozhilov: Stoimost versus reality, Slavic Review 20(3), 402–418.
Case. A. and Deaton, A. (2020). Deaths of Despair and the Future of Capitalism (Princeton: Princeton University Press).
Daugavet, O.K. and Romanovsky, I.V. (2012). O deyatel’nosti i rabotakh L.V.Kantorovicha v oblasti programmirovaniya, Zhurnal NEA, 13(1), 185–190. NEA is an abbreviation for Novaya Ekonomicheskaya Assotsiatsiya (New Economic Association). (On the Activity and Works of Leonid Kantorovich in the Field of Programming. In Russian).
Dmitriev, A.L. (ed.) (2019). L.V.Kantorovich glazami kolleg i druzei (k 105-letiyu so dnya rozhdeniya), in Istoki. Ekonomika – ‘’mrachnaya nauka’’? (Moscow: Izdat.dom VShE), 619‒700.This is a collection of interviews about Kantorovich with his colleagues and friends carried out in 2011 by final-year students at St.Petersburg State University. (L.Kantorovich in the memory of his colleagues and friends. In Russian).
Dobb, M. (1967). Kantorovich on optimal planning and prices, Science and Society 31(2), 186‒202.
Dorfman, R., Samuelson, P.A. and Solow, R. (1958). Linear programming and economic analysis (New York: McGraw-Hill). There is a paperback edition first published in 1987 (New York: Dover).
Ellman, M. (1973). Planning problems in the USSR: The contribution of mathematical methods to their solution (Cambridge: Cambridge University Press).
Ellman, M. (2014). Socialist planning 3rd ed. (Cambridge: Cambridge University Press).
Gardner, R. (1990) L.V.Kantorovich: The price implications of optimal planning, Journal of Economic Literature XXVIII, 638‒648.
Hicks, J. (1960). Linear Theory, Economic Journal 70(4), 671‒709.
Kantorovich, L. (1939). Matematicheskie metody organizatsiya i planirovaniya proizvodstva (Leningrad: Izdatel’stvo LGU). There is an English translation in Management Science 6(4) 1960, 366‒422. (Mathematical Methods of Organization and Planning of Production. In Russian).
Kantorovich, L. (1958). On the Translocation of Masses, Management Science 5(1), 1–4. This is a reprint of an article originally published in Comptes rendues (Doklady) de l’Académie des Sciences de l’URSS 1942 37 (7‒8).
Kantorovich, L. (1946). Teoriya veroyatnostei (Leningrad). (The Probability Theory. In Russian).
Kantorovich, L. (1965). The Best Use of Economic Resources (Oxford: Pergamon).
Kantorovich, L. (1987). Moi put’ v nauke, Uspekhi matematicheskikh nauk 42(2), 183‒213. (My Way in Science. In Russian).
Kantorovich, L. and Gorstko, A. (1972) Optimal’nye resheniya v ekonomike (Moscow: Nauka). (Optimal Solutions in Economy. In Russian).
Kantorovich, L. and Akilov, G. (1982) Functional analysis 2nd ed (New York: Pergamon).
Katsenelinboigen, A. (1978‒79). L.V.Kantorovich: The political dilemma in scientific creativity, Journal of Post-Keynesian Economics 1(2), 129‒147.
Khanin, G. (2008). Ekonomicheskaya istoriya Rossii v noveishee vremya vol.1 Ekonomika SSSR v kontse 30-x godov – 1987 god [Economic History of Russia in the Modern Times. Vol 1. The Economy of the USSR inthe late 1930-ies - 1987]. (Novsibirsk: Novosibirsk State Technical University). (In Russian).
Kontorovich, V. and Wein, A. (2009). What did the Soviet rulers maximise? Europe-Asia Studies 61(9), 1579‒1601.
Koopmans, T. (1957). Three essays on the state of economic science (New York: McGraw-Hill). The first essay is the relevant one.
Koopmans, T. (1960). A note about Kantorovich’s paper, ‘’Mathematical methods of organizing and planning production’’, Management Science 6(4), 363‒365.
Kornai, J. (1967). Mathematical Planning of Structural Decisions (Amsterdam: North Holland). 2nd ed, 1975.
Kornai, J. (1970). A general descriptive model of planning processes, Economics of Planning 10 (1/2), 1‒19.
Kornai, J. (2010). Reflections, in Rosser, J.B., Holt, R.P.F. and Colander D. (eds.) European economics at a crossroads (Cheltenham: Edward Elgar), 187‒203.
Kreps, D. (1990). A Course in Microeconomic Theory (Princeton: Princeton University Press). There is a paperback edition published in 2020 (Princeton: Princeton University Press).
Kutateladze, S.S. (2012). K stoletiyu so dnya rozhdeniya L.V.Kantorovicha, Vestnik NGU. Seriya Matematika, mekhanika, informatika 12(1), 3‒6. (The 100th Anniversary of L.V.Kantorovich. In Russian).
Marx, K. (1865). Wages, Price and Profit (speech delivered in English at sessions of the General Council of the First International). First published in London in 1898. Available in numerous editions and languages.
Nelson, R. (1981). Assessing private enterprise: an exegesis of tangled doctrine, Bell Journal of Economics 12(1), 93‒111.
Nemchinov, V.S, ed. (1959‒65) Primenenie matematiki v ekonomicheskikh issledovaniyakh (Moscow: Sotsekgiz and Mysl’), Vol.1 1959, Vol.2 1961, Vol.3 1965. There is an English edition of Vols. 1 and 2 edited by A.Nove and published in 1964 by Oliver and Boyd in Edinburgh and MIT Press in Cambridge Mass. (The Use of Mathematics in Economic Research. In Russian).
Safronov, A.V. (2016). Mirazh optimal’nosti: vnedrenie matematicheskikh metodov v ekonomiku kak otvet na problemy reformy upravlenie promyshlennostyu 1957 goda [The Mirage of Optimality: the Use of Mathematical Methods in Economics as a Reaction on the Problem of Reforming Industrial Management in 1957], Ekonomicheskaya istoriya 1(32), 76‒86. (In Russian).
Samuelson, P. (1947). Foundations of economic analysis (Cambridge Mass.: Harvard University Press).
Vladimirov, V.S. and Kublanovskaya, V.N. (2002). Vychisleniya dlya atomnogo proekta, in V.L.Kantorovich, Kutateladze S.S., and Fet, Ya.I. (eds) Leonid Vital’evich Kantorovich: chelovek i uchenyi [The Calculations for the Atomic Age] Vol.1 (Novosibirsk: Siberian branch, Russian Academy of Sciences), 153–160. (In Russian).
Zalgaller, V. (2003). O zamechatel’nom cheloveke ― Leonide Vital’eviche Kantoroviche (1912‒1986), http://www.vestnik.com/issues/2003/0820/win/zalgaller.htm Accessed 20 January 2021. (On a Wonderful Man Leonid Kantorovich. In Russian).
Acknowledgements
I am grateful to V. S. Avtonomov, A. Belykh, I. Boldyrev, M. Harrison, G. I. Khanin, V. Kontorovich, P. Ellman, and P. N. Teslya for helpful comments on the draft and helping me access relevant literature.
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Ellman, M. (2022). Leonid Kantorovich. In: Avtonomov, V., Hagemann, H. (eds) Russian and Western Economic Thought. Springer Studies in the History of Economic Thought. Springer, Cham. https://doi.org/10.1007/978-3-030-99052-7_20
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