Who he is and his times
Leonid Vitalyevich Kantorovich was born in 1912 in Petersburg. At the age of 14 he entered the mathematics department of Leningrad University, graduated in 1930, became a professor in 1934, and in 1935 received the degree of Doctor of Physical and Mathematical Sciences without defending a dissertation. Fame first came to him as a specialist in functional analysis — the branch of mathematics that studies spaces of functions; for this work he received the Stalin Prize in 1949. What brought him into economics was not ideology but an applied production problem. That is why his path is so revealing: a mathematician solved a particular factory question, saw in it a general principle of economic calculation, and then spent almost a quarter of a century seeking recognition of that principle.
The times were unfavourable for any quantitative economics. After the destruction of the Conjuncture Institute at the end of the 1920s and the repressions of the 1930s, economic science in the USSR, in the assessment of the historian I. Boldyrev, almost disappeared as an academic discipline; its place was taken by the political economy of socialism, built on the interpretation of classic texts. Gosplan drew up plans using the method of material balances: it matched requirements and resources item by item, without systematically comparing alternative ways of using the same resources. The choice between options was made administratively, and the word “optimum” sounded suspicious.
Kantorovich's biography runs through every stage of Soviet science. During the war he served at a military engineering and technical school that was evacuated from besieged Leningrad to Yaroslavl in January 1942; from 1948 he headed the computing department of the Leningrad branch of the V. A. Steklov Mathematical Institute, which carried out calculations for the atomic project. In 1958 he was elected a corresponding member of the USSR Academy of Sciences, in 1960 he moved to Novosibirsk, in 1964 he became a full academician, and in 1971 he moved to Moscow, to an institute dealing with problems of managing the national economy. He died on 7 April 1986, at the very beginning of perestroika.
Main ideas
In 1938 engineers from the central laboratory of the All-Union Plywood Trust approached Kantorovich with a question: how should work be distributed among veneer-peeling machines so as to obtain the greatest output for a given product mix? Kantorovich saw that the problem comes down to finding the maximum of a linear function of many variables subject to a large number of constraints in the form of equations and inequalities, and that the economy is full of such problems: cutting materials, loading equipment, allocating crops, transport. To solve them he proposed the method of “resolving multipliers”, a modification of the classical method of Lagrange multipliers. Today this field is called linear programming; in the West it was independently rediscovered at the end of the 1940s by G. Dantzig.
Kantorovich presented his results in a talk at Leningrad University in May 1939, and within a week the university press issued the booklet Mathematical Methods of Organizing and Planning Production in a print run of 1,000 copies. According to A. A. Belykh, it was sent to 9 research institutes, 23 editorial offices, 12 people's commissariats, the Council of People's Commissars, the Academy of Sciences, Gosplan and the Agricultural Academy, with an offer of consultations. Nothing is known about any responses to this mailing.
The main economic idea lies in the multipliers themselves. Solving an optimization problem yields not only a plan but also numbers showing how much the result would grow if one more unit of a given resource were added. If a resource is in surplus, its valuation is zero; if it is a bottleneck, its valuation is high. In Western literature such quantities are called shadow prices: prices that are neither set from above nor formed on the market, but follow from the very problem of making the best use of limited resources. In a 1942 manuscript Kantorovich called them “most expedient valuations”, and in the 1959 book “objectively determined valuations”. The change of name, as I. Boldyrev and T. Düppe note, was protective: the plain word “price” would have provoked accusations of departing from the labour theory of value.
From this followed conclusions that were radical for Soviet practice. If the valuations of resources can be calculated, they can be used to compare capital investments, to charge for land and natural resources, to test the economic accountability (khozraschyot) of enterprises and to decentralize decisions: an enterprise guided by correct valuations would itself choose the option consistent with the interest of the economy as a whole. As Belykh presents it, Kantorovich described a process resembling competition, but taking place not on the market but in planning calculations — a “competition” of plan variants that leads, without material losses, to a balanced optimal plan. The book The Best Use of Economic Resources (USSR Academy of Sciences Publishing House, 344 pages) developed these conclusions into a programme for transforming planning.
What became of the ideas in practice
The first attempt to bring the ideas to Gosplan came to nothing. By November 1942, in Yaroslavl, Kantorovich had completed the manuscript Economic Calculation of the Most Expedient Use of Resources (Ekonomicheskiy raschyot naiboleye tselesoobraznogo ispol'zovaniya resursov). With the support of Academician S. L. Sobolev it was sent to Gosplan, where, according to Belykh, it was rejected without any discussion. After Kantorovich appealed to the chairman of Gosplan, N. A. Voznesensky, a discussion did take place in 1943, but it turned hostile: the statistician B. S. Yastremsky pointed out that an optimum had also been proposed by “the fascist Pareto”. In his memoirs Kantorovich writes that he realized he had to set this work aside for a time. His son, V. L. Kantorovich, citing an oral account by a participant, reports that the question of an arrest was discussed at a closed meeting; there is no documentary confirmation of this.
It became possible to return to the subject only after 1953. In 1957 Academician A. N. Kolmogorov, who had read the manuscript carefully, insisted on its publication, and in 1959 the book came out. In 1960 a negative review by Boyarsky appeared in the Gosplan journal Planovoye Khozyaystvo (Planned Economy), and on 10 April 1964 Pravda printed a letter from economists headed by Academicians S. G. Strumilin and K. V. Ostrovityanov, “In the Captivity of Theoretical Errors” (V plenu teoreticheskikh oshibok): in the authors' opinion, the book contradicted the labour theory of value and did not deserve a prize. Kolmogorov wrote in reply that if the multipliers were declared in advance to be a harmful “marginal utility”, the calculus of variations would also have to be recognized as anti-Marxist. In 1965 Kantorovich, V. S. Nemchinov and V. V. Novozhilov received the Lenin Prize, and the open ideological campaign against Kantorovich ceased.
Recognition did not turn into planning practice. Linear programming was applied to individual problems — cutting materials, transport, loading equipment. According to the magazine Sankt-Peterburgsky Universitet, the introduction of rational cutting at a railway car plant, carried out by Kantorovich's student V. A. Zalgaller, reduced waste from 13 to 4 %. But the central plan was still drawn up by the balance method, and prices were set administratively and were not recalculated on the basis of objectively determined valuations. Boldyrev and Düppe characterize the application of the methods as fragmentary and experimental; Belykh states that the “mathematical revolution” in the Soviet economy did not take place. Tellingly, as late as 1986 Kantorovich, together with M. Albegov and V. Bezrukov, published an article in the journal Kommunist with the exhortatory title “Make Wider Use of Optimization Methods in the National Economy”.
The reasons were informational and institutional, not computational. An optimal plan and shadow prices are only as accurate as the initial data on technologies, capacities and stocks. These data were held by enterprises and ministries, which had an interest in distorting them. D. V. Didenko, drawing on material from late Soviet planning, shows that ministries engaged in administrative bargaining, seeking larger capital investments and smaller plan targets. A model that receives understated capacities and overstated consumption norms as input produces a neatly calculated but false optimum, and no outsider could check the initial figures: the data were closed.
The institutional side is no less important. Objectively determined valuations made visible what the system preferred not to show: which productions are loss-making when resources are honestly valued, where resources lie idle, which decisions of agencies are inefficient. Introducing such calculation would have meant admitting that disputes over resources are settled by methodology rather than by bureaucratic clout. Gosplan had no incentive to hand the right of decision over to an external model, the ministries had none to disclose their reserves, and the political economists had none to give up their monopoly on interpreting the law of value. Didenko sums up the general outcome as follows: no mechanism for the direct and systematic participation of scientists in planning work ever took shape, and technological improvement of planning was to a large extent cancelled out by a deterioration in the interaction between its participants.
What worked and what did not
What worked was the mathematics itself and what could be built around it. The joint work with M. K. Gavurin on freight flows, written back in 1940 and published in 1949, provided a complete theory of the transportation problem, including the relationship between the primal and dual problems. Methods for cutting materials developed with Zalgaller were used in industry. In the 1959–1960 academic year, on Kantorovich's initiative, the Faculty of Economics of Leningrad State University organized the so-called sixth year, in which economics graduates received mathematical training; among its students were the future academicians A. I. Anchishkin and S. S. Shatalin. In April 1960 the first conference on the application of mathematical methods in economics was held in Moscow, with more than 600 participants and 59 papers. In 1963 the Central Economic Mathematical Institute (TsEMI) of the USSR Academy of Sciences was founded. The new profession of the mathematical economist arose in large part thanks to Kantorovich.
What did not work was the main thing — the restructuring of pricing and planning on the basis of the valuations. Optimization took root at the level of the workshop, the plant and the transport scheme, that is, where the data are collected and checked by the same party that uses the result, and where no one loses power because the calculation has shown a better option. At the level of the national economy, where the calculation would have had to redistribute resources between agencies, it remained a recommendation. Even after the Lenin and Nobel Prizes, the author of the method had no right that would oblige planning bodies to take the result into account or at least to explain a refusal publicly.
The approach itself also has limitations. A linear model assumes that technologies are known and given as a list, that costs grow in proportion to output and that the goal is set from outside — for example, by a required set of products. The model answers the question of how to achieve a goal at the lowest cost, but not the question of what the goal should be. In Kantorovich's classical formulation the product mix is set by the planning body, which means the model is built into the existing system of goal-setting and does not replace it.
Debate and criticism
Orthodox Soviet criticism amounted to the claim that objectively determined valuations were a disguised theory of marginal utility, incompatible with the labour theory of value. This line was represented by Yastremsky's remark in 1943, the review in Planovoye Khozyaystvo in 1960 and the letter by Strumilin and Ostrovityanov in 1964. Boldyrev and Düppe explain the sharpness of the reaction by the fact that Kantorovich was intruding into an area that the political economy of socialism regarded as its own: the right to determine how the planned economy is arranged. Kantorovich himself, as Belykh shows, did not come out against Marx; as early as the 1940s he was preparing a memorandum on the difference between the subjective theory of utility and the marginal product as a fact of production technology.
Western literature raised other questions. The American economist R. Campbell, in his 1961 article “Marx, Kantorovich, and Novozhilov: Stoimost' versus Reality”, argued that the concepts of Kantorovich and Novozhilov essentially diverge from Marx's theory of value. A. Charnes and W. Cooper claimed in 1962 that in 1939 Kantorovich had not yet understood the economic meaning of the dual problem. Belykh disputes this thesis: according to his data, the meaning of resolving multipliers as indicators of value was clear to Kantorovich from the very beginning, but the political situation did not allow him to say so openly. He also shows that if the data from the tables of differential rent in the third volume of Capital are substituted into Kantorovich's model for plots of land, the valuations coincide with Marx's values of rent.
The third line of debate is the old question of whether rational calculation is possible under socialism, known from the debate between Mises, Hayek and Lange. Kantorovich's work is often cited as proof that such calculation is possible in principle. But the critics of centralized planning objected not to mathematics but to the premise that the centre can obtain complete and truthful data on technologies and needs. Soviet experience, if anything, confirms this part of the objection: the method existed, but the system created neither honest initial data nor incentives to disclose them. It does not follow that calculation is useless; it follows that calculation without a mechanism for obtaining and verifying data does not work.
There were also disagreements within the school itself. As V. V. Okrepilov presents it, Novozhilov and Nemchinov approached the criterion of optimality differently from Kantorovich: they interpreted the valuations as a special transformed form of value, expressed in differential costs of labour, whereas Kantorovich believed that the prices of an optimal plan could be determined entirely as resolving multipliers that take the scarcity of resources into account.
Legacy today
In 1975 Kantorovich and T. Koopmans received the Nobel Prize in Economics “for their contributions to the theory of optimum allocation of resources”. Koopmans had requested copies of Kantorovich's works as early as 1956, and in 1960, when publishing an English translation of the 1939 booklet, he called it a remarkable document in the history of management science and economics. Kantorovich remains the only scientist from our country to have received this prize; according to Belykh, only after it was he able to travel abroad.
Linear programming and dual valuations have become an everyday tool of logistics, energy, production planning and military affairs. Kantorovich's 1942 article “On the Translocation of Masses”, devoted to the problem of optimal transport, has, according to Boldyrev, entered cutting-edge economic theory and econometrics only in recent decades. In this sense Kantorovich's ideas triumphed globally, but through market companies and the state systems of other countries, not through Gosplan.
For the history of planning, Kantorovich's legacy is a clear separation of two problems. The problem of finding the best option given known data has been solved. The problem of obtaining honest data and making institutions comply with the result of a calculation has not, and it is solved not by mathematics but by the design of responsibility: who supplies the data, who checks them, who is obliged to follow the calculation and who may challenge it.
What open planning takes
- Shadow prices as a mandatory by-product of calculation. If quotas, capacities or a budget are allocated using an optimization model, the dual valuations are published together with the solution: which constraint is binding and what relaxing it would be worth. This fits into the reproducible calculation layer and the publication layer, and gives the goal-setting circuit a clear price for every trade-off.
- The model does not choose the goal. For Kantorovich the required set of products is given from outside; in our model the criterion and constraints are set by the goal-setting circuit, and the calculation merely finds the best way to meet them. This is a direct consequence of the separation rule: those who calculate do not decide what is to be calculated.
- Input data come from the measurement report, not from the executor's report. The main lesson of the failure at Gosplan: an optimum based on understated capacities and overstated norms is false. That is why, in our architecture, the model's input data are taken from the measurement layer and the registries, while agency figures are marked in the second column under the two-column rule.
- Reconciling calculated valuations with market ones. Where quotas are allocated at auction, the clearing price shows the real value of the resource; its divergence from the model's shadow price is a signal to revise the methodology or the data. This links the execution circuit to the verification circuit.
- An obligation to explain any departure from the result of a calculation. Kantorovich's recognition did not create any obligation for planning bodies to take his conclusions into account. In our model the version of the methodology is a legally significant artefact, and a decision that diverges from the calculation must be accompanied by a public justification.
What we do not repeat
- We do not build a closed model on agency data. Optimization within a single body that simultaneously collects the data, calculates and allocates reproduces the logic of Gosplan: an outsider can check neither the inputs nor the result.
- We do not hide the substance behind safe names. Kantorovich was forced to call prices “valuations”, and this made it harder to argue on the merits. We call a charge for a resource a charge, a rate a rate, and rent rent.
- We do not use a single criterion of optimality where values are incommensurable. A linear model requires one objective function; in care, education, medicine, culture and science our model applies no metrics at all, and in other spheres it uses several indicators.
- We do not count on scientific recognition leading to implementation by itself. The Lenin and Nobel Prizes did not change the way the plan was drawn up; implementation requires rights and obligations fixed in rules, not the authority of a method.
Links between ideas
Whom the author argued with, whose ideas they developed, whom they answered and whose fate they shared. All links are on the shared graph. Graph of ideas
- Stanislav Strumilin
Debate and criticism ←
A 1964 letter by Strumilin and Ostrovityanov in Pravda declared Kantorovich’s book contrary to the labour theory of value.
- Nikolai Voznesensky
Debate and criticism ←
Gosplan did not approve Kantorovich’s 1942 manuscript; after he appealed to Voznesensky, the 1943 discussion was hostile.
- Viktor Novozhilov
Parallel path →
Independently and almost simultaneously, in 1939–1941, they arrived at scarcity prices: resource valuations and differential costs.
- Viktor Novozhilov
Debate and criticism ←
A dispute within the school: Novozhilov read the valuations as a transformed form of value, Kantorovich as resolving multipliers.
- Viktor Novozhilov
Practice and institutions →
Together they secured the opening of the sixth year at Leningrad State University in 1959 and prepared the 1960 conference on mathematical methods.
- Vasily Nemchinov
Debate and criticism ←
Nemchinov did not regard objectively determined valuations as planned prices: prices should form in orders and contracts.
- Vasily Nemchinov
Practice and institutions →
They held the 1960 conference together; the 1965 Lenin Prize went to them and Novozhilov.
- Nikolai Fedorenko
Develops ideas →
According to Belykh, the SOFE concept relied to a large extent on Kantorovich’s optimisation ideas.
- Ludwig von Mises
Debate and criticism ←
Mises’s followers object that shadow prices depend on an objective function and data that the centre cannot specify.
- Friedrich Hayek
Debate and criticism ←
Critics of central planning objected not to Kantorovich’s mathematics but to the premise that the centre would receive truthful data.
- Oskar Lange
Parallel path ←
The late Lange accepted the need for mathematical programming with shadow prices and moved closer to optimal planning.
- Vitaly Naishul
Debate and criticism ←
Naishul shows that bargaining distorts requests and reports before optimal calculation even begins.
Timeline
- 1912
Born in Petersburg
- 1939
Talk at Leningrad State University and the booklet Mathematical Methods of Organizing and Planning Production in a print run of 1,000 copies
- 1942
Manuscript Economic Calculation of the Most Expedient Use of Resources (Ekonomicheskiy raschyot naiboleye tselesoobraznogo ispol'zovaniya resursov) completed; sent to Gosplan and rejected
- 1943
Hostile discussion of the work at Gosplan; Kantorovich sets the economic subject aside for a time
- 1959
The book The Best Use of Economic Resources is published
- 1960
All-Union conference on the application of mathematical methods in economics; move to Novosibirsk
- 1964
Letter by Strumilin, Ostrovityanov and others in Pravda against Kantorovich's book; elected a full academician
- 1965
Lenin Prize, together with V. S. Nemchinov and V. V. Novozhilov
- 1975
Nobel Prize in Economics, together with T. Koopmans
- 1986
Article in Kommunist calling for wider use of optimization methods; death on 7 April
Key works
- 1939Mathematical Methods of Organizing and Planning Production
- 1942On the Translocation of Masses
- 1942Rational Methods of Cutting Metal (Ratsional'nye metody raskroya metalla)
- 1949Application of Mathematical Methods to Problems of Freight Flow Analysis (Primenenie matematicheskikh metodov v voprosakh analiza gruzopotokov), with M. K. Gavurin
- 1959The Best Use of Economic Resources
- 1986Make Wider Use of Optimization Methods in the National Economy (Shire ispol'zovat' optimizatsionnye metody v narodnom khozyaystve), with M. Albegov and V. Bezrukov, the journal Kommunist, No. 9
Sources
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- Boldyrev I., Düppe T.. Programming the USSR: Leonid V. Kantorovich in context. 2020
- Boldyrev I.. Soviet Mathematics and Economic Theory in the Past Century: An Historical Reappraisal. 2024
- Диденко Д. В.. Изменение качества планирования экономики в позднем СССР: технологическая и институциональная динамика. 2021
- Окрепилов В. В.. Творческое содружество Л. В. Канторовича и В. В. Новожилова по формированию экономико-математического направления в отечественной науке и практике. 2012
- Большая российская энциклопедия. Канторович Леонид Витальевич. без даты
- Нобелевский комитет. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1975. 1975
- Журнал «Санкт-Петербургский университет». Л. В. Канторович: «Не всё должно быть в каждом блюде…». без даты
- Сафронов А. В.. Автоматизированная система плановых расчётов Госплана СССР и технологические ограничения внедрения ЭВМ в государственное управление в СССР. 2020
- Википедия. Канторович, Леонид Витальевич. без даты
Prepared from open sources. Dates, titles and quotations were checked against the source list at the bottom of the page; where sources disagree, the text says so.