The 1920s

During the 1920s, mathematical methods made rapid progress in Soviet economics for a variety of reasons. Difficult economic conditions meant that solutions to many economic problems had to be found rapidly, especially in the fields of organization of planning and in finance.

[T]he rise of mathematical economics during the NEP period can be interpreted as a response to the challenge posed by the emergence of the Soviet economy during the years of War Communism. When their Western colleagues were still largely preoccupied with the finer points of marginal utility theory... Soviet mathematical economists were opening up new frontiers in economic research. (Smolinski 1971: 140)

These new frontiers included: planning of the national economy, the theory of inflation and problems of economic growth. Some pioneering works on optimization models were produced.

Most attention was given to problems of planning - first, to economic balances and then, later, to problems of economic growth. Discussions on the methodology of plan­ning began in 1920. It was only natural that the system of War Communism, with its administrative allocation of resources and high inflation, led to approaches in planning that utilized physical indicators. Accordingly, major contributions were made in the field of input-output analysis.

In January 1921, A.A. Bogdanov delivered a report to a conference on the Scientific Organization of Labour and Production, in which he advocated a particular system of planning (Bogdanov 1921). Central to his approach was the idea of chain links between branches of the economy. The existence of such links, including feedback links, deter­mines certain proportions in the economy.

The starting point of Bogdanov’s planning methodology was a calculation of the ultimate needs of the population. To cater for these needs, consumer goods had to be produced which entailed the utilization of producer goods. The production of producer goods entailed, in turn, the production of other producer goods. The elaboration of the plan was conceived as an iterative process. Bogdanov does not use the terms “techno­logical” or “input-output” coefficients, but he does make it clear that for the output of any given product, inputs of other specific products have to be calculated. This was an important contribution to what later became input-output analysis.

L.M. Kritsman adopted the same approach. He published several articles on the meth­odology of planning. Kritsman further developed Bogdanov’s iterative process, adapting it to the real economy and dividing products into three groups: those produced in the state sector, those purchased in the private sector and those purchased from abroad. Kritsman formulated the task of planning as follows: “to determine the sizes of branches of the economy in such a way that they will be able to develop without disturbance, producing the maximum possible by utilizing existing resources” (Kritsman 1921: 44). Kritsman already used the term “input coefficients” and emphasized that the reliability of planning rests upon the reliability of these coefficients. Later, in 1922, he proposed the use in planning of a kind of chess-board table (Kritsman 1922: 24-5).

Another important contribution to the development of planning theory was made by S.G. Strumilin. In January 1921, Strumilin put forward a solution to the optimization problem. The utility function (a kind of social welfare function) was to be maximized. The quantities of labour devoted to the production of different goods were variables and the single constraint was the total labour fund for the year.

V.A. Bazarov, a prominent economist, also made a contribution to the theory of opti­mization during this period. For Bazarov, there were three requirements for any optimal economic plan:

Firstly, the progress of the national economy from its present state to the target indicated in the General Plan must be smooth... Secondly, the economy must be conceived of as a harmoni­ous, organic whole - a system of mobile equilibrium that is as stable as possible... The third precondition of optimality is that the path chosen as leading towards the goal projected in the General Plan should be the shortest possible path. (Bazarov 1926 [1964]: 366-7)

However, during the 1920s neither Bazarov, nor any other Russian economist, was able to develop a formal optimization model for such an approach.

Better practical results were achieved in the construction of economic balances. In 1926 the Central Statistical Board published the Balance of the National Economy of the USSR (the first versions of this balance were published in 1925). This work was posi­tively reviewed by W. Leontiev:

What is essentially new in this balance when it is compared with the usual economic investi­gations such as the American and English censuses, is the attempt to embrace in figures not only the output but also the distribution of the national product, so as to obtain in this way a comprehensive picture of the whole process of reproduction in the form of a kind of “Tableau Economique”. (Leontiev 1925 [1964]: 88)

A further step was taken by M. Barengolts, who in 1928 created a chess-board table for 12 branches of the economy of the USSR. He also discussed the idea of technological coefficients and argued that in the absence of technical and price changes these coeffi­cients can be considered as stable.

The creation of the planning system in the USSR and the introduction of Five Year Plans raised questions of long-term planning and rates of further economic growth. In 1928, G.A. Feld’man put forward his own model of economic growth, which can be considered as a further contribution to mathematical economics. Feld’man’s model was used for the calculation of the general plan of the national economy for the period of 15 years. Feld’man was convinced that “it is impossible to imagine that a phenomenon as complicated as the national economy could be planned by a simple method” and that “the perfect planning can be implemented only on the basis of mathematical theory” (Feld’man 1928 [1964]: 177-8). Feld’man modified the Marxian theory of reproduction and divided the economy into two parts: one in which “simple reproduction” (replace­ment investment) took place and another, which provided the means for “expanded reproduction” (net investment). E. Domar, who was the first in the West to draw atten­tion to Feld’man, interpreted Feld’man’s binary distinction along Marxian lines as refer­ring to, on the one hand, the production of the means of production and, on the other, to the production of consumer goods. Domar considered Feld’man’s model to be similar to the later developed Western models of economic growth (Domar 1957).

During the 1920s mathematical economics as a branch of Soviet economic science developed rapidly.

This promising development of mathematical economics in the Soviet Union was interrupted at the end of the 1920s. Radical changes in economic policy that revived the methods of War Communism, the political defeat within the Communist Party of the so-called “right wing” headed by Bukharin, the end of the NEP - all these events had important consequences for Soviet economics. In his speech to a conference of Agrarian Marxists in 1929, Stalin denounced equilibrium theory as anti-Marxist. Instead he called for “the development of reproduction theory and the balance of national economy”, because “what the Central Statistical Board published in 1926 as the balance sheet of the national economy is not a balance sheet, but juggling with figures. Nor is the manner in which Bazarov and Groman treat the problem of the balance sheet of the national economy suitable” (Stalin 1929: 178). Soon afterwards, both Groman and Bazarov as well as many other gifted mathematical economists (Chayanov, Kondratiev, Litoshenko, Yurovskii) were arrested. Bogdanov died in 1928. Strumilin was severely criticized and lost the important position of the Deputy Head of GOSPLAN (the State Planning Committee). Feld’man was arrested in 1937 and was released only in 1953.