R. Boiarskii

ON THE THEORY OF THE

DIMINISHING GROWTH RATES OF THE SOVIET ECONOMY

...We economists have a duty not only to point out the results and to refute on theoretical grounds the conclusions of the “learned” saboteurs, but also to expose the way these conclusions were reached, in order to preclude the repetition of such occurrences in better camouflaged forms.

That is why we must dwell here on Bazarov et al. If we were simply trying to refute his main conclusion about the diminishing growth rates of our economy, we should not have to bother to go to these lengths. This conclusion has long since been disproved by our very development and it is being disproved every day by the tremendous growth we are experiencing.

Thus the task of the economist is to point out the falseness of the premises adopted by Bazarov to arrive at his conclusions. This will equip us better and make us more vigilant in case we ever have to face such theoretical sabotage again....

In the literature Bazarov (as a planner) is mostly known for his theory on slackening growth rates. Bu his theoretical sabotage goes well beyond this. A closer look at his work reveals the total absence of differentiation in his approach to our economy under capitalism and under the Soviet system. It is a repetition of Groman’s theory about the constant proportion between agriculture and industry and the view, common to all the wreckers, that the prewar level is the limit to which the Bolsheviks can raise the country and beyond which they can never go. This proposition appears in Groman in the form of the constant proportion between agriculture and industry and it is found in Bazarov in a somewhat different form.

To prove his views, Bazarov introduces several curves. Unlike the others, he tries to explain the curves he uses to approximate the actual figures of our economic growth. Kondratiev and the others unabashedly use parabolas of “corresponding order.” Bazarov makes a serious attempt to justify the curve he uses. This attempt can be roughly represented as follows. Economic development is the process of the growth of production. This process manifests itself in the fact that the production figures grow. Therefore, if we present this production figure as a function of time, we shall be able to judge how our economy develops. Now, what sort of function is this? Bazarov constructs its differential equation. The rate of production growth, or the derivative of our function, in the first place is in proportion to the magnitude of this function itself because the more production grows, the better is the organization of labor, the acquired skill of the workers, etc. (as to the material base for the further growth of production, Bazarov never mentions it); in the second place, there is a certain level A which is above the attained size of production, and the growth of production is in proportion to the distance that still remains to this level.

Thus:

where t is the time; y, the size of production; A, the level of 1913. When solved, this differential equation gives the following S-type curve:

The curve not only grows at a diminishing rate, it never even reaches the limit A, i.e. the level of 1913, which it approaches asymptotically. That is why, besides the slackening rate of growth, Bazarov also has the unattainable ideal of 1913.

Now let us see on what his differential equation is based. Imagine that under capitalist conditions an amount of some product for which there is certain demand, expressed by the value A, is put into the market. Let us see now how this amount is marketed. It is obvious that the greater the unsatisfied demand (i.e. the larger [A - yl), the faster the product will sell. Moreover, each unit of this commodity that is purchased publicizes it, if its quality is adequate. Both these facts lead to the differential equation given above. But at this point Bazarov performs a spectacular about-face. Having written the equation for the marketing of the amount of the product put into the capitalist market, he simply decides that it applies equally unaer Soviet conditions.

From what precedes, it is easy to see that for the application of this ill-fated differential equation to be valid, one should first prove that the rate of increase in production is in proportion to (1) the size it has reached and (2) the difference between the latter and a certain constant level A. In the chapters dealing with the Soviet economy, Bazarov states that the differential equation is valid and strengthens this assertion by references to the organization of labor, etc. But all this refers to the first part of the proof. To this (the proportionality of the rate of increase of production to the size it has reached), we do not even have any special objections. All we have to do is to eliminate the references-strongly reminiscent of Bogdanov-to organization, etc., and simply point out that the increase in production is not taking place in a vacuum but on a material base, whose width and strength are determined by the level already attained. The second part (the proportionality of the rate of increase of production to the lag in fee level of production, i.e., A - y) is precisely the part which causes the slackening and sets the 1913 level as unattainable limit to total growth. This has been expanded in detail in Bazarov’s book but does not apply at all to the growth of the Soviet economy. True, in the opening pages of his book, Capitalist Cycles and the Recovery Process of the Soviet Economy, Bazarov declares that our plans are based on the demands of a free market. However, our plan is not to attempt to adapt ourselves to the free market, but to have an active influence on it and to drive it out of existence; our plan is the expression of the deliberate direction of our whole national economy toward the most rapid realization of socialism, a leap from the domain of necessity into the domain of liberty. All this the members of the Kondrat’ev-Bazarov-Groman group of saboteurs cannot, or rather refuse to, understand. The conclusion based on the above-mentioned differential equation is without any justification and is dictated by the refusal to see the difference between our economy and a capitalist economy. Bazarov has used it to help him find the answers he wanted and not as an instrument for a scientific investigation of what really happens.

Now, we ought to say a few words about the use of differential equations in general. Generally speaking, if we have in mind a process of variation and if we wish to find the pattern of this variation, the use of differential equations is no doubt very useful. It is not for nothing that Engels said that with the variable, mathematics has entered the domain of dialectics. And the decisive role of the variable in mathematics is in differential and integral calculus. The essence of differential and integral calculus lies precisely in differential equations. Therefore, wherever we deal with the variation of quantity, it can best be studied by the means of differential equations. But this equation, unlike Bazarov’s, must be based on qualitative analysis.

We also ought to say a few words about the figures used by Bazarov to establish his S-type curve. How is it possible that he failed to see a sharp discrepancy between the series of figures and the theoretical S-type curve? The actual explanation is quite simple. Since the recovery period is followed by the reconstruction period, we may not draw one single smooth curve through both periods. Comrade Khotimsky dwelt on this subject when he criticized the Leibnitz aphorism that nature abhors leaps. If one period is followed by another that differs from it qualitatively and if a curve suits one period, then the curve for the next period must be quite different. What happens then at the point of juncture of the two periods? There are here two distinct curves, and therefore a leap must of necessity take place. If we take the recovery period and the reconstruction period, we find that each of them has its own curve of the rate of growth. During the transition from recovery to reconstruction, these two curves meet and a leap occurs. But it is not always possible to see this leap in figures, and for a very simple reason. The leap, i.e. the changeover from the recovery period to the reconstruction period, does not occur simultaneously everywhere. At one enterprise it can happen earlier, at another, later, and these differences may be substantial if we take not simply a few enterprises of the same industry but rather the national economy as a whole. What, then, is the result? A mass of leaps occurring at different times are superimposed on one another and thus soften the sensation of the leap and create the illusion of a smooth curve running over the two periods (see diagram).

Seeing this softening effect shown by the dotted line on the graph, Bazarov mistook it for a falling growth rate, for the natural continuation of the curve of the recovery period, and rushed to generalize his blindness in his theory of falling growth rates. Mach’s philosophy hid from him the true process of development and his political hostility toward our regime prompted him to make hasty, far-reaching conclusions.

I believe that the continuation of the ideological struggle against those who have been arrested by the GPU does not in the least free us from continuing the fight against our enemies still at large. Therefore after having dealt with Bazarov, I want to touch upon some alleged corrections to his theory made by Podtiagin (see my articles in Ekonomicheskaia zhizn, January 4 and February 1, 1929). Podtiagin’s corrections consisted in the following: he denies the necessity for basing the curve on anything except the figures from which it is plotted. Following many other economic vulgarizers, he simply uses a straight line and then tries to prove that if our planners produce directives with growth rates that exceed those of his straight line, then this proves that the plan violates the actual facts and must inevitably fail. And we all know that a straight line is a line with a diminution in the growth rate.

Thus, the outright Machism-with its formula “apply a straight line to whatever comes into your hands”-and the more subtle variety of Machism, involving differential equations and other refinements, easily come to an agreement on the role of planning as well as on rates of growth....

“O teorii zatukhaiushchego tempa razvitiia sovetskogo khoziaistva,” Planovoe khoziaistvo, 1930, No. 10-11, pp. 158-163.