G. A. Fel’dman

ON THE THEORY OF GROWTH RATES

NATIONAL INCOME · I

1. NATIONAL INCOME AND ITS GROWTH

...The primary objective of this work is to determine the potential volume of consumption of the masses, and its rate of growth as a function of the structure of the economy.

It is quite clear that the volume of consumption and its rate of growth are not simple functions of arbitrarily taken structural indices. It would be futile to attempt to establish a direct dependence of the rates of growth in question on relationships between urban and rural industry, between extractive and manufacturing industry, or, to take a clearly absurd example, between the country’s river and sea transportation.

The idea suggested itself of following Marx’s example by introducing data on capital invested in the production of consumers’ goods and of producers’ goods as basic indicators of the magnitude and structure of the economy. However, more detailed analysis indicates that this “principie of division” is inadequate to accomplish by mathematical methods the particular concrete objective stated above.

To the extent that the rate of growth of production depends on the rate of growth of the equipment of the labor force, and productive equipment is made in sector A (producers’ goods sector), it may be stated outright that the increase of the rate of growth of production depends on the increase of the capital of sector A as compared with the increase of the capital of sector B (consumers’ goods sector).^1.

With expanding reproduction, sector A must supply sector B not only with producers’ goods required to continue production at the current level of output, but also with additional fixed and circulating capital necessary for expansion of reproduction, given constant efficiency of capital utilization.^2.

This gives rise to the idea of dividing the capital of sector A into two sections, of which one (A₂) supplies sector B with the means of production required to sustain output at a given level, and the other (A,) supplies all industries in both sectors with additional capital to enable reproduction to expand. Given constant efficiency of capital utilization, A₂ must be proportional to B, while the magnitude of A. is determined entirely by the rate of growth of production as a whole, and of its separate parts.

Since capital consists of constant and variable parts, consistent application of the foregoing principle of classification requires the transfer to sector A of that portion (B,) of sector B which provides the increments of variable capital, leaving in sector B only the portion (B₂) required to maintain consumption at any given level. Hence the specific expression on which the rate of growth of total consumption depends will be the ratio

The numerator includes everything that provides the basis of expanded reproduction, while the denominator includes everything that serves current direct consumption.^3.

From the viewpoint of the proposed division, there is no basis for including the capital invested in a weaving factory in sector B, and capital invested in cotton plantations which produce cotton for the manufacture of yarn, or capital invested in spinning factories, in sector A, since in either case both spinning and weaving will take place in the same factory, and weaving divides itself into a number of consecutive productive processes which yield semifinished products that are themselves means of production for subsequent stages of production.

A specific structural division with quantitatively interrelated components must therefore be formulated before the dependence of the rate of growth of national income on these structural relationships can be determined. The basic step is a precise economic division of production, in accordance with the principal objective of this work. An absolute and precise criterion is necessary in order to determine the exact extent of the capital required to produce consumer goods at a level sufficient to satisfy current consumer needs.

From the viewpoint of the capacity of the productive apparatus to expand reproduction, there is, therefore, no reason to separate from sector B any portion of production concerned in one way or another with producing final products, and particularly consumer goods, up to the level sufficient to satisfy current needs. It must, therefore, be concluded that in the formulation of the problem it is appropriate to place in sector B all the industries concerned in any way with creating the values of consumer goods up to the level sufficient to satisfy current needs.

In this sector [B], in which Marx’s schema places the entire value of consumers’ goods, must be included also all of the capital used in producing the consumers’ goods. It is understood that this includes neither the increase of fixed and circulating capitals in sector B nor their replacement when they become technically obsolete.

This capital can be obtained only from sector A. The value of the output of sector B can include only the value of raw materials and that portion of the equipment and producers’ goods actually used up in the production of consumers’ goods. In sector B must not be included the value of producers’ and consumers’ goods accumulated for expanded production, which will only later, as they wear out and are used up, enter into the value of consumers’ goods produced with the expanded capital. Thus the wear and tear of productive equipment in sector B must, by definition, be made good within that sector.

Thus defined, sector B possesses the remarkable property of being capable of existence without sector A, but only for purposes of simple reproduction. Thus, starting from an analysis of what is required for a more precise division of output-from the viewpoint of determining the value of consumer goods required to satisfy the existing level of needs-we have arrived at a confirmation of the above idea: that production must be divided into sector B, capable of maintaining consumption at a given level even with a cessation of the inflow of producers’ and consumers’ goods from sector A to be added to the capital of sector B, and sector A, which provides both sector B and itself with all the capital required for expansion of reproduction.

Thus, starting from Marx’s division, we have arrived at a new division which corresponds, however, to another division, the Marxian simple and expanded reproduction, the “production of income’’ and the “production of capital.” To avoid confusion, the letter p will henceforth be used for what has been developed from Marx’s sector B, and the letter u for the remaining part of production, developed from Marx’s sector A.

All parts of sector p consist merely of the stages of a single productive process resulting in the consumers’ goods required to satisfy the existing level of needs. The value of net output in the course of a year consists only of labor outlays:^4.

v + m.

Consequently the end product of sector p is expressed by

v_p + m_p,

and the value of net output of sector u is defined by

v_u + m_u.

These expressions exclude the possibility of overlapping accounts [between p and u].

The only criterion for classifying production into the proposed sectors is whether it serves to increase capital (or replace technically obsolete capital) or only to maintain consumption at a given level.

For greater clarity, the process of expanded reproduction in a closed economy has been schematically represented in Figure 1, on the basis of the division which has been developed from Marx’s sectors.^5.

The left part of the figure (area u) represents production serving to increase capital and to replace productive capital becoming technically obsolescent. The total net output (without double counting) of sector u consists of the total value of the end products of sector u-specificallythose producers’ and consumers’ goods which replace the technically obsolescent capital of both sectors (u and p), or which increase the capital.

fig.1

The right part of the figure (area p) represents production serving to produce consumers’ goods and the producers’ goods required for maintaining the production of consumers’ goods at any given level. The total net output (without double counting) of sector p consists of the total value of the end products of sector p-consumers’ goods used to satisfy the existing level of needs.

K_u and K_p represent the total fixed and circulating capital of sectors u and p respectively. ND_U and ND_p represent the net outputs of the means of production and consumers’goods in sectors u and p. K = K_u + K_p, therefore, represents total capital, and ND = ND_u + ND_p represents total net output under conditions of expanded reproduction.

Let the effectiveness of capital utilization be defined by

Let A_m represent the value of equipment and means of production used to replace the obsolescent portions of both K_p and K_u. A_m consists of two parts, A_mp and A_mu, used to replace the obsolescent portion of K_p and K_u respectively. Thus

Δ will be used to denote annual increments. Thus ΔK_u represents the increment of K_u, ΔK_p represents the increment of K_p, and

The consumers’ goods produced in sector p are divided into a part v_p used up bythe working class employed in sector p, and surplus’value (surplus production), m_p. In turn, m_p is divided among consumers so that the following basic categories result:

1) m_pg-consumers’ goods absorbed by the government apparatus;

2) m_po-consumers’ goods for the bourgeoisie (large, middle, and small) not engaged in any phase of production;

3) m_pp -consumers’ goods for the bourgeoisie active in sector p;

4) m_pmu-consumers’ goods for the bourgeoisie active in sector u;

5) m_pvu-consumers’ goods for the additional workers of sector u.

Therefore,

However, the exchange of goods between sectors u and p need not be equivalent, i.e., it is not necessary that

The interrelationship of the elements of production and consumption will be considered for three cases: (1) where total consumption is constant; (2) where total consumption increases at a constant geometric rate; and (3) where total consumption increases at a rising rate.

Let the rate of growth be defined as the ratio of the increment per unit of time to the quantity which is increasing. In mathematical language, this is the derivative of the reciprocal of the function with respect to time, or the derivative of the logarithm of the function with respect to time.

The rate of growth of [net] output (ND) in sectors p and u will be denoted by T_p and T_u, and that of total [net] output by T. The rates of growth of K, K_p, K_u, S, S_p, S_u will be denoted by G_k, Gfcp, G_ku, G_s, G_sp, G_su.

Finally, the ratio K_u/K_p is denoted by the symbol I_k. This ratio characterizes the potential of the entire productive apparatus for the expansion of reproduction and is the basic index of the structure of the productive apparatus of a country with given S_p and S_u.

As the basic index of the structure of production we consider the ratio

From the previous definitions of effectiveness of capital utilization and of rate of growth, the following formulas are deduced:

Similarly,

This indicates that the rate of growth of total national income and of its parts equals the sum of the rates of growth of the corresponding capital and of the effectiveness of its utilization. These formulas indicate the dependence of T [and of T_p and Tj upon the increase of the corresponding capital and of the effectiveness of the use of this capital, but they do not give the interdependence of the rates of growth of the two sectors. This will be discussed in succeeding sections.

On the other hand, ND = n · e, where n stands for number of workers employed in production and e for the output per man. By analogy it is easy to deduce that

Therefore the rate of growth of capital and of its effectiveness, of the labor force employed in production and of its productivity, determine the rate of growth of production.

These relationships will be discussed in more detail in what follows. It will now be shown only that, if there is a labor surplus, the rate of growth of production is determined by the rate of growth of capital and of the effectiveness of its utilization.

With a limited labor force, the rate of growth of production is determined by labor productivity, because in this case the growth of the effectiveness of capital utilization is inseparably connected with the growth of labor productivity, since the effectiveness of capital utilization can be expressed in the following way:

and

The numerators of both expressions are equal, and this defines the relationship between e and S.

2. CONSTANT TOTAL CONSUMPTION (ND_p CONSTANT)

We begin with the analysis of amortization due to obsolescence under conditions of constant total consumption in order to clarify the influence of obsolescence on productive processes, independently of any general expansion of reproduction.

With constant consumption and constant percentage replacement of equipment, it can be assumed that ΔK = 0 and ND_U = A_m, since the production of sector u serves either to replace obso^ lescent equipment or to increase the productive apparatus, and the need for the latter is obviated by constant total consumption and a stable rate of replacement of equipment.

Then

where a is the percentage of capital replaced annually because of obsolescence. Thus f (I_k, a) is a hyperbola, and S_u = a when I_k = ∞ [i.e., S_u = a/I_k + a is a hyperbola, with asymptote a]. Hence a, the rate of amortization due to obsolescence, cannot exceed S_u.

Now the total value of consumption can be defined by

ND_p = S_p · K_p.

If Sp, the effectiveness of utilization of capital K_p, is fixed, then Kp must be constant if ND_p is constant. Under these conditions the percentage rate of capital replacement a is a function of the ratio I_k, which is a basic index of the structure of the productive apparatus of a country with given S_p and S_u.

For clarify, Figure 2 presents graphically the dependence of I_v on a for various values of S_u.

fig.2

This graph also reveals that capital invested in sector u must grow, even with constant total consumption, if the rate of replacement of the productive apparatus increases, and that it must grow most rapidly when the effectiveness of capital utilization (SJ is low.

Thus an increase in the rate of replacement of capital necessitates a significant and rapid increase either of utilization of equipment or of the productive apparatus of u, even when total consumption remains constant.

The last conclusion can also be based on the following considerations.

The dependence of the structure on the rate of amortization due to obsolescence is given by the formula:

But the quantity of newly expended labor constant labor productivity) according to:

ND = ND_p + ND_u.

Hence with constant S_u, S_p, and ND_p, the increase of ND_u, consequently also of ND, will inevitably be determined by the increase of a. The amount of expended labor must also increase while equipment is being replaced, even with constant total consumption, and only then can an increase in labor productivity be obtained (except by organizational measures, of which that formula takes no direct account).

According to data on American industry, the effectiveness of capital utilization (S) in leading capitalist countries has not tended to increase during the last decade. Since we are going to go through an analogous stage of development, this could also be true in the future in our country, if we followed blindly in the footsteps of capitalist economies. Particular attention should be devoted to increasing the effectiveness of old as well as of new capital. A change in our attitude toward the problem of the effectiveness of capital investments may result in a significant change in the behavior of the value of the coefficient S, since we have lagged very far behind outstanding industrial nations in the rational utilization of our productive apparatus....

Table 1 and Figure 3 have been compiled to give a clear notion of the degree of dependence on changes in the percentage rate of amortization due to obsolescence, a, and the coefficient of effectiveness of capital utilization (S) of the following ratios:

(1) The ratio of all labor expended in production (S · K) to labor necessary to maintain consumption at a constant level (NDp = constant),

Table 1

Constant Consumption of the Population (ND_p = constant)

(2) The ratio of the value of replaced capital (S_u- K_u) to the value of the production of consumers’ goods (S_p · K_p) with constant NDp.

fig.3

(3) The ratio of the value of capital (K_u) serving capital replacement to the value of capital (K_p) serving the production of consumers’ goods, with the income of the population constant (NDp = constant).

Conclusions from these data are formulated as follows:

(1) the tactions , and increase as a does;

(2) the growth of S_u and S_p is reflected by the rates of growth of us follows:

Maximum results are obtained when S_u and S_p increase simultaneously. Thus even with constant total consumption, a once-and-for-all replacement of industrial equipment must result in an increase in the utilization of the productive apparatus and of the labor force. Following the replacement there must come again a decrease of capacity utilization and a decrease of employment of labor. This means that sharp fluctuations in economic activity are inevitable in a capitalist economy.

Even in our system, the replacement of fixed capital cannot be continuous in every individual enterprise, but with planned regulation capital can be renewed alternately in various individual sectors of the economy, and this will result in greater stability both of a and of the utilization of the labor force.

Let us consider the question that has been analyzed from a somewhat different viewpoint. An increase in the amortization of capital due to obsolescence requires an additional outlay of labor which can be justified only by a corresponding economy in labor outlays following the re-equipment.

Moreover, amortization due to obsolescence requires an increase inthe outlay of labor which is not feasible-with constant total consumption-without a temporary decline of wages, and this is as difficult to bring about as it is to lengthen, even temporarily, the working hours of employed workers and then to shorten them once re-equipment is completed.

In general, constant amortization due to obsolescence can be justified only by a correspondingly constant growth of labor productivity and capital effectiveness.

3. GROWING CONSUMPTION OF THE POPULATION (Closed Economy)

Assume that the percentage increment of total consumption is constant and that there is no amortization due to obsolescence. These conditions may be expressed as follows:

The interrelationships and dependence on each other of the following quantities must be discovered:

These quantities are related by the following equations:

Given these six equations in 13 variables, a broad range of possibilities would appear to exist for the economist to “plan” the economy for a maximum final goal. However, in reality the number of possibilities to choose from for the development of the economy is limited.

First of all, for any year, K_u and K_P must be assumed given. A rolling mill cannot, so to speak, be constructed with the aid of a weaving loom, nor can a rolling mill be adapted for the production of cloth.

The labor force required will not be discussed here, since it is assumed that labor is available in any quantity and composition.

It must also be noted that an arbitrary increase in efficiency of the utilization of K_u and K_p is limited at any given moment by the availability of raw materials. In actuality the planner must take into account many initial premises and realities. This does not lessen the need to discover all the laws which determine the character and degree of the interdependence of economic elements. Furthermore, the longer the period for which the economy is planned, the less the restriction due to the initial situation.

The dependence of T_p on the allocation of accumulation between Kp and K_u, i.e., on their relative magnitudes, will be determined first.

It will be noted that T_p depends on three components: first, on the relative increment of the efficiency of the utilization of capital Kp, i.e., on ΔS_P/S_P; second, on the relative increment of this capital itself; and third, on their product, (ΔK_p · ΔS_p)/(K_P · S_P). The following law can be formulated: in calculating the rate of growth of production by means of terminal [as distinct from, say, average] magnitudes (e.g., of annual change), the rate of growth of consumption equals the sum of the rates of growth of capital and of its effectiveness, plus the product of these rates.

The problem will be developed up to the determination of the possible increments of K_p. With given K_u and K_p, recalling that ΔK_p = ND_u - ΔK_u at any given time, ΔK_p, the increment of the capital utilized for the production of consumers’ goods, will be maximized when ΔK_u is at a minimum and ND_u at a maximum, i.e., when the entire apparatus, K_u, producing means of producition for further accumulation of means of production will produce only ΔL_p when fully utilized.

However, it is not difficult to notice, even without mathematical calculation, that if ΔK_u = 0, then ND_u, and hence also ΔK_p, will remain constant with growing consumption ND_p. Conse-quently, a decline of T_p from year to year will be inevitable. It is quite evident that T_p can be maintained at a given level only if the relationships given for the variables in the six equations are satisfied.

In the ensuing analysis of the equations in this section, S_u and S_p will be fixed, so that the effects of changing them can be traced numerically.

The initial equations now take the following form:

From equations (1), (2), and (5) we obtain:

Thus with constant effectiveness S_P of the utilization of capital K_p, the increment of K_p must be proportional to the increment of consumption. From equations (7), (4), and (3) we obtain:

Thus

and

So, with a constant ratio K_P/K_u, there must be a constant percentage increment, G_ku, of K_u. The magnitude of G_ku is determined by the interrelationships of the variables S_u, T_p, K_p, and K_u.

For a clear picture of the dependence of G^ on the change of the ratio K_p/K_u let the following figures be substituted for the unknowns:

Then

and when

This indicates that, for this value of K_p/K_u, incomes can be increased only by using up capital K_u. If K_p/K_u = 4.7, then G^ = 0. Thus incomes can be increased by 20 per cent without impairing K_u if K_p/K_u = 4.7.

However, this condition is valid only at a given time, since to increase ND_p by 20 per cent (with S_p constant) it is necessary also to increase K_p by 20 per cent. Thus if G_ku = 0, then in the following year the ratio K_p/K_u would become 5.65 and then the rate of growth T_p could be maintained only by using up K_u.

From the same formula,

The graph of the function is a straight line (Figure 4).

fig.4

What is the significance of the unusual fact that the growth of G_ku decreases K_p as a component of total productive wealth? To understand this, it must be recalled that definite interrelationships have been established among all the elements of the economy. By definition, K_u serves must satisfy these requirements. Thus, whatever remains of the production S_n · K_n after deducting the portion needed to maintain the constant growth of K_p and to cover the depreciation of K_u, must be used to increase K_u, without increasing Kp and consumption.

Such production for its own sake is conceivable in a socialist economy only if it is temporary, and if its goal is to raise the structure of the productive apparatus by increasing the ratio K_u/K_p in order subsequently to give rise to higher rates of growth of consumption It must also be noted, however, that the increase of capital in sector u must lead to increased consumption in u, unless there is a corresponding increase in labor productivity or a decrease in wages, or unless there is no accumulation of reserve capital in u for future use. Thus, even with constant consumption in p, an increase in production in u maybe caused either by an increase in production in p, or by an increase in accumulation in p. Mathematically these relationships are expressed as follows:

If α_p and α_u denote the fraction of net output whose purpose is the accumulation of capital, then, by virtue of the hypothesis u depends wholly on production in p,

and

Therefore, even with G_{(1 - au)} = 0 and G_su = 0, G_su can be larger than G_kp only if G_αp > 0 or G_sp > 0.

G_sp > 0 possible w’ith inching accumulation; G_sp > 0 may result from an increase in labor skills, from an increase in the number of man hours (several shifts), or from technological improvements.

In the opposite case [G_ku < G_kp, capital accumulated in category u cannot be utilized. In a capitalist economy such a development leads to a crisis.

But what must be the value of the ratio K_p/K_u so that, with T_p constant, it shall be a minimum and shall satisfy exactly the needs of a fixed, constant rate of growth of total consumption?

These requirements can be satisfied if G_ku = 0 [providing ΔS_u = 0], or if K_u · ΔK_P - ΔK_u · K_p = 0 and, finally,

This shows that, with constant effectiveness of capital utilization, a constant percentage increment, T_p, for all parts of the productive apparatus is necessary and sufficient ior the existence of a constant increment of total income. In our case it is necessary that G_ku = 20 per cent.

However, the additional condition of “proportional growth” in formula (9) transforms formula (8) into

This shows that the ratio K_p/K_u predetermines the possible rate of growth, and that, with fixed effectiveness of capital utilization, the rational development of the economy in the interest of consumption requires a definite relationship between K_p and K_u for any given rate of growth, T_p.

This shows that the ratio The following data in Table 2 are a consequence of this.

Graphically, the function has the form shown in Figure 5.

It is extraordinarily interesting that, with constant effectiveness of capital, the rate of growth of total income cannot exceed a definite limit, namely S_u, the effectiveness of the utilization of capital K_u. Physically this becomes clear if one considers that

Table 2

the means of production produced with K_u cannot exceed what effectiveness, S_u, of the utilization of K_u will permit. ND_U = ΔK_p + ΔK_u cannot exceed the total output S_u · K_u. In our example, S_u = 0.94, and

A fortiori, therefore,

The nature of this curve is of great importance in planning the economy, since it indicates that an increase of K_U/K_P beyond 2 yields [proportionally] insignificant results.

fig.5

The curve also indicates how the rate of growth of income increases as a function of the industrialization of the country at every stage of its development, for the ratio K_u/K_p is undoubtedly one of the primary indicators of the level of industrialization of the country, by virtue of the constantly increasing significance of industry in the contemporary economy. Thus an increase in the rate of growth of income demands considerable industrialization. In order to raise the constant increment of income from 10 per cent to 15.7 per cent, it is necessary to almost double K_u/K_p.

Thus an increase inthe rate of growth of income demands industrialization, heavy industry, machine building, electrification....

It is evident from the foregoing that the growth of S_u is enormously important to the development of rates of growth. Therefore the dependence of T_p on K_u/K_p will be traced for three values of S_u:

Table 3

A graphic representation of these relations is given in Figure 6.

fig.6

From these curves we determine:

(1) that increases in K_u/K_p are particularly effective only up to 1 to 2;

(2) that the rates of growth vary directly with S_u;

(3) that the slopes of the initial sections of the curves, which are of the greatest interest, increase with S_u, and that, as a result, the effectiveness of “industrialization” also increases with S_u....

Up to this point we have considered the rate of growth T_p only as a function of S_u and S_p, the effectiveness of the utilization of capital K_u and K_p, respectively.

But the effectiveness of the utilization of capital K_u and K_p can also be considered from the viewpoint of the distribution of “national income” as a whole. Consider the distribution of “national income,” first, as a result of a change in the rate of growth T_p due to a change in K_u (with constant S_u), and second, as a result of a change in S_u (with constant K_u/K_p).

Consider the ratios

In accordance with the previous argument indicating that

it follows that

In other words, for uniform growth of the entire productive apparatus, with constant S_u and S_P, productive accumulation must be distributed in the same proportions as capital, no matter what the value of T_p. Given the ratio K_u/K_p, these proportions are independent of Su. Therefore, for given constant values of T_p, independently of the magnitude of S_u, we shall have the values of the ratio K_U/(K_p + K_u) shown in Table 4.

This table indicates that a decrease in S_u lowers the rate of growth of income but does not lessen the necessity of allocating capital to sustain a constant rate of expansion of reproduction. Thus the table underscores anew the tremendous significance of full utilization with maximum effectiveness of the capital at our disposal in order to raise the income of the population.

This is the source of the slogans calling for rationalization of the economy and for multishift production.

However, it must be noted that, by hypothesis, K_u and K_p inelude not only fixed capital but also circulating capital. Raising Sp and S_u usually necessitates increasing the circulating capital. It is therefore appropriate to consider the following possibilities:

Table 4

(1) S_p and S_u increase, but in such a way that the ratio K_u/K_p remains constant. Then the growth of T_p, according to formula (7) on page 188, is given by ΔS_p/S_p and by the increment obtained from formula (9) on page 192;

(2) S_p and S_u increase, but in such a way that K_u/K_p also increases by virtue of a greater increase in S_u than in S_p.

Then the growth of T_p is again given by formula (7) on page 188, with an increased contribution from formula (9) on page 192. Meanwhile, the industrial structure of the economy is strengthened.

(3) S_p and S_u increase, but K_u/K_p decreases by virtue of a greater increase in Sp than in S_u.

In this case T_p will still increase, but it will be moderated to an unknown extent by the decrease in K_u/K_p. Determining the extent of this moderating effect requires further analysis.

Consider again the ratio

The values of the ratio ND_u/(ND_u + ND_p) for nine cases are shown in Table 5 (T_p and ND_u/ND in per cent).

For clarity, T_p and ND_u/ND are presented in Figure 7 as functions of the growth of the index of “industrialization” of the country, K_u/K_p.

Table 5

What deductions can be made from the series of figures and graphs introduced?

(1) The larger the S_p, for a fixed S_u, the smaller the portion b(2) With a fixed portion of national income allocated to productive accumulation and a fixed S_u, the rate of growth of income (T_p) increases with S_p. However, this increase of T_p with S_p depends on a higher level of industrialization of the country.

The foregoing analysis does not exhaust the problem, because it fails to give any indication of the extent to which it is advantageous (in quantitative terms) to change the value of T_p to a larger one, whether by means of an increase in the ratio K_u/K_p or by means of an increase in S_p and S_u, which, in turn, depends on an increase inthe ratio of circulating capital to fixed capital. Neither does it indicate where it is most advantageous to direct our efforts in the first instance: whether to increase S_p or S_u, and consequently whether to attempt to increase the circulating capital portion of K_p or of K_u.

However, on the basis of the relationships introduced, it is possible to conclude that the following, in the order given, are necessary for achieving the maximum rates of growth within the shortest period:

(1) maximum utilization of K_p, increase of S_p, and expansion of the circulating capital in K_p;

(2) maximum utilization of K_u and increase of S_u inthe same sense as in (1) above;

(3) increase of the ratio K_u/K_p.

These requirements will be illustrated by a rough example taken from Table 5 and Figure 7.

fig.7

Assume that the consumption of the population (ND_p) grows at the rate of T_p = 8.1 per cent annually. Assume also that it is desired to double the rate to 16.2 per cent.

(1) This can be achieved by increasing S_p by 8.1 per cent (see formula [7]). Assume now that circulating capital is proportional to S_p and that it forms 20 per cent of all capital K_p. To increase S_p by 8.1 per cent, K_p must therefore be increased by 1.62 per cent.

(2) If it should be desired to increase T_p from 8.1 per cent to 15.7 per cent (a somewhat smaller increase than before) by increasing S_u, then S_u would have to be increased by [slightly less than] 100 per cent. In Table 5, Une 2, T_p = 15.7 corresponds to the ratio K_u/K_p = 2. Assuming that circulating capital constitutes, as above, 20 per cent of K_u, and that it is proportional to Su, a 20 per cent [100 percent] increase in S_u requires a 20 per cent increase in K_u and [this Implies] a 4 per cent increase in K_p.

(3) Finally, assume that it is desired to increase T_p by “industrialization” of the country, i.e., by increasing K_u/K_p. Table 5 indicates that an increase in T_p from 8.1 per cent to 16.2 per cent, with S_p = .485 and S_u = .485, requires an increase in K_u/K_p from 0.2 to 0.5. With constant K_p this implies increasing K_u by a factor of 2.5, or 250 per cent. Expressed as a fraction of K_p, this increase in K_u forms 0.30 of K_p.

Thus, doubling the rate T_p (from 8.1 to 16.2) requires the allocation of capital from the entire national income to implement the following increases:

S_p to be increased by 1.62 per cent of K_p;

S_u to be increased by 4.0 per cent of K_p;

K_u/Kp to be increased by 20.0 per cent of K_p.

This numerical example gives some indication of the extent to which the foregoing arguments are correct. This example, it must be understood, does not settle the question, since it does not account for those outlays which are connected with the increase in the labor force (workers’ homes, etc.).

Of course, there is a limit to the increase in S_p and S_u. From United States data we know that S_p and S_u do not have an intrinsic tendency to grow. However, in our case, there are still considerable opportunities for raising S_p and S_u, both by the introduction of multi-shift work and by the rationalization of production....

“K teorii tempov narodnogo dokhoda,” Planovoe khoziaistvo, 1928, No. 11, pp. 146-171.

[Note of the editor of Planovoe khoziaistvo:] The present work is a report presented by the author (a worker of the World Economics Section of the Gosplan of the USSR) before the Commission for the General Plan of the Gosplan of the USSR, concerning the question of the interrelationship of the rate of growth of reproduction of individual sectors of the economy among themselves and of the structure of the reproduction process as a whole.

Certain typographical errors in equations in the Russian text of this article have been corrected.-Ed.

1. Fel’dman uses in this article, in preference to the usual Marxian symbols, the following notations:

2. By efficiency of capital utilization we mean the ratio of the value of net output per unit of time to the value of the fixed and circulating capital in a given enterprise or sector. Both value of net output and capital must be expressed in terms of the cost of reproduction as of the same time.

3. This division is realizable only by the accounting method and does notcorrespond to the actual breakdown of production according to enterprises. Analytical evidence of the practicability of the proposed division is not introduced in this article, but in another one specifically devoted to this subject. [Fel’dman, “Analiticheskii metod postroeniia perspek-tivnykhplanov,” Planovoe khoziaistvo, 1929, No. 12.

4. Marx, Capital, Vol. II, Book 2 (Gosizdat, 1922), p. 413.

5. The ensuing analysis assumes constant prices.