G. A. Fel’dman

ON THE THEORY OF

GROWTH RATES OF NATIONAL INCOME, II

4. THE INTERDEPENDENCE OF THE RATES OF GROWTH OF THE QUANTITIES ND_p, ND_U, S_p, S_u, K_p, K_u IN THE GENERAL CASE

...Use of differential calculus introduces new mathematical content into the concepts of national income, increments of capital, and rates of growth, especially by use of the concept of an infinitely small change or shift in a quantity during an infinitely smalltime interval. In what follows, we are no longer concerned with national income produced in a year, but with the “rate” of production of national income at any given instant, with an infinitely small increment of crystallized human labor as a function of an infinitely small increment of time.

The velocity of this production at any given instant can be measured by the magnitude of the national income which would be obtained if it were produced at a given constant rate all year. This, however, gives only the velocity of production-the volume of output divided by time-at given instant.

The same is true of the growth of capital: the formulas give only the velocity of the growth. The rate of growth is defined as the ratio of the acceleration per unit of time to the velocity at a given instant.

It will be assumed for the present that there is no amortization due to obsolescence. The limiting conditions (see section 3) of the equations will also be discarded, and it will be assumed that the rates of growth G_ku and G_kp, can be maintained by increasing S_p anda_p, i.e. by increasing toe effectiveness of capital and the portion of output channeled into accumulation....

and

Four basic equations in differential form will represent the basis for the ensuing analysis.

Four basic equations in differential form will represent the basis for the ensuing analysis.

The following have also been defined:

The following are also known from the first part:

These equations hold whether the rates of growth are positive or negative.

These formulas raise the paradoxical possibility that an increase in productive capital may result in a lowering of the rate of growth of income as the effectiveness of capital utilization decreases. From this it is clear that an increase in labor productivity can increase the rate of growth of income only if it results ultimately in an increase in the effectiveness of capital utilization. Yet such a connection is far from compulsory, since frequently an increase in labor productivity is purchased at too high a price. We shall return to this question again in what

The interdependence of the rates of growth of capital in sectors p and u is expressed as follows:

and

or

or

The first conclusion that must be drawn from this formula is that if the rates of growth are to be increased, with S_u constant, the ratio K_u/K_p = I_k (see section 3) must also be increased. The following relationship between the rates of growth of output No special limiting conditions have been placed on the size or behavior over time of the rates of growth G_ku and To this end, differentiate the equation:

No special limiting conditions have been placed on the size or behavior over time of the rates of growth Gku and Gkp and the functional relationships will therefore be analyzed for arbitrary G_ku, G_kp, and S_u.

To this end, differentiate the equation:

Thus:

where

or:

With no amortization due to obsolescence, this is the most general formula expressing the interdependence of the rates of growth and their changes for all variables of interest.

That Gkp and G_ku determine the rate of growth of total consumption follows from the equation T_p = G_kp + G_sp and the differential equation

or

Substituting for T_p from the first equation gives

T_p is thus a function of the variables G_kp and G_sp and their rates of growth.

If G_sp is constant, the formula becomes

If G_sp = 0, then and T_p = G_kp.

Thus we have shown an* extremely close dependence (even equality, with S_p constant) of T_p and on G_kp and .

The fact that the right-hanã side of the quation of growth rates (1) consists of the sum of G_kp and G_kp determines the character of the dependence. If , then G_kp increases, but remains less than the left-hand side of the equation. However, if the left-hand side of the equation increases at the same rate as G_kp, then G also increases the same rate.

If the left-hand side of the equation increases faster than Gkp, then must also increase faster than G_kp. Only in the case when the left-hand side of the equation increases more slowly than G_kp does decrease to zero; having attained a maximum, G_kp stops increasing.

Consider first the case when the sum of the second and third terms of the left-hand side of the equation is zero.

There is nothing impossible in the existence of the equality:

The experience of recent decades in the United States has indicated that the variables Gsu and G_ku have negative values. But it is not impossible for these variables to take on positive values under certain conditions. It is entirely possible to establish a constant rate of growth, G_ku, and in that case G_ku will be zero. The same is also true of S_u and G_su.

When , the general formula for the rates of growth is transformed into can increase, and hence can be positive only as long as . At the same time, if , _ku may also be growing.

What are the limits of the general increase of the capital of sectors p and u and of the rate of this increase?

In order to clarify this question, the equation

is transformed into

with the aid of

Consider these equations when G_su = 0. Then

If G_ku increases, diminishes gradually and most ultimately become zero. Now, on the right-hand side of the equation, Kp and G_kp increase gradually, while Gkp remains constant in the extreme case. The numerator must therefore generally be positive. In the denominator, G_ku can be no greater than S_u. Thus, when the left-hand side becomes zero, the equality can be preserved only if Ku goes to infinity.

This is clearly a limiting case and one that is of only theoretical interest, but it clarifies the nature of the given function. As G_ku increases and approaches S_u in magnitude diminishes, and it becomes zero, in the limiting case, when G_ku = S_u.

Thus the rate of growth of capital K_u is limited by the effectiveness of the utilization of this capital. The growth of S_u and G_su can increase this limit.

, then at the limit .

G_ku = S_u is also the limit of G_kp, and when G_sp = 0, the limit of T_p is zero. These limits are attained as K_u increases to infinity. However, S_u is the limit for G_ku and G_kp not only when K_u = ∞. It may be noted from the equation

that when G_ku = S_u, and K_p and K_u approach their limits, G_kp = 0. This indicates that, even when the entire production of sector u is used to increase K_u, the rate of growth of K_u cannot exceed S_u. This is also apparent from the equation ND_u = S_u · K_u, or

These considerations indicate that there are various possible ways of raising the rate of growth of the capital of sector p.

(1) A fixed, constant rate of growth can be established for the capital of sector u. With a given initial ratio K_u/K_p and a fixed value of S_u, the initial rate of growth G_kp is determined by the equation

G_kp will increase until it equals G_ku. I_k = (K_u/K_p) increases gradually to the limit

(2) Given an initial value for G_ku (which must be greater than G_ku, its later values can be predetermined. Thus it may be arbitrarily determined how and when G_ku shall attain a desired magnitude, and when it shall become zero. In case (2) the initial magnitude of G_ku might be larger than in case (1), but the projected magnitude of G_kp can be attained over an extended period of time. The policy maker must determine the rate of growth G_kp, and consequently also Tp, which is acceptable and desirable, and the final magnitudes these rates are to attain. Technicians and statisticians must provide indications as to the coefficients of effectiveness which are attainable, and in what periods of time. Then the social planner can formulate a plan of development for the economy.

The calculations so far have not taken the labor force into account. But the limited growth of the labor force with insufficient growth of labor productivity will serve as a limiting condition, though a distant one. This question will be examined in the next section.

So far has remained positive in all cases, approaching a limit of zero in the process of development. Thus the rate of growth of the capital of sector p was taken to be increasing, but approaching stability in the process of development. With constant S_p, total consumption must vary as K_p.

T_p = G_sp + G_kp. So, with constant G_sp, T_p = constant + G_kp. But implies that, if Su is constant and , then G_ku > G_kp [equation (1)] up to the limit, i.e. that a relatively larger proportion of productive accumulation is directed to se c tor u than to sector p.

We have thus an increased industrial (“rate of growth”) structure of the productive apparatus, leading at the limit to a stable growth of the industrial (“rate of growth”) structure.

With constant S_u this would indicate [equation (1)] that

is possible under the following conditions:

(1) If , i.e. if the rates of growth of capital of both sectors u and p diminish. Depending on whether the rate of decline of G_kp is greater or less than that of G_ku, either G_kp will approach G_ku and the deterioration of the industrial structure will cease when G_kp = G_ku, or such a state of equilibrium will recede. In the latter case the deterioration of the productive apparatus will continue indefinitely. This would indicate that the rate of growth selected for K_p is beyond the capacity of the economy to sustain.

only if

or

Whereas under our conditions, and very likely also in other countries, K_u is less than K_p, G_ku is, by hypothesis, less than G_kp. Now must be many times greater than , and this leads to a rapid lowering of the rate of growth of K_u, until G_ku becomes negative and any further growth of K_p is possible only at the cost of decreasing Ku. This is the case of rapid deterioration of the industrial structure of the productive apparatus of the country, and of its being brought to a condition in which G_kp = 0 and K_u = 0.

if

It is not difficult to prove that this is the case when the deterioration of the industrial structure of the apparatus comes toan end. G_ku increases, while G_kp decreases. At the limit, G_kp = G_ku and equilibrium will be reestablished with a lower rate of growth G_kp, but with a stable industrial structure of the productive apparatus.

Changes in S_p and S_u may radically alter relationships in the development of the productive apparatus. This is apparent from the equality

With a given productive apparatus, the ratio between accumulation and consumption changes in favor of the former as S_u increases-and the index of the productive structure [I_nd] is in creased. An increase in I_nd is possible even if I_k is decreased. On the other hand, if S_p is increased, the structure of production can be preserved only if I_k or S_u is also increased. This does not mean that an increase in S_p leads to a decrease of ND_p; rather, if NDP increases at the cost of the growth of S_u, any further increase of the rate of growth T_p, or even its maintenance at the new level, is impossible without an increase in S_u or I_k.

We may soon arrive at this point in our own development if T_p continues to be maintained at a high level by means of a rapid growth of S_p and S_u, unless we also concern ourselves with increasing I_k.

The economy in which

deserves particular attention. The preceding analysis indicates that all development of the economy leads to this at the limit. This situation is the only condition of dynamic equilibrium which can last indefinitely, leading neither to conflicts nor changes. It will therefore be called “the condition of stable and harmonious, or proportional, dynamic equilibrium of the economy” or, briefly, the condition of “harmonious development.”

Under full utilization of capital K_p and K_u, at a given level of technology, S_u will have a maximum and constant value. Departure from a condition of harmonious development may result from technological discoveries, from an increase in The last is not feasible without decreasing, and even temporarily interrupting entirely, the growth of K_p and the increase in the supply of consumers’ goods. Thus under full utilization of capital, and with both population and consumption increasing, it is rather difficult to get along without some straining of the market at a time of transition to a higher industrial level. Thus the task of increasing the effectiveness of utilization of capital, S, becomes more pressing....

5. CONDITIONS OF “HARMONIOUS DEVELOPMENT”

With constant S_u and Gkp = Gku, equation (1) on page 308 gives

and

Since both both K_u and K_p are by nature positive, this condition shows that G_kp and G_ku cannot both grow under conditions of harmonious development when S_u is constant. This is also apparent from the basic equation relating G_ku and G_kp,

Simultaneous growth of G_kp and G_ku is not feasible if S_u and K_p/K_u are constant. With constant K_p/K_u, G_ku and G_kp may grow simultaneously if S_u increases correspondingly.

These conditions were examined in section3. Let the concept of harmonious development be extended to the case when I_k is constant and S_u varies.

Similarly, it can be proved that .

Then, if G_ku and are replaced by G_kp and equation (2) (p. 308) takes the form

At the initial moment,

6. DISHARMONIOUS DEVELOPMENT WITH CONSTANT RATES OF GROWTH

Consider again the fundamental equation:

using

and differentiating the fundamental equation with respect to t,

Therefore

By equations (1) and (2),

and, finally:

Therefore

and, since

Although derived under the restriction that all rates of growth are constant, these formulas disclose the process of expanded reproduction in all its complexity, since for short periods of time the rates of growth can be taken to be actually constant. These formulas again confirm that the quickest and most effective way to increase T_p is to increase first S_p and G_sp, then S_u and G_su, and finally i/and I_k and I_nd. The last is possible*even when G_sp and G_su are zero....

With constant T_p,

where ND_po is initial total consumption. Together with equations (3) and (4), equation (5) gives the law of growth for total consumption when the ratio of growth of all the variables is constant.

It must be noted that when the rates of growth [G_ku and G_kp are constant but unequal, I_k changes continuously.

In the case when , and S_u, I_k, and G_su are all variable, the following differential equation gives G_kp :

7. RATE OF GROWTH OF TOTAL CONSUMPTION. DISTRIBUTION OF INCOME AMONG DIFFERENT GROUPS. WAGES AND LABOR PRODUCTIVITY.

Up to this time the productive process has been considered without regard to the labor force, labor productivity, and the distribution of national income. Yet the necessity of allocating consumers’ goods to persons not employed in productive labor, and at the same time of maintaining and increasing the wages of the workers, creates additional conditions for the development of the reproductive process.

Denote the consumers’ goods distributed among persons employed in productive labor by ND_pv, and the consumers’ goods distributed among all the rest of the population by ND_pm.

Then

or

where V_p is an arbitrary coefficient.

If the number of persons employed in productive labor is denoted by n, labor productivity by e, and the real wage by nd_pv, the following equalities hold:

where V_e is an arbitrary coefficient.

From equations (1) and (2) and from the preceding,

whence

Consider now the dependence of the effectiveness of capital utilization S on labor productivity.

The total production is given by the expression S · K. Since e denotes labor productivity, and n the number of workers,

S · K = n · e

and

In particular

and

or

where k_n denotes capital per man employed in production.

Thus the effectiveness of capital utilization is determined also as the relations between labor productivity and capital per worker.

In the last analysis, the rate of growth G_kp = T_p - G_sp as a function of the distribution of national income, of labor productivity, and of capital per worker, is determined by the following expressions:

The following deductions can be made from these formulas: (1) increasing the rate of growth of total consumption is a function not only of an increase in the productivity of labor, but also of the ratio of labor productivity to capital per worker; (2) the rate of growth of total consumption varies inversely with the proportion of the national income represented by consumption, and directly with accumulation....

Note that the higher the ratio of wages to labor productivity (Ve), and the smaller the proportion (Vp) of total consumption going to the working masses, the smaller the rate of growth of income.

However, oversimplified deductions from these propositions should be avoided. The fact is that both labor productivity and the effectiveness of capital (S) depend to a very considerable degree on the scientific, educational, and regulative apparatus of the country, and a decrease in ND^ may under our conditions create the most cruel conflict, due to the lack of skilled workers in our country and the weakness of the accounting, regulating, and planning apparatus of the government.

Only the study of the experience of industrial countries and of our experience can solve the question of the correct size of V_p. For obvious reasons, the necessary outlays for defense cannot be determined mathematically.

So far the analysis has been carried out under the assumption that a labor surplus exists, and this assumption will also hold in what follows. It is assumed that with significant unemployment in the country and with continuous rural overpopulation, when for millions of workers in our country there is no other productive equipment than such things as work gloves and shovels, there is a shortage not of labor force but of tangible capital. Under such conditions, the rate of capital accumulation and effectiveness of capital utilization determine the rate of growth of national income.

Nor can the availability of skilled labor serve as the limiting condition, since present-day mass production is based on finer divisions of labor and makes possible the rapid adaptation to work of the peasant masses coming in from the villages. The training of skilled labor force is not a problem comparable with the availability of basic material investments.

Consider all the conditions under which the available labor force may prove insufficient.

In general,

Then

and if

then the growth of national income is determined by the equation

If G_e + G_n < G_s + G_k, the growth of national income is determined by the equation

In this last case, the system of fundamental equations determining the rates of growth remains the same, but two additional independent equations are obtained:

To determine the growth of n_p and n_u is not very laborious; our economists have repeatedly predicted the growth of population and its structure. The task is a more difficult one in the case of labor productivity. In going from a very backward technology to a highly technical organization such as that of industrial nations, by concrete reconstruction of the economy, it will be possible to determine both e and n for the coming years and, possibly, for a couple of decades. But when planned economy assumes the leadership in world technology and the labor force is utilized to the limit, then the prediction of technical improvements will be a pressing problem and the forecasting of technical reconstruction will be central to all planning.

The rate of growth of consumption, T_p, will be expressed as a function of the increase in consumption due to the increase of the number of workers, and of the increase in wages which will inevitably accompany expanding production if the unemployed masses are to receive a smaller share than the employed workers.

where nd_pv, as before, is the average real income (excluding savings) per man employed in production.

Then

and

Then

and

This formula expresses the dependence of T_p on labor productivity, wages, number employed in production, and the consumption of nonproducers.

8. AMORTIZATION DUE TO OBSOLESCENCE

In section 2 the relationships of the elements of the economy were expressed in terms of the replacement of equipment when the output of consumers’ goods is constant.

The dependence of the rate of growth of consumption on amortization due to obsolescence will now be traced. The limiting condition will again be that the rates of growth and amortization due to obsolescence be constant.

Recall that K_u + K_p = K. If amortization due to obsolescence constitutes, per unit of time, a proportion a of K, then the production of sector u must, during that interval of time, provide a · K for the replacement of capital depreciated through obsolescence. Then

Now, the first derivative of Gm equals zero, so that

Therefore

Thus amortization due to obsolescence is immediately reflected in a decrease in the rate of growth of real income, unless there is a corresponding increase in G_sp, and G_su.

The dependence of G_sp and G_su on the effectiveness of the utilization of the capital per man employed in production was demonstrated in the preceding section; it is necessary now to dwell on the question of the structure of the capital.

We observe that

If S is to be increased, the growth of e must surpass the growth of k_n; k_n consists of productive equipment k_nt and of circulating capital k_no. It is reasonable that labor productivity e shouldgrow proportionately to the value of productive equipment k_nt . Therefore e/k_n can increase if the circulation of the circulating capital, k_no, is accelerated, while its growth remains less than the growth of eandk_nt.

Acceleration of the rate of work can also be reflected in relative diminution of k_nt with the same output. A characteristic example of this appears to be the transition from a low-speed steam engine to a rapidly revolving steam turbine. The rise in the price of machinery, which is due to the greater complexity demanded by the increasing automatization of production, is an influence in the opposite direction.

Two opposite but equally erroneous views of this question exist. Some think that an increase in the effectiveness of capital utilization inevitably accompanies any technical improvement of production and increase in labor productivity. It has been shown above that this depends not on an increase in e, but in e/k_n, which is far from the same thing. In a capitalist economy, entrepreneurs are preoccupied not with increasing e/k_n> but with increasing profit. Profits can be increased because the value of labor per unit of output (with constant wages) decreases with the increase of labor productivity, even without a decline of the ratio of constant capital to the value of output. Surplus value increases as variable capital decreases. One must not forget that the effectiveness of capital utilization, with a given number of hours of utilization, a given degree of labor skill, and constant prices is a technical coefficient, and not a purely economic category, and is not purely a function of the structure of capital....

The second erroneous view involves the assumption that raising the organic composition of capital must inevitably lead to lowering the effectiveness of capital utilization. This is true only when prices are falling, and then only if the technical factors operating to increase the effectiveness of capital utilization fail to resist the decrease in the value of labor and in surplus value per unit of production.

To repeat, the effectiveness of capital utilization is, in this treatment, which represents economic processes in constant prices, a technical coefficient whose growth is not controlled directly by the laws of capitalist development. Under our conditions it has a tremendous significance, and the socialist economy must cause its growth.

However, this causal relationship is not something so basic as to be taken for granted.

We have become accustomed to the absolute importance of profit, and all technical processes in the capitalist economy are determined by the law of maximum profit. By adopting the improved techniques of the leading countries without analysis, and without application of the criterion that has been developed, we would risk falling far short of doing all that could be done in approaching the problem correctly. In this connection, amortization due to obsolescence without a corresponding increase inthe effectiveness of capital utilization represents a particular danger....

9. GROWTH RATES UNDER CONDITIONS OF FREE WORLD MARKET RELATIONS

...In a closed economy..., the structure of the entire productive apparatus K predetermines to a considerable extent the ratios

The situation differs somewhat under free external relations. Any portion of ND_p can be exchanged in foreign markets for an equivalent quantity in terms of world prices, of the products in ND_U. (This is understood to be so unless prevented by the capacity of foreign markets and competitive conditions.)

Therefore, if it is considered only from the viewpoint of production, the value of K_u/K_p may be selected arbitrarily in any given case. The only limitation is the necessity for a definite minimum satisfaction of the consumer wants of the population, and this predetermines the size of

The entire residual, K - K_p, can be utilized either for direct production of new physical capital, or for production of goods which maybe exchanged abroad for goods to Ee used in increasing capital K_U and K_p .

Thus, having analyzed the various relationships mainly in terms of the ratio I_k in a closed economy, and belüg interested to a large extent in the rates of growth of capital G_kp and G_ku, then under free external relations we should turn our attention largely to the ratio

The basis of the ensuing analysis will be the equation

which is obtained from

Consider the meaning of equation (1) under increasingly complicated conditions, starting from simple cases.

(1) Let S_u = constant, S_p = constant, S_u = S_p, G_sp = G_su = 0 and Tp = T_u.

Then equation (1) becomes

Tp and T_u increase with S_u and are an inverse hyperbolic function of S_p/S_u and I_nd .

Under these conditions it is advantageous to export what is produced with maximum efficiency, and to import what is produced with minimum efficiency.

The following expressions are obtained from the equation:

Thus with constant and proportional growth of the whole national income and of its parts, and with equal and constant effectiveness of capital utilization in sectors u and p, the rate of growth of national income is proportional to the portion of national income going into productive accumulation and to the effectiveness of capital utilization.

Then

If T_p = T_u and I_nd = constant, then T_p = T_u increases with G_sp. The larger I_nd is, the larger is S_u.

(3) Let T_p = T_u.

Then

Setting βG_sp = G_su, the equation takes on the following form

[This equation is valid, with G_su, in the first term instead of G_sp only if the substitution made is βG_sp = G_su, insted of βG_su = G_sp -Ed.]

This equation is of a more general form than the preceding one. For β the equations are identical. If β > 1, T_p = T_u will be larger than before, while if β < 1, the reverse is true.

With free foreign trade, I_nd can be chosen arbitrarily. The larger I_nd, the higher the rates of growth, but the less the initial satisfaction of the wants of the population.

(4) Consider the case G_kp = T_p - G_sp + constant and G_ku = T_u - G_sp + constant.

Equations (1) and (2) [p. 308] are now modified as follows. It is shown in section 6 [p. 315] that in this

(5) Finally, consider the relationships of the rates of growth under a single limitation-that the effectiveness of capital utilization be constant (G_sp = G_su = 0).

The argument will be based on equations (1) and (2), p. 308

Now

and equations (1) and (2) are transformed into

These expressions differ little inform from equations (l)and (2) [p. 308], and the discussion of those equations can be applied to these in its entirety.

It must be emphasized that the increase of the ratio S_u/S_p is of tremendous significance to the increase of the rates of growth. The greater the effectiveness of the capital used for the production of export goods, in comparison with that of the capital on which domestic consumption is based, the more significant the growth of consumption.

Under capitalist encirclement, we must make every effort to industrialize our country within the shortest possible time. Therefore our development must correspond to a large extent to the conditions of a closed economy.

However, what has been derived in the present section must be taken into account to some extent even under our conditions of development, in order to determine our viewpoint on the development of the export branches of our production.

A warning is necessary against possible errors in connection with the determination of the coefficient of the effectiveness of capital utilization. It must not be forgotten that effectiveness is determined by the ratio of the value of net output to the value of all capital. The error is often made in this connection of taking the ratio of total value of output to the value of a part of capital. Naturally, this leads to completely distorted results.

10. EXAMPLE OF A PROPOSED PARTIAL APPLICATION OF THE METHOD OF INVESTIGATING GROWTH RATES OF NATIONAL INCOME...

The experience of past years provides some foundations for planning for the future. This experience becomes more necessary as we can depend less on some finished “theory of planning,” on a worked-out, logically finished method. During past years definite rates of growth of the national income have been observed. It is now proposed to determine the extent to which these rates of growth resulted from the increase of capital and from improved utilization of that capital. The answer is of considerable interest since it will facilitate determining the extent to which national income can continue to be increased in the future by improved utilization of the available capital. The material for this investigation will consist of the Control Figures for 1927/28.

On the basis of the material now available, it is not possible to classify p and u in accordance with the preceding exposition, and we must therefore consider total production and total national income as a whole. As indicated in section 1 (Part I) of this article, this will give the work a conditional character. Nevertheless, if the fundamental results obtained from the following calculations sufficiently reflect reality, it will be impossible not to take them into account.

The ensuing calculations are based on the equation

and the difference equation that follows it:

Thus any increment of national income is divided into three basic parts. The first part, S · ΔK, is determined by the increment of productive capital. The second part, · K, is determined by the increase in the effectiveness of utilization of capital. The third part, ΔS · ΔK, results from the increase of both S and K, and is the least significant. It is the interrelationships of these three parts that are of interest.

It is necessary to emphasize that the values of S and obtained by calculation are average statistical values and do not fully reflect true conditions.

More realistic would be the equation

since the increment of the utilization of old capital, AS,, need not equal the increment of utilization of new capital [ΔS_nov].

The error obtained is not great. In the first place, by performing the calculation uniformly for all years compared, an established trend will be revealed without regard to errors. Inthe second place, from the experience of the United States it is known that as industry develops, S does not tend to grow, so that if it does grow under our conditions, it will do so mainly because of general causes, and for all capital as a whole, because of rationalization and an increase in the number of hours of utilization of all capital. Therefore the estimate of the relationships would yield a sufficiently true picture even by use of a statistical average....

[The total income in current prices of the USSR, net income of the socialized sector, and price indices are given in the Control Figures for 1927/28.] Table 6 has been compiled on the basis of these data.

The table of “Fixed Capital of the Economy,” in the Control Figures for 1927/28, may be used to evaluate the behavior over time of national wealth. All capitals are valued in 1925/26 prices. (See Table 7.)...

[With S = ND/K. the following values can be obtained from data in the tables on p. 330-Ed.]

S(1924/25) = 0.53140

S(1925/26) = 0.61642

SU926/27) = 0.65032

SU927/28) = 0.68866

ΔS(1924/25) = 0.08502

ΔS(1925/26) = 0.03390

ΔS(1926/27) = 0.03834

On the basis of these data, numerical coefficients can be inserted in the difference equation

For the three intervals (1) 1924/25-1925/26, (2) 1925/26 -1926/27 and (3) 1926/27-1927/28:

Table 8, compiled from these equations, gives some idea of the rate of growth of national income, and of the extent to which growth was due to the increase of capital and to the increase of the effectiveness of capital utilization.

The calculations yielded rather interesting results. It will be noted that increasing the effectiveness of capital utilization remains extraordinarily significant, and in 1926/27 it still surpassed new capital formation in importance. Yet between 1924/25 and 1927/28 S increased only from 0.53 to 0.69, or by 30 per cent. We believe that there remains ample room for further improvement, and we do not consider it impossible to raise S to 1.5.

Table 6

Table 7^a

Table 8

This presents tremendous possibilities for maintaining the rate of growth of the country’s income until the ratio K_u /K_p can be increased, i.e., until a much higher degree of industrialization has been attained. Apparently the main task of our planning organizations must consist specifically of regulating the growth of Sp, S_u, and K_u/K_p.

We believe that, with the aid of the models outlined in this article, the problem that confronts us could be successfully solved....

This is the second part of the article “K teorii tempov narodnogo do-khoda,” Planovoe khoziaistvo, No. 12, December, 1928, included in our section Macro-economic Models. For the list of symbols see page 175.

Certain typographical errors in mathematical symbols inthe Russian text of this article have been corrected.-Ed.