S. Rozentul

FORMULA OF EFFICIENCY OF CAPITAL INVESTMENT

WHAT IS MEANT BY “EFFICIENCY” OF CAPITAL INVESTMENT

Despite the fact that, with the intensification of the reconstruction of our national economy, the problem of the efficiency of capital investment has acquired major importance, we still do not possess a sufficiently elaborated formula for the quantitative determination of that efficiency, nor does the very concept “efficiency of capital investment” have a firmly established meaning. Thus some people consider it as a cost reduction achieved through investment outlays, others as an increase in profits, still others as labor-saving or as an increase in the volume of production, etc.

In order to produce an exhaustive definition of the concept of efficiency of capital investment, we must first establish the point from which we are studying it. From the viewpoint of a capitalist or of our enterprises operated on a commercial basis, efficiency is measured by the increase in the profitability of an enterprise’s operations owing to an increase in invested capital. From the viewpoint of the labor force, efficiency is manifested in an increase of the wage fund and in the reduction of labor input per unit of production. Finally, from the viewpoint of other physical or legal persons who receive a part of the surplus value of the entrepreneur from the nonproductive expenses, the efficiency will obviously be determined by the size of the increase in these nonproductive expenses.

We shall dwell in more detail on the effects manifested (a) by an increase in profitability; (b) by benefits obtained by the labor forces; and (c) by an increase in income received from nonproductive expenses.

As to an increase in entrepreneurial profits, it can be determined by two factors: (1) a general, extensive increase in the value newly created in the production process without a change in the general conditions of production, i.e., with fixed capital, labor force, and the nonproductive expenses unchanged (interest on capital, rent, etc.); (2) an intensive improvement of the production process which makes it possible to reduce the input of labor and materials per unit of production.

Let us assume hereafter^1. that the cost of a physical unit of production, as well as the wage level, rent, etc., remains unchanged. In practice, this will happen when the reduction of production costs brought about by technological improvements in a given enterprise is of purely local significance and does not affect the general market value of the produce. In this case, the total effect of the reduction of the working cost goes to the capitalist in the form of an increase in his relative surplus value; whereas with an extensive increase in net production, his absolute surplus value increases proportionately. It is easy to see that, with our assumption, the exchange value of a product changes in proportion to its physical volume. Thus the wage fund of workers and employees changes in proportion to the expenditure of labor. We can therefore measure the changes in the physical volume of production and in the expenditure of labor by the changes in their cost.

Returning to the two factors on the basis of which the entrepreneurial profits of the capitalist increase, we note that in particular cases profits can increase on the basis of either one or both of these factors. We can also conceive of an instance when one of the factors would contribute to an increase in entrepreneurial profits while the other would contribute to a reduction. In that case it is still to the entrepreneur’s advantage to invest new capital if the total effect is positive. For instance, during business cycle expansions and when the demand exceeds the supply, it is definitely to the entrepreneur’s advantage to expand the operations of his enterprise and increase his profits through an increase in absolute surplus value. Moreover, he may find it advantageous to spend his capital on obsolete equipment and less qualified labor, since, although this will reduce the relative surplus value, it will increase the absolute surplus value by more and hence have a positive total effect.

On the other hand, during business cycle contractions, when marketing goods is difficult, the capitalist is sometimes forced to reduce the volume of production. At the same time, however, he may still find it to his advantage to invest new capital in his enterprise if this is conducive to raising the labor productivity or reducing the input of raw materials, fuel, etc., per unit of production, because at the same time the production costs decrease and the relative surplus value increases.

If we consider the efficiency of capital investment from the viewpoint of labor, we can break it down into the following effects:

(1) The effect obtained from a general increase in the wage fund by an extensive increase in the volume of production (disregarding changes in labor productivity).

(2) The effect of wage increases due to changes in labor productivity. Since we assume the level of hourly wages to be constant, this effect will be negative if labor productivity increases, and vice versa.

(3) The effect obtained through labor-saving due to the fact that, as labor productivity increases, the number of man-hours spent on the production of the same physical volume of new value is reduced.

In the same way, we can calculate the increase, due to extensive and intensive increase in production, in the share of other physical and legal persons in the surplus value through an increase in nonproductive expenses.

Finally, an increase in production in one enterprise can lead to more productive and economical operations in other enterprises. This happens when the volume of output in one industry limits the output of other industries. Thus an increase in the production of fuel resulting from capital investment outlays in the fuel industry can cause an increase in the output of other industries without additional investment outlays in these industries, if the obstacle to increased production was a lack of fuel rather than a lack of capital. Furthermore, since a greater utilization of the existing capacities of an enterprise usually reduces the input of fuel and labor per unit of output, we can say that capital investment in one industry can also increase the efficiency of the operations of other industries. This effect will also include increases in entrepreneurial profits in these industries, in wages, in labor-saving, and, finally, in the income of various persons connected with an increase in nonproductive expenses.

Adding up the individual shares of efficiency gained from capital investment outlays by the entrepreneurs, labor, and other beneficiaries of efficiency pointed out earlier, we find the total efficiency of the capital investment funds from the standpoint of the national economy as a whole. This efficiency can also be found by adding up the efficiencies of various industries corresponding to different variables brought about by capital investment.

These variables are:

(1) An extensive increase in the physical volume or in the quality of the net output, disregarding the effect caused by the reduction of input of materials and labor.

(2) A reduction of input of materials per unit of production.

(3) A reduction of input of labor per unit of production.

(4) An improvement of working conditions and safety measures for labor.

Of the enumerated variables, (4) has an independent social significance and must therefore be considered separately.

The economic efficiency is determined entirely by the first three variables. The first one consists of an increase in production, quantitative or qualitative; the second and third, in a reduction in the input of labor or materials per unit of newly created value. We call the first part of efficiency productivity, and the second part labor and material savings.

It is easy to see that, whatever the distribution of the increment of production and the saving of materials among entrepreneurial profits, the wage fund, and the incomes of various physical and legal persons from nonproductive expenses, in the true formula, the over-all economic efficiency is determined by the two main variables: the quantitative or qualitative increase in the volume of newly created value and a more economical expenditure of actual and materialized labor (labor force and fixed capital). We believe that the entire concept of efficiency is limited to these variables.

It is evident that when we speak of the efficiency of capital investment, we compare the absolute economic effect obtained through these investment outlays with the outlays themselves. Therefore it would be more correct to speak of the rate of efficiency of capital investment.

Further we have:

in which

and

We distinguish the over-all economic efficiency from the social and political effectiveness that results from the fact that capital investment funds contribute to the industrialization of the country, to national defense, to a balanced supply and demand, to increased safety measures, etc.

Of course, an analysis of our policy of capital investment must take into account all these forms of social and political effectiveness. This, however, does not detract from the importance of determining the maximum efficiency of capital investment outlays in the aggregate economic sense, which is one guiding principle (although not the only one) that we should adopt in choosing the direction of capital investment.

FORMULA FOR THE EFFICIENCY OF CAPITAL INVESTMENT

We shall designate by E the absolute economic effect obtained in connection with the capital investment outlays; by K_x the value of the stock of fixed and working capitals available before the investment; by K₂ their value (in fixed prices) after the investment. Thus the amount of these investment outlays is K₂ – K₁ and the rate of efficiency of the capital investment outlays is

where E_n is the productivity effect and E_e the economic effect.

As for the productivity effect, it consists of the quantitative increment in net output (of the newly created value). We shall designate by D_x net output for original capital K_x; and by D₂ net output for capital K₂ after the effect of the capital investment outlays is felt. Then D₂ – D₁ will represent the total productivity effect of the capital investment outlays on the national economy E_n, and the productivity rate will be

The labor and material savings of capital investments have a more complicated expression. As we have pointed out earlier, the economic effect consists of savings on fixed capital and labor. Let us assume that, if K₁ is the capital and D₁ the net output, C₁ is the outlay on materials and F₁ the outlay on labor. Let C₂ and F₂ designate outlays on materials and labor, respectively, after the effects of the capital investment outlays are felt. It is obvious that, without the economic effect, the expenditure of materialized and actual labor would have increased in direct proportion to the increase in net output, and would be

Therefore, the absolute economic effect E_e will be

Hence, the rate of labor and material savings is:

Let us assume that I₁ = C₁ + F₁ and that I₂ = C₂ + F₂ · Then we have

where I₁ and I₂ represent the total expenditure of materialized and actual labor for capital K₁ (before investment) and K₂ (after investment).

Combining the formulas for productivity and labor and material savings, we obtain a general formula for the efficiency of

This is the formula for the efficiency of capital investment outlays in the most general form.

The productivity effect of the capital investment outlays (D₂ – D₁) can be broken down into extensive and intensive effects. The first represents the physical increase in the volume of output in proportion to the increase in capital; the second represents an increase in net production (or the equivalent qualitative improvement) at a rate exceeding that of the increase in capital.

The rate of productivity for capital K₁ was B₁. During the extensive growth of D₁ this rate does not change, and, therefore, if the capital increases from K, to K₂, we obtain the extensive productivity effect D₁/K₁ = (K, – K₁).

If, however, D grows at a faster rate than K, we obtain the additional intensive effect

The total productivity effect will be

and

Inserting this value into our formula for the efficiency of capital investment outlays, we obtain

Thus the total effect of capital investment outlays is composed of the four individual effects

where E₁, = (D₁/K₁) (K₂ – K₁) is the extensive increase in net output in proportion to growth of K; E₂ = K₂ (D₂ /K₂) – (D₁K₁) is the intensive quantitative increase, or the equivalent qualitative gain, of net output at a rate exceeding that of the growth of K; E₂ = D₂ (C₁/D₁ ) – (C₂/D₂) is the effect of a more economical expenditure of fixed capital per unit of output; E₄ = D₂ (F₁/D₁) – (F₂/D₂) is the effect of a more economical expenditure of actual labor per unit of output.

Of course, in specific instances, one or several of these individual effects can be nil or even negative. We note that the effect E₂ = K₂ (D₂/K₂) – (D₁/K₁), despite its considerable importance due to the shortage of capital in this country, will still be negative because of the change of the organic composition of capital (with an increase in fixed capital). In reality, the ratio D/K represents the relation between the quantity of actual labor D expended on a given production process and the quantity of material labor K that had gone into tools and materials. But, as labor is further mechanized, the ratio D/K will decrease and therefore tend to become negative, i.e.,

The following example with figures will illustrate our formula.

Let us assume that the stocks of fixed and working capital of a given industry, say the textile industry, are 200 million rubles. Let us assume further that the annual value of output is 500 million rubles, of which 400 million represent materials, fuel, amortization, etc., and 100 million the net output. We have then D₁ =100 million rubles: C₁ = 400 million rubles; K₁ = 200 million rubles. Finally, we shall assume that the later expenditure is 100 million man-hours with a general productive capacity of F₁ = 100 million rubles.

If later we invest another 50 million rubles, the new capital stocks will be K₂ = 250 million rubles. Let us assume the corresponding net output D₂ = 120 million rubles, the expenditure of materials C₂ = 440 million rubles, and the expenditure of actual labor F₂ = 100 million man-hours with a productive capacity of 110 million rubles, its level remaining unchanged.

We have then the productivity effect E_n = D₂ – D₁ = 120 – 100 = 20 (million rubles).

Of these, the extensive effect will be

and the intensive effect,

Here the intensive effect is negative since production increased by 20 per cent while capital stocks increased by 25 per cent.

Further, we have the effect due to material savings

and, finally, the actual labor-saving is

with a total productivity capacity of 10 million rubles.

Thus through the investment of 50 million rubles we have obtained:

(1) The effect due to the increase in productivity E_n = 20 million rubles consisting of (a) the extensive effect E_t = 25 million rubles and (b) the intensive effect E₂ = –5 million rubles.

(2) Saving on fixed capital E₃ = 40 million rubles.

(3) Saving on labor E₄ = 10 million man-hours with a productive capacity of 10 million rubles.

Altogether 60 million rubles, plus 10 million man-hours. Translating the labor-saving into the value it has created, we obtain a total of 70 million rubles. Hence the rate of efficiency of the capital investment outlays is 70/50 = 1.40.

REMARKS AND CONCLUSIONS

(1) We deliberately calculate the productivity and labor and material savings on the basis of value added rather than gross value of output. The reason is that capital investment outlays contribute to the increase created precisely in the given production process. If, on the other hand, this increase in the newly created value also makes it necessary to increase the production of the fixed capital stocks (raw materials, fuel, amortization, and other material expenditures), then additional capital funds must be spent on the industries that produce these fixed capital stocks. In the same way, savings on actual or materialized labor brought about by capital investment outlays in a given industry is achieved precisely in that particular industry, whereas the reproduced value is automatically transferred to the value of the final product and is not an active factor in saving. For example, if the manufacture of the final product requires 100 man-hours with 80 man-hours having been spent earlier on the preparation of materials and tools of production and 20 hours spent in that industry itself; and if, then, through capital investment outlays, labor productivity is doubled, then the expenditure on the product will be 80 + 10 = 90 man-hours and the saving of actual labor brought about by the capital investment outlays will be 10/20 = 50 per cent rather than 10/100 = 10 per cent….

A similar example of saving on fixed capital could also be given.

(2) The growth of productivity not accompanied by the savings effect causes an increase in the expenditure of actual and materialized labor in proportion to the growth of net output. Thus the quantity of the product per work unit does not increase and there is therefore no reason to raise individual wages unless redistribution of the national income occurs simultaneously, otherwise a wage increase for one group of workers would be gained at the expense of the income of other groups of workers or other citizens. However, such a growth of productivity causes a large influx of labor into the industry.²

On the contrary, the savings effect not accompanied by growth of production reduces the need for manpower while creating a basis for a wage increase or for a shorter work day, or else for an increase in accumulation.

If the productivity effect is combined with the savings effect, there will be both an increase in the number of workers and a reduction of labor input. This, as pointed out above, will result in either an accumulation, a wage increase, a reduction in the work day, or all of these.

(3) We can see that the savings effect can be obtained not only through an increase in labor productivity but also through more economical expenditure of fixed capital. A better boiler using less fuel per unit of steam or a device to utilize waste products or to reduce transportation yields the same results as an increase in labor productivity. And since the amount of materialized labor used in production exceeds as a rule the amount of actual labor, we gain more in saving 1 per cent of materialized labor than by increasing the productivity of the actual labor by 1 per cent. In our earlier example, when the fixed capital accounted for 80 per cent of the final product and the newly created value for 20 per cent, a saving of 1 per cent of materialized labor is tantamount to a 4 per cent increase in labor productivity. (The average ratio of the expenditure of actual to materialized labor in all branches of state industry is higher, about twothirds, but in the building industry it is lower.)

It is interesting that our labor management officials consider an increase in labor productivity as the only way of achieving higher wages, shorter working hours, and accumulation, and seem to forget completely the possibiliy of saving on materialized labor which, in the U.S., for instance, has already had a spectacular effect….

(4) While the materialized labor (fixed capital) is estimated at its full value (disregarding here the possible deviations of prices from values), actual labor is evaluated in terms of wages, whereas the surplus value should also be taken into account. Based on such an estimate, the value of the savings on labor expenditure will be less than the true value based on the productive capacity of labor.

Thus if the saving reaches 100 million man-hours and the wages are 0.5 rubles per hour, we usually evaluate the savings effect due to the increase in labor productivity at 50 million rubles. It would, we submit, be more correct, under Soviet conditions, to evaluate the savings in man-hours not in terms of its market value but rather in terms of its productive capacity. Thus if a value of one ruble is produced in one man-hour, we would estimate a saving of 100 million man-hours as worth 100 million rubles. However, this matter requires some additional clarification….

“O metodakh ischisleniia effektivnosti kapital’nykh vlozhenii,” Put’ industrializatsii. No. 11, 1929, pp. 10-24.

“Formula effektlvnosti kapital’nykh vlozhenii,” Planovoe khozialstvo, No. 6, 1929, pp. 99-116.

1. Here is a list of symbols used in this article:

2. Inasmuch as we estimate the value of actual labor on the basis of the productive capacity, the number of the new workers N, the length of the work day remaining constant, can be expressed by the formula

where k is the value of net output per worker (labor productivity).