METHODS OF CALCULATING

THE EFFICIENCY OF CAPITAL INVESTMENTS

…If by efficiency we understand the ratio of results to outlay, we must first of all draw a clear line between national economic efficiency and efficiency from the viewpoint of a private enterprise. But since we are not concerned here with a capitalist national economy developing haphazardly, but with a planned socialist economy, we of course do not understand by private enterprise an enterprise pursuing some “private” goals, but an enterprise which, for certain organizational reasons, has been made into an independent economic unit with a defined assignment and supplied with a clearly limited part of the national economic capital. Such individual “private” enterprises cannot, of course, function effectively without giving an accounting of their activities—both of their achievements and of their outlays. The greater the achievement and the smaller the expenditure, the more favorable the results of the accounting are bound to be, however it is done, in monetary units or in man-hours or in any other system of measurement. Individual enterprises can be operated at a loss, but even then maximum achievement for minimum outlays will give the measure of the entrepreneurial efficiency of the capital invested in them….

But the principle of maximum achievement for minimum expenditure is the principle of profit; and thus it can be affirmed with certitude that whatever the system of measurement used, the concept of the entrepreneurial efficiency of capital is included in the concept of profitability provided, of course, that by profitability we are not so naive as to mean a drive for a maximum direct profit-a drive that would not allow for the prospects of long-range use of the capital, of possible changes in its form, and, in general, of all the positive and negative factors that could affect its further rational utilization….

A planned economy, by definition, cannot fail, during the preparation of the plan, to have a definite purpose which determines the evaluation of the various developmental factors and the application of qualitative weights to certain quantitative results. Hence, on the one hand, we have the absolute necessity of taking into consideration the qualitative comparison of the factors of the plan in accordance with the authoritatively established main lines of national economic development, i.e., the determination of what constitutes the concept of national economic efficiency, and, on the other hand, if we may put it thus, we have the historical approach, the realization that this concept is a conventional one that can change with a change in economic policy.

From this point of view, national economic efficiency can be determined by finding an indicator which would combine the positive and the negative elements that characterize the national economic process, in a certain proportion corresponding to the general direction of economic policy, and would thus indicate the extent to which the actual picture corresponds to the results and the expenditures foreseen in the plan.

Reasoning theoretically, we can imagine a triple solution of this problem: (1) a single and simple indicator of efficiency, (2) a series or a system of separate indicators, (3) a composed and complex indicator in the nature of a more or less complex formula.

A sample of a single, simple indicator of efficiency is the following, which is frequently used:

or

It must be recognized that this indicator, which, by the way, was used in the Leningrad Province National Economic Five-Year Plan, is absolutely unsatisfactory. It is impossible to maintain from any viewpoint that gross value of output obtained per one ruble of capital would by itself measure the national economic efficiency of the capital investment. If we use this formula we find a proportional increase in efficiency simply because the price of the raw materials has increased. This formula would not help to detect a difference in efficiency if the output per worker dropped; it does not enable us to compare the efficiency of various enterprises operating with different compositions of prices, i.e., with different ratios of gross value of output to value added, or with a difference in the share of raw materials in the price of the product. There is no doubt that this formula has been used as a result of confusion.

Of course, replacing the gross value of output by value added in the formula would improve it considerably, but this still would not make it theoretically and practically acceptable….

Thus we must seek a solution in a more or less compound indicator containing, in the form of a formula, the basic positive and negative factors of production which are decisive from the viewpoint of the entire structure of our economic system.

As we have said, the ratio of output to capital cannot by itself measure efficiency. But it cannot be denied that, other conditions being equal, the efficiency is greater, the greater the output per unit of capital. One cannot deny the validity of the equation η₁ = a(P/C), where η₁ is a partial indicator of efficiency; P, the gross value of output; C, the initial capital; and a, the coefficient of proportionality, constant when P and C vary.

Along with this equation, we can write, with the same validity, a second equation which will give us a second partial indicator of efficiency, η₂ = b(P/W), where b is the coefficient of proportionality remaining constant when P and W vary; W, the number of workers working a normal work day and producing output P. There is no doubt about this equation either since, from our viewpoint, the efficiency of the capital is so much the greater, the larger is one worker’s daily output.

Multiplying these partial indicators η₁ and η₂, we obtain

This equation, despite its simplicity, reveals under closer scrutiny several peculiarities which we shall now study.

Since the coefficient a is assumed to be constant when all the other factors are constant except P and C, while coefficient b is assumed to be constant when all the other factors are constant except P and W, there is no ground to assert that a is constant when W varies and b is constant when C varies. Therefore it cannot be asserted that k is constant. In order to determine the nature of this coefficient and of the entire formula we shall now try to grasp its economic meaning.

We shall assume, to start with, that coefficient k is constant, and we shall try to discover how efficiency is determined from the formula under the simplest conditions: η = P^2./CW.

This equation conveys the information that the efficiency of the capital tends toward infinity when the capital and the number of workers are zero—which is logically correct but impossible in practice. Further, if the production doubles simultaneously with the doubling of the capital and of the number of workers, efficiency does not change. This is the situation when, alongside one plant, another similar one is opened having the same assignments and the same machines, with no technological or organizational improvements. In this case, the efficiency of the capital obviously does not change. But if output doubles when capital doubles but the number of workers remains unchanged or, vice versa, if the number of workers doubles while capital remains unchanged, the efficiency increases in proportion, which is also logical. Thus, introducing two work-shifts instead of one, we obtain theoretically a doubling of output with a double number of workers for the same capital, and the efficiency of capital doubles, too.

Let us now assume that despite an increase in capital, output remains the same because the capital increase is used on an auxiliary enterprise for the preparation of raw materials. In this case, the formula P^2./C-W ceases to be valid because it will show a decrease in efficiency which has not occurred. In such a case, for a capital increase of, say, 50 per cent and a 20 per cent increase in labor, we shall have at the initial period η = 1 and in the subsequent period

We can see from this example that we can use the gross value of output figure, P, to determine efficiency only if the share of value added remains unchanged. If this share changes, then gross value of output should be replaced in the formula by value added, P₀.

This can be seen more clearly in the following example:

Calculating on the basis of the gross value of output, we have

Calculating on the basis of value added, we obtain:

…Thus the proposed formula passes a series of tests which, of course, are quite elementary. We are, however, immediately faced with a series of more complex questions:

(a) Since the size of the capital and the number of workers are not two independent variables and since, on the contrary, we know a priori that a change in capital determines a change in the number of workers one way or the other, we must find out how the proposed formula deals with this contingency.

(b) Since calculation of national economic efficiency must not be replaced by calculation of the same old profitability in disguise, and since it must make it possible to give to individual factors certain weights corresponding to our economic policy, we must find out whether this is possible using the proposed formula.

(c) Formula P^2./(C·W) or ties together three factors: gross product P or net product P₀; capital C; and number of workers W. Is it possible, however, to maintain that the size of the product is determined by the size of the capital and by the number of workers to the same extent as the efficiency of the capital is determined by these two factors, and that no further factors need be included in the formula?

(a) An independent change of capital C and of the number of workers will occur only in special cases: on the one hand, if the number of man-hours or shifts decreases or increases and if purely organizational changes increasing or decreasing the output per worker per day are introduced without any increase in capital; and, on the other hand, if the old equipment is replaced by new, more expensive equipment, yielding the same output for a smaller number of workers. The efficiency of this type of independent change in C or W is fully allowed for in the proposed formula.

However, generally speaking, a change in capital much more often determines a change in the number of workers, and the ratio of capital to number of workers in concrete conditions varies according to a definite pattern: industrial development is accompanied by an increase in capital per worker, when by worker is understood not the man but one normal work day.

According to the data of the American economists Cobb and Douglas,… during the period 1899-1922 fixed capital per worker has increased in the U.S. from $940 to $2,850, i.e. it has tripled. This increase was interrupted only in the years of crises when the number of workers was automatically reduced or, as production fell, working hours were cut. These figures take no account at all of the general reduction of working time (about 11 per cent) which took place in the period 1899-1922. If this fact had been elaborated upon and if instead of the workers we had been given the number of man-hours expended on production each year, then the increase of C/W would have been even greater.

Comparing the figures for capital per worker and gross production per worker, it is easy to see that, in the U.S., the growth of the latter lagged considerably behind the former….

The inversely proportional variation of capital and number of workers, according to the proposed formula, does not change the efficiency if output remains unchanged. Efficiency increases when the rate of growth of capital lags behind the rate of reduction in the number of workers, output remaining unchanged. Efficiency drops when the rate of growth of capital exceeds the rate of reduction in the number of workers.

The above-mentioned dependence can be best observed in a numerical example. Let us assume that in the initial year we have for output, capital, and number of workers, respectively, one million rubles, 500,000 rubles and 400 men. Then efficiency, according to the formula, will be

We shall further assume that

(a) the capital has trebled and the number of workers been reduced to one half:

(b) the capital has doubled and the number of workers been reduced to one-third:

Does this formula correctly determine the efficiency of capital in these cases? We cannot simply answer no to this question because we are dealing here not with a verification but with an evaluation. The fact that we have included in the denominator of the formula the product of the first degrees of the two values C and W certainly means that, independently of the functional dependence between these values, we evaluate their change equally, both of them being particular negative determinants of efficiency. If the expenditure of capital represents for us a greater sacrifice than bringing new workers into the work, we must weight these values correspondingly, i.e., not take them to the first power but to some other power which will not be the same for C and W.

Applying economic logic, it is impossible to object in principle to the rejection of the conclusion that the efficiency remains unchanged when C and W vary in inverse proportion and when production is constant.

(b) With respect to the second question, it must be noted that, as we have pointed out earlier, the proposed formula makes possible any weighting of all the values P, C, and W. It would be incorrect, however, to take the price-forming role of various factors as a basis for the weighting.

In the price of the product, capital accounts for 10 to 12 per cent while the number of workers, through wages, determines the greater part of the rest of the price after subtraction of the raw materials. An attempt to give appropriate weights to capital and to the number of workers would only produce a distorted picture of profitability and no picture at all of national economic efficiency.

Obviously, the weighting must correspond to an authoritative interpretation of national economic efficiency and to an authoritative, qualitative standardization of the relative values of capital and of the number of workers.

(c) The third question presents the greatest interest. Are the values included in the formula sufficient? Is it possible to determine national economic efficiency from the ratio of one positive and two negative factors without taking into account other factors such as profit, cost of production, working capitals, turnover, etc.?

This question can be answered as follows:

If a formula enables us to determine product P with sufficient accuracy, especially its rate of variation as a function of only two variables C and W—i.e., the capital and the number of workers—then it is not necessary to include additional positive and negative factors in the formula. If, however, the national economic plan as a whole ascribes a considerable importance to some positive factors such as wages or negative factors such as expenditure on fixed capital, which may require expenditure of foreign currency, etc., then, of course, the formula must be correspondingly modified.

Extremely interesting studies on the extent to which the size of the output is determined by the size of the fixed capital and by the number of workers have been made by the American economists Cobb, Douglas, and Clark. Cobb and Douglas studied the indexes of the variations in physical output P, fixed capital C, and number of workers W and found that the size of the physical output P can, with a considerable degree of accuracy, be determined as a function of C and from the formula

(where b is a constant coefficient)....

It is, however, easy to see that product P can always be presented with adequate accuracy as a function of the capital and the number of workers. In fact, the product is nothing but the sum of prices, each of which by the very nature of the methods of calculation has the form

where m is the cost of the raw material, a value almost always constant for a given enterprise and industry under the capitalist conditions of the U.S. (From 1899 to 1914, m dropped from 42.3 per cent to 40.7 per cent, and in 1927 it rose to 44 per cent.) aC is the sum by which the capital is represented in the price of the product. In it, the coefficient a is also almost constant since it is determined by the amortization rate and by current repairs. bW is the sum of wages and extra expenses. The wages of one worker in fixed money terms change slowly, the extra expenses are determined in percentage of the wages, and this percentage also fluctuates within narrow limits for each individual product….

Analyzing the discrepancy between the actual figures for individual years and the figures obtained on the basis of the Cobb-Douglas formula, Clark pointed out many factors that could account for it, in particular the shortening of the work week between 1899 and 1922 and the low labor productivity during the war years due to the use of inexperienced workers. Clark proposed a modification of the Cobb-Douglas formula. He suggested it should be

where W is the actual number of workers, W_n the number of workers required if the utilization of capital were 100 per cent.

Both the work of Douglas and Cobb and the views of Clark and Shlicter would suggest that the merit of the Cobb-Douglas formula lies not so much in enabling us to determine the product from C and W but rather in defining the value of P under conditions sufficiently close to reality. Moreover, it must be assumed that as technology progresses and a greater and greater share of capital goes to equip one worker, C and W must, by their very nature, be variable rather than constant, and, with the increase in the technical efficiency of the capital, the index of C must grow while the index of W must diminish.

The basic economic meaning of the laws established by Cobb and Douglas has been expressed by Clark as follows. Assuming that, in an industry, 4 units of capital correspond to one unit of labor, then the result of the work of one labor unit and four capital units will be

Under these conditions, five units of production would require

units of labor and 11 3/7 units of capital.

The differentiation brings us to a formula of the type C^1./^4. × W^3/4.

The above formulas enable us to determine the efficiency of capital investment in the Soviet Union through a comparison of the production obtained in our country with that which would have been obtained in the United States with the same W and C.

Indeed, if P is the size of the output (actual or planned) and we know the figures C and W for the capital and the number of workers, respectively, we can determine from the Cobb-Douglas formula product P_am, which, for the given C and W, would be obtained in the United States. By comparing our product P with the product P_am obtained through the formula P_am = 1.01 · W^3./^4. · C^14., we can find out the extent to which the efficiency of C and W is higher or lower in the USSR than in the U.S. It is necessary, of course, to translate P and C into the same currency, either rubles or dollars.

We can attain the same objective by using the formula we proposed earlier, η = P^2./(W × C), taking W and C with the exponents appropriate for our economic policy.

It is easy to see that there is no difference in principle in calculating efficiency by either of these formulas. In effect, the Cobb-Douglas formula has the form

and, as has been shown, the efficiency is measured by the ratio of our actual product to product P¹, which the same C and W would have given under the American conditions prevailing between 1899 and 1922, i.e.,

where the coefficient of proportionality q = 1/1.01.

Now, using the formula proposed earlier, we have

, where m and n are equal to

one if we ignore the effect of the other factors. Squaring both sides of the first formula we have

i.e., a formula that is at variance with ours only in the size of the constant coefficient and in the weightings of C and W. Thus our formula measures the phenomenon by the square of a determined ratio of values, while the Cobb-Douglas formula measures it by this ratio in the first degree.

Below, we illustrate this by some results of the application of the two formulas. We must note here that in these examples, because of the absence of data, we have had to base ourselves on the sizes of the gross rather than the net product. For this reason the comparison of the values of efficiency obtained for different cases will be incorrect theoretically, since the coefficients of net product are different everywhere.

The USSR Five-Year Plan’s control figures for the final year put the growth of fixed capital at 239 per cent of the initial year and the increase in the labor force at 268 per cent.

According to the formula P^2./WC the increase in efficiency is

per cent of the initial value.

According to the formula 1.01 W^3/4 · C^1/4, the efficiency for the final year is determined as

per cent of the initial value.

In other words, under American conditions, the increase in the number of workers to 135 per cent and in the fixed capital to 239 per cent would have increased the product not to 268 per cent but only to 171 per cent = 268/157.

The five-year plan for the industry of Leningrad gives the following coefficients for the final year:

From these figures, the increase in efficiency is determined by the following figures:

…Before we leave this interesting topic, which is important both from the point of view of theory and from that of practice, we must touch upon two additional matters.

(1) If we use the formula P^2./WC to determine the efficiency of American industry, we obtain the following figures:

From these figures we obtain what would seem at first glance to be a rather paradoxical picture, namely, one of capital efficiency in the United States falling for the first decade and a half and rising a little in recent years. This conclusion is confirmed by a comparison of the figures of output per worker and of the amount of the fixed capital per worker, as well as by several studies by such American economists as Clark, Cobb, Douglas, and Thomas. But what then is the secret of American prosperity? The most plausible explanation seems to be that this prosperity is caused, above all, by the fact that American industry has not only been expanding production but, at the same time, has been paying wages which enable the workers to buy the output, i.e. has not only produced the goods but also increased the purchasing power of the consumers.

The wages changed as follows:

In this connection the question arises whether it would not be appropriate, when evaluating efficiency from a broad national economic viewpoint, to include the indicator of the growth of wages as a major positive factor in the efficiency formula and to write the formula

where L is the relative or the absolute value of one worker’s wages.

If we do not include the growth of wages, then from 1921 on, the efficiency of American industry for the 1899 value of η(1.00) varied as follows:

If we now introduce the indicator of the growth of yearly wages, the efficiency will vary as follows:

The question of the positive significance of wages as a factor in national economic efficiency warrants special study.

(2) The second question claiming at least brief consideration concerns the importance to the national economy of determining financial profitability in the light of what has been said here about efficiency in general.

In the introduction to this paper it has been shown that entrepreneurial efficiency of capital is determined by profits and that, whatever the system of accounting, the management that follows basic economic principles cannot do so without determining profitability. It is equally clear that when the national economy is conceived of as a system of interdependent but separate economic units, the algebraic sum of the entrepreneurial profitabilities is of first-rate importance to the national economy, since it is precisely this sum that determines the size of accumulations, i.e., of the funds out of which the resources for the expansion of productive capital are obtained.

Therefore, however we measure the national economic efficiency of capital outlays, we cannot reckon that this measure will render a careful watch over profitability unnecessary. Those who believe this to be so on theoretical grounds are not only naive in their theorizing but, in addition, will find themselves in complete disagreement with the facts, because every day and everywhere profits are being assessed, although perhaps by the most haphazard, antedeluvian, and home-made methods. The absence of an authoritative interpretation of the most elementary concepts leads to these haphazard computations of profitability, to the concealment of its true size, to excessive amounts of working capital, etc.

There is an especially popular theory which considers the determination of profitability impossible or unnecessary because of the special nature of our price policy and of the independence of these prices from supply and demand. This theory is surprising in a planned economy based on accounting, and if it were correct, it would have undermined not only the principle of profitability but the entire concept of a planned economy. Of course, the fact that money is an imperfect gauge of prices makes the determination of profitability more difficult, just as it makes planning and plan-fulfillment calculations and estimates more difficult. But certainly this does not mean that we may eliminate the concept of profitability from view and replace it by some more or less satisfactory indicator of national economic efficiency.