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## 2. The Law of Returns

Quantitative definiteness in the effects brought about by an economic good means with regard to the goods of the first order (consumers' goods): a quantity a of cause brings about--either once and for all or piecemeal over a definite period of time--a quantity {a} of effect. With regard to the goods of the higher orders (producers' goods) it means: a quantity b of cause brings about a quantity {B} of effect, provided the complementary cause c contributes the quantity {y} of effect; only the concerted effects {B} and {y} bring about the quantity p of the good of the first order D. There are in this case three quantities: b and c of the two complementary goods B and C, and p of the product D.

With b remaining unchanged, we call that value of c which results in the highest value of p/c the optimum. If several values of c result in this highest value of p/c, then we call that the optimum which results [p. 128] also in the highest value of p. If the two complementary goods are employed in the optimal ratio, they both render the highest output; their power to produce, their objective use-value, is fully utilized; no fraction of them is wasted. If we deviate from this optimal combination by increasing the quantity of C without changing the quantity of B, the return will as a rule increase further, but not in proportion to the increase in the quantity of C. If it is at all possible to increase the return from p to p1 by increasing the quantity of one of the complementary factors only, namely by substituting cx for c, x being greater than 1, we have at any rate:p1>p and p1c<pcx. For if it were possible to compensate any decrease in b by a corresponding increase in c in such a way that p remains unchanged, the physical power of production proper to B would be unlimited and B would not be considered as scarce and as an economic good. It would be of no importance for acting man whether the supply of B available were greater or smaller. Even an infinitesimal quantity of B would be sufficient for the production of any quantity of D, provided the supply of C is large enough. On the other hand, an increase in the quantity of B available could not increase the output of D if the supply of C does not increase. The total return of the process would be imputed to C; B could not be an economic good. A thing rendering such unlimited services is, for instance, the knowledge of the causal relation implied. The formula, the recipe that teaches us how to prepare coffee, provided it is known, renders unlimited services. It does not lose anything from its capacity to produce however often it is used; its productive power is inexhaustible; it is therefore not an economic good. Acting man is never faced with a situation in which he must choose between the use-value of a known formula and any other useful thing.

The law of returns asserts that for the combination of economic goods of the higher orders (factors of production) there exists an optimum. If one deviates from this optimum by increasing the input of only one of the factors, the physical output either does not increase at all or at least not in the ratio of the increased input. This law, as has been demonstrated above, is implied in the fact that the quantitative definiteness of the effects brought about by any economic good is a necessary condition of its being an economic good.

That there is such an optimum of combination is all that the law of returns, popularly called the law of diminishing returns, teaches. There are many other questions which it does not answer at all and which can only be solved a posteriori by experience.

If the effect brought about by one of the complementary factors [p. 129] is indivisible, the optimum is the only combination which results in the outcome aimed at. In order to dye a piece of wool to a definite shade, a definite quantity of dye is required. A greater or smaller quantity would frustrate the aim sought. He who has more coloring matter must leave the surplus unused. He who has a smaller quantity can dye only a part of the piece. The diminishing return results in this instance in the complete uselessness of the additional quantity which must not even be employed because it would thwart the design.

In other instances a certain minimum is required for the production of the minimum effect. Between this minimum effect and the optimal effect there is a margin in which increased doses result either in a proportional increase in effect or in a more than proportional increase in effect. In order to make a machine turn, a certain minimum of lubricant is needed. Whether an increase of lubricant above this minimum increases the machine's performance in proportion to the increase in the amount applied, or to a greater extent, can only be ascertained by technological experience.

The law of returns does not answer the following questions: (1) Whether or not the optimum dose is the only one that is capable of producing the effect sought. (2) Whether or not there is a rigid limit above which any increase in the amount of the variable factor is quite useless. (3) Whether the decrease in output brought about by progressive deviation from the optimum and the increase in output brought about by progressive approach to the optimum result in proportional or nonproportional changes in output per unit of the variable factor. All this must be discerned by experience. But the law of returns itself, i.e., the fact that there must exist such an optimum combination, is valid a priori.

The Malthusian law of population and the concepts of absolute overpopulation and under-population and optimum population derived from it are the application of the law of returns to a special problem. They deal with changes in the supply of human labor, other factors being equal. Because people, for political considerations, wanted to reject the Malthusiam law, they fought with passion but with faulty arguments against the law of returns--which, incidentally, they knew only as the law of diminishing returns of the use of capital and labor on land. Today we no longer need to pay any attention to these idle remonstrances. The law of returns is not limited to the use of complementary factors of production on land. The endeavors to refute or to demonstrate its validity by historical and experimental investigations of agricultural production are as needless as they are [p. 130] vain. He who wants to reject the law would have to explain why people are ready to pay prices for land. If the law were not valid, a farmer would never consider expanding the size of his farm. He would be in a position to multiply indefinitely the return of any piece of soil by multiplying his input of capital and labor.

People have sometimes believed that, while the law of diminishing returns is valid in agricultural production, with regard to the processing industries a law of increasing returns prevails. It took a long time before they realized that the law of returns refers to all branches of production equally. It is faulty to contrast agriculture and the processing industries with regard to this law. What is called--in a very inexpedient, even misleading terminology--the law of increasing returns is nothing but a reversal of the law of diminishing returns, an unsatisfactory formulation of the law of returns. If one approaches the optimum combination by increasing the quantity of one factor only, the quantity of other factors remaining unchanged, then the returns per unit of the variable factor increase either in proportion to the increase or even to a greater extent. A machine may, when operated by 2 workers, produce p; when operated by 3 workers, 3p; when operated by 4 workers, 6p; when operated by 5 workers, 7p; when operated by 6 workers, also not more than 7p. Then the employment of 4 workers renders the optimum return per head of the worker, namely 6/4p, while under the other combinations the returns per head are respectively 1/2p, p, 7/5p and 7/6p. If, instead of 2 workers, 3 or 4 workers are employed, then the returns increase more than in relation to the increase in the number of workers; they do not increase in the proportion 2:3:4, but in the proportion 1:3:6. We are faced with increasing returns per head of the worker. But this is nothing else than the reverse of the law of diminishing returns.

If a plant or enterprise deviates from the optimum combination of the factors employed, it is less efficient than a plant or enterprise for which the deviation from the optimum is smaller. Both in agriculture and in the processing industries many factors of production are not perfectly divisible. It is, especially in the processing industries, for the most part easier to attain the optimum combination by expanding the size of the plant or enterprise than by restricting it. If the smallest unit of one or of several factors is too large to allow for its optimal exploitation in a small or medium-size plant or enterprise, the only way to attain the optimum is by increasing the outfit's size. It is these facts that bring about the superiority of big-scale [p. 131] production. The full importance of this problem will be shown later in discussing the issues of cost accounting.