4. Complementary Factors of Production. The “Law of Diminishing Returns” and the Principle of Marginal Productivity

Of the simplifications that we just assumed in deriving the law of costs, the most important one was that the entrepreneur employed only one single factor of production. Even the example of the entrepreneur in the house-cleaning business was hardly an accurate description of reality. Wherever technical production processes are carried out, it will have to be assumed that several factors of production are used next to one another. If we now incorporate the use of “complementary goods” as factors into our previous account of the law of costs, then the essence of the problem we are faced with can be summed up easily. In the market for individual factors of production, prices have been formed based on the supply of the owners of factors of production and the demand of entrepreneurs, and these prices appear in the entrepreneur’s cost calculations. The average total cost must be compared to the price of the product, and the mechanism of the law of costs will have to bring about an adjustment. While we said before that the entrepreneur takes on the demand of the consumers and relates this demand to a single production factor, in the case of several co-existing factors of production the problem arises of how to break down the uniform consumer demand for the product into a multitude of demand curves for various individual factors of production. In short, the question is how to break down one demand into a multitude of demands. Closely related to this question is a second question which arises from the interaction of a multitude of factors of production. Generally, in combining several factors of production in one production process the situation will not be such that these factors of production will only be able to be employed in one uniform, unchangeable combination. Instead, it is almost always the case that the productive combination can be varied so that one of the factors of production can be utilized in a greater quantity to the disadvantage of others, but also that a factor of production can be completely dispensed with and replaced by another that previously had not been used. Thus, in addition to the problem of breaking down demand, the problem of substituting factors of production arises. Both problems can only be solved together.

Let it be noted that we thus find ourselves confronted with one of the central problems of an economy. If one must begin by assuming the existence of factors of production and consumer demand, then now the question is how the factors of production are employed. Whether a factor of production shall be part of one or another production process, whether it will produce one or another consumer good, whether more will be produced of one or another consumer good and will be made available to the consumers, whether the owners of individual factors of production receive much or little for their contribution to the economic process, even whether one or another factor of production is used at all; all of this becomes an issue here. The decisive function of every question related to the law of costs in determining the economic process is clear. It is no wonder, then, that the questions themselves requiring such far-reaching answers will also cause some difficulties. However, economic theory has found a tool which makes possible an extremely simple solution to the problem. Perhaps what matters today is merely that it be used in a correct way, and not lead to distorting reality. The principle is the law of marginal productivity.

Let us assume that of several different factors of production—for example two, although it could be any number—several units are employed in a production process, and let us assume, given a specific combination of these factors of production, that for one of them the number of employed units is increased or decreased. It will then be possible to find a specific relationship between such variations and the size of the return from production that is expressed in the law of diminishing returns. We will discuss this relationship by first considering its most simple formula, the so-called law of diminishing returns from agricultural production.

An increase in labor expenditures on a given piece of soil can bring about an increase in returns, yet this increase in returns is not necessarily proportionate to the addition of labor expenditure, but instead lags behind. This follows with necessity from the fact that one is concerned here exclusively with economic goods. If the law of diminishing returns were not valid, and thus if a doubling of, say, labor expenditures, brought about a doubling of returns, then no farmer would desire an increase in his land holdings for economic reasons, and hence he would not be prepared to pay anything to increase his land in order to produce a larger return. For doubling his acreage while simultaneously doubling the labor expenditures would only result in a doubling of the output; yet if the law of diminishing returns were not true, this doubled return would already be possible by doubling the labor expenditures with the given land. If, however, a doubling of the acreage appears desirable to every farmer in our economy, and if every farmer knows that for this doubling of acreage a payment is justified, then it follows that in doubling the land and simultaneously doubling labor efforts, more can be produced than by solely doubling labor efforts without doubling land. On the other hand, if the law of diminishing returns were not true, a reduction of land by half, too, would be irrelevant, since the same expenditure on half as much land would imply that on this amount of land the labor expenditure had been doubled. If his doubling of labor expenditures brought about a doubling of returns, the farmer could turn over half of his land without hesitation.²³

If one represents this relationship in the familiar graphic model, then each increase in return associated with an additional laborer employed on a given piece of land is depicted such that each laborer, represented on the X-axis, is related to an increase in output, represented by a narrow rectangle. Each additional laborer produces an increase in output which will become smaller with each addition. With each given number of laborers, the marginal product of labor is to be measured by the output of the last employed laborer or by the loss of output caused by the loss of such a laborer.

Before we continue, however, it will be necessary to extend the argument to the generally valid law of marginal productivity. In our derivation we also could have spoken of factors of production in general instead of land and labor. This is obvious from the fact that in the case of diminishing agricultural returns, we could simply reverse the roles of labor and land. There is also no reason to assume that the principle of diminishing returns is valid only for the use of soil and land as a factor of production. What makes the “law of diminishing returns” so vivid in the case of land is only the accidental circumstance that apparently a strongly diverse intensity of utilization, i.e., the employment of more or less labor, is possible here and that this unrestricted variability of factors of production, especially with regard to a continuous increase or decrease in returns brought about by adding or subtracting a complementary factor, can be imagined without difficulty. The situation appears to be different if one considers a modern machine in combination with other factors of production. With a modern cigarette machine, for instance, by adding more labor and more raw materials an increase in the output will only be possible if the daily work time is lengthened.²⁴ According to the law of diminishing returns, an increase in returns beyond this will not be possible. Likewise, a reduction in the expenditure of labor and raw materials will shorten the output linearly because the machines will operate for a shorter time daily. The marginal product of labor could not be registered there at all. But even this difficulty can be overcome. One must only be able to rid oneself of a purely technological perspective. Let us regard the cigarette machine as a product of iron and human labor—whereby we must not yet consider the peculiarities resulting from the time consuming roundabout method of production. The actual machine we see can, of course, not be retransformed into the factors of production from which it was created. But this is insignificant. Let us consider the problem as it appears when considering the general law of marginal productivity. Instead of the combination of labor and iron resulting in a machine that can only be combined with a specific amount of labor, a different sort of combination shall be considered. Less iron and less “previous” labor, but more “current” labor shall be employed. If we pose the problem in this way, a solution to the question of the marginal productivity of labor is possible. From the most primitive production of rolling and filling the cigarette by hand to the most modern automats, all conceivable combinations of iron, previous labor, and current labor are possible. We are faced with endless possible combinations of factors of production. From whatever “cleverly chosen”²⁵ combination we wish to proceed, we would always see that the increase of one of these factors of production brings about an increase in output, but that the return cannot grow in the same proportion as this one factor of production. Only a parallel increase of all factors of production can result in a proportional increase in output. Based on this argument, the principle of marginal productivity can be applied to every factor of production.

It is now clear that with this explanation of the law of marginal productivity we have avoided a number of significant problems. Even regarding the example of the cigarette machine one could make objections. If a factory has a number of machines, then the loss of one laborer after another always means an equivalent loss of products. If half of the laborers leave, then half of the machines will have to remain idle and only half of the products can be produced. No connection that would correspond to the law of diminishing returns can be observed here; the calculation of a marginal product of labor is completely impossible. Beyond this, however, additional objections could arise. Today one hears only too often of cases in which the increase in one factor of production can bring about an overproportional increase in returns. A factory in which significant expenditures are necessary in order to prepare for a production process will be able to increase its returns over-proportionally by expanding production from a very low production level by means of a relatively minor expansion in its expenditures for additional factors of production. The “law of increasing returns” will apply. We will not be able to tackle such cases in detail until later. The path along which we indicated the solution to this problem in the example of the cigarette machine will also lead us to a clarification. In essence, it will always be that production can be organized so that it takes advantage of the principle of marginal productivity, and production which is not so adjusted must prove to be misled in some way. This will be discussed later. Here, however, we want to arrive at a final consideration of the law of costs in which we will work solely with the principle of marginal productivity.

The problem of breaking down different demands vis-à-vis the supply of individual factors of production is solved with one stroke by using the principle of marginal productivity: The demand for an individual product unit is faced with the supply of individual factor units. Every increase in products does not mean an increase in all factors of production that are employed in a productive combination, but rather an increase of one or another factor of production. The entrepreneur will compare the demand for factors of production which signify possible production and a possible sale of a product with the supply of various individual factors of production, and will do business with the owner of a factor of production who makes him the best offer. Each factor of production whose marginal product can obtain a price larger than the price of this factor will be employed up to the point at which these two prices are equal. And similarly, of each factor of production that costs more than the price of its marginal product, individual units will no longer be employed. This process will continue until a price adjustment is reached. One sees that the entire argument here is completely consistent with that which we presented earlier in discussing the example of a sole factor of production.

The mechanism of the law of costs must bring about two equivalencies:

1. The equality of the price of each factor of production with the price of the marginal product of this factor of production; and

2. The equality of the price of all cost-expenditures (including the entrepreneur’s profit) with the total revenue.

Thus, the solution to the question of the relationship between factor prices and product prices, which is of decisive importance regarding the employment of different factors of production and which arises whenever there is a multitude of different factors, has been reached.²⁶