Law of Diminishing Returns; Whether on Crusoe’s island or Manhattan Island, production involves the use of labor, land, and capital. These resources may be combined in different proportions. Which proportion to use in producing a given output is one of the decisions confronting the manager of the firm, whether he be Robinson Crusoe or the president of General Motors. Let’s define the Law of Diminishing Returns.
DEFINITION OF LAW OF DIMINISHING RETURNS
In making this decision, the manager of the firm encounters one of the underlying principles of economic activity, the law of no proportional outputs, or, as it is more commonly known, the law of diminishing returns. This law defines a relationship between inputs (resources) and outputs (goods and services), with a given level of technology. It states that, as an increasing number of units of one resource are applied to a fixed number of units of other resources, output first increases at an increasing rate, then at a diminishing rate, and eventually decreases absolutely. That point in the application of the variable resource beyond which output increases at a diminishing rate is known as the point of diminishing returns.
ASSUMPTIONS OF LAW OF DIMINISHING RETURNS
The assumption of an unchanging technology is an essential part of the law of diminishing returns. The law does not deny that progress in the technical arts may delay indefinitely the tendency to diminishing returns. However, at a given moment of time, the production plan of the firm must be constructed with the use of specific techniques of production. Once the plan is in operation, it cannot be revoked overnight; the buildings, machines, and tools cannot be revised each day to take account of changes in technological possibilities. In other words, the assumption of a given level of technology does not destroy the usefulness of the law of diminishing returns as an explanation of behavior in economic life. All that is necessary to establish the validity of the law is to ask what the world would be like if it were not true. The world’s food supply could be grown by simply adding increased “doses” of labor and capital to a few plots of ground. The total supply of any given manufactured good could be produced by simply adding larger and larger quantities of labor to one plant. Even a cursory inspection of the world about us is sufficient to establish the fact that production takes place under the constraint of diminishing returns.
Let us create a small manufacturing plant producing some standardized product. The plant itself represents a fixed “bundle” of land, capital, and management. To this fixed input of resources are added successive units of the variable resource, labor. The resulting outputs are shown in column 2. The increase in output (marginal product) per unit increase in man power is shown in column 3. The output per man or average product is shown in column 4. It can be seen that total output increases at an increasing rate through the point at which two men are employed. Beyond this point, output continues to increase but at a diminishing rate. This point, where two workers are hired and the total output is 12 units, is the point of diminishing marginal product, or diminishing re-turns. The point at which three men are hired and the total output is 18 is the point of diminishing average product. The point of diminishing marginal product should not be confused with the point of diminishing total product. It may pay this firm to hire three, four, five, or even six workers; it would never pay this firm to hire a seventh worker inasmuch as he would make a negative contribution to total output. So long as an extra worker makes a positive contribution to total output (so long as marginal product is positive rather than negative), it may pay the firm to hire the extra worker. In other words, the point of diminishing returns does not necessarily define the optimum rate of use of the variable resource. As a matter of fact, we shall find that the optimum rate of use of the variable factor usually lies beyond the point of diminishing returns but short of the point of diminishing total output.
GRAPHIC PRESENTATION OF THE LAW OF NON-PROPORTIONAL OUTPUTS
The graph pictures the relationship between the output of the firm and the number of units of labor (the variable input) employed by the firm. The workers are assumed to be of equal quality and to be used in conjunction with a fixed plant, i.e., in conjunction with a given-sized “bundle” of land, capital, and management.
Inspection of the graph shows that the total output of the firm (TP) increases as the amount of labor hired increases, until the addition of a seventh worker causes total output to decrease. It will be further noted that the use of, first, one and, then, two workers causes total output to increase at an increasing rate, i.e., the increase in output is more than in proportion to the increase in the number of workers hired. This stage in the expansion of output (often called the stage of increasing returns) is identified as Stage I. During this stage all three measures of output—total, marginal, and average—are increasing.
In Stage II total output and average output continue to increase, but marginal product is decreasing. In other words, with this Stage the firm encounters diminishing marginal returns. Total output is still increasing but at a diminishing rate, i.e., the increase in output is less than proportionate to the increase in the variable input, labor.
In Stage III total output continues to increase, but now both marginal and average product are decreasing. The firm is encountering diminishing marginal and diminishing average returns as measured against the additional workers hired.
In Stage IV all three measures of output are decreasing. Clearly no firm would deliberately and voluntarily push its hiring of labor into Stage IV. Where, then, should the firm stop? What number of men should it employ? No precise answers can be given to these questions on the basis of the data presented here. We would have to know what the firm would have to pay in the way of wages for each additional worker hired and what it could expect to earn from the sale of the additional output. Lacking these data, all we can say is that the firm will try to balance extra revenues against extra costs in trying to determine the right-sized labor force.
We can say, of course, that the firm will get the most out of its labor, i.e., obtain the highest average product, if it hires three workers. But this does not help us. What the firm wants to do is get the most out of a combination of labor and the land, capital, and management which represent the fixed input. Only if these other resources were free goods would it be best for the firm to stop with the hiring of the third man. To get the most out of the combination of all of the resources used, the firm will normally be compelled to operate with a labor force and total output that places it somewhere in Stage III.
We selected labor as the variable resource in our illustration. This does not mean that labor is always the variable resource, and that land, capital, and management are always the fixed resources. On the contrary, labor may be taken as the fixed resource, and land, capital, or management (or some combination of the three) may be taken as the variable input. The law holds whatever the variable and whatever the fixed resources.
MANAGEMENT AND THE LAW OF DIMINISHING RETURNS
We have recognized management as a special kind of labor, so special that it is separated as a resource class, coordinate with labor, land, and capital. If we treat management as the fixed and indivisible factor, and labor, land, and capital as variable factors, we find that the analysis of diminishing returns answers some very important questions.
Why do the firms in some industries grow to such a size that only a few firms (or even just one firm) are needed to supply the total output? Why is even the largest firm in other industries still so small relative to the total market that it produces but a fraction of one percent of the total output? If we treat management as the fixed and indivisible factor, we find that as more land, capital, and labor are gathered together under the direction of one man, output can be increased at first more than in proportion to the increase in the size of the “plant,” then less than in proportion, and finally a stage is reached beyond which output actually declines. There are limits to what one man or one group of men can do. Even under an exceptionally able businessman, operations can get “too big.” He is simply unable to make the innumerable decisions that have to be made promptly and wisely, and, what is no less important, he is unable to see to it that his decisions get executed with vigor and effectiveness. Improvements in the techniques of business organization and administration have pushed back the stage of diminishing returns to size of plant but have not eliminated diminishing returns as a restraint on the growth of the firm.
The stage of diminishing returns sets in much later under very able business executives than under mediocre ones. However, as more and more resources are placed under the control of the able executive, a stage is reached where additional resources could be better used by a mediocre but less-burdened executive. Here is probably the most important single reason why a single firm in an industry rarely absorbs all its competitors. It should be recognized that technological and other forces may “overpower” this factor and produce industries in which one or a few firms supply the entire output.