XX. LAW OF DIMINISHING RETURNS

(This section was written by Roger Adkins at Marshall University for his principles of microeconomics classes and is used with his permission.)

The law of diminishing returns applies only to the short run. It examines the behavior of output as we add more inputs to the production process. In particular, since we are examining the firm in the short run there must be at least one factor of production (input) that is fixed and cannot be altered for a period of time. So to this (let us assume one) fixed factor we will add a variable input or we can think of this as a bundle of inputs. For instance our bundle would be so much labor, raw materials, and energy.

One further assumption is necessary. Each variable input (or bundle) is just like any other; they are homogeneous in the terminology of economics. The firm would be indifferent as to the order in which the variable inputs would be put to work.

The law of diminishing returns is best illustrated by a numerical example as in Table 8. Column one shows the increase in the homogeneous variable input (which we will call labor or L) that is being added to a fixed factor. The second column shows the behavior of output as more and more labor is added to the fixed factor. Output (total product or Q) increases for the first eight workers then levels off before declining with the 10th worker. The last column, marginal product, is of greatest interest. We will use the concept of marginal product often.

Table 8. Total and Marginal Product

(1)	(2)	(3)
Variable Input	Total Product	Marginal Product
(L)	(TP or Q)	(MP)
0	0	---
1	5	5
2	12	7
3	21	9
4	31	10
5	40	9
6	46	6
7	50	4
8	51	1
9	51	0
10	49	-2

Marginal Product: The increase in total product (output) that arises from the use of an additional unit of the variable input.

We formulate the law of diminishing returns based on the information found in column three.

The first worker when combined with the fixed factor produces five units. If we add a second worker, total production increases to 12 units. The second worker's marginal product (MP) is seven units. Notice MP has increased going from worker one to worker two. The MP of the second worker is not higher than the first because worker tow is a better worker. Recall that we have assumed that all labor inputs are identical. The rising marginal productivity of the first four workers is an indication that the fixed factor of production is not being efficiently utilized. Too little of the variable factor is being used with the fixed resource.

Another point ought to be made. By going from one to two workers total product goes from five to twelve units, and we conclude that the MP of the second worker is seven units. This does not mean the second worker actually produced seven units himself. Workers one and two together produced 12 units. The consequence of adding worker two to the efforts of worker one is a gain of seven units. The second worker works with the first worker in the production process.

Our interest is drawn to the fifth worker's MP. His MP is less than the MP of the worker who preceded him. We have entered the stage of diminishing returns. This phase is characterized by having the marginal product of each successive worker being less than the MP of the worker before him. In our example MP ceases to be positive and, in fact, becomes negative with the 10th worker.

Law Of Diminishing Returns: As equal units of a variable input are added to a fixed factor, beyond some point the marginal product of some unit of input will be less than the MP of the preceding input.

What is the major lesson to be learned from this? The supply response (desire to increase output) of the firm is limited in the short run. Given the fixed factor, only so many units of the variable factor can be added before MP approaches zero. A large supply response requires a long run adjustment. Also, it is important to understand that we do not have sufficient information to indicate how may workers ought to be hired in our example. A tentative guess might be that the firm would not operate beyond the fourth worker since each additional worker produces less and less. We do not know the selling price of the good being produced nor do we know the cost of hiring labor; all we have is a technical relationship but inputs and outputs when a fixed factor of production is present. We will not develop the argument now, but it can be demonstrated that the firm will operate somewhere in the range of diminishing returns. There is an intuitive argument for this point. If marginal product is rising per person, then cost per person must be falling. The firm does not worry about falling costs. Only when costs are increasing per person hired (output per person is falling) must the firm move ahead with care.

See if you can figure out the average product here. Does it follow the principle outlined in the section Marginal Versus Average Values?

Plot the total product curve on one diagram and the marginal product and average product below it on another.