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### Law of Diminishing Returns In Agri

A correct understanding of the law of diminishing returns both as to its application, as well as to its statement as a principle, is fundamental in any study designed to measure the effect of increasing units of an input factor upon the output and whether this output is in the form of plant growth or animal production.

Immediately following Von Liebig’s emphasis of the need by plants of various mineral nutrients necessary for growth, attempts were made to bring under some law the relation existing between added units of any input factor necessary for plant growth and the additional outputs caused by those additional units.

Von Liebig developed his law of the minimum, namely, that the productivity of a field is in direct relation to the necessary constituent contained in the soil in the smallest quantity, In this law he recognized not only the importance of the limiting factor in plant growth but also the necessity of a balanced plant-food supply.

The law itself, however, was not correctly stated, and it took the thought and research of four generations of soil chemists to develop a sufficient body of data under carefully worked out control conditions to show (1) that the law as Von Liebig stated it was incorrect and (2) to make a correct statement of the law possible.

It was Mitscherlich {10, 11, 12, IS, 14, 15, 16, 17) preceded by Mayer (9) and Wagner (20) who, following years of experimentation, finally restated the law to express the diminishing increments ^ of output with the addition of like units of any input factor.

He first experimented with different forms of phosphoric acid fertilizer in pot experiments and showed that as the applications of either of the forms of phosphoric acid were increased the yield also increased, but at a decreasing rate.

As the appHcation of monobasic phosphate of lime was increased from 1 to 10 units, for example, the yield increased at the following rate Later experiments were performed with other fertilizing elements, and these were followed in turn by experiments in which the water and sunlight were varied.

The experiment varying the amount of sunlight is interesting. Plants were grown in greenhouse pots shaded by nets varying from 2 to 10 in number for different pots, and the observed growth was compared with full growth in the open.

Some of the results are shown in table 1. The increments of growth (or yield) in this instance showed, in general, a decreasing rate in each of the different plants used in the experiment.

It is needless to add to the number of experiments that may be referred to in the United States and in England as well as in Germany to prove the existence of this particular relationship, and it was this type of work that was positively accepted by scientists as proof of the inaccuracy of Von Liebig’s statement of the law.

It also showed that as any element necessary for plant growth became less (assuming the quantity in the soil to be less than the optimum) the yield was reduced at an increasing rate.

Out of this came Mitscherlich’s well-known law of the soil. The next conspicuous development in the theoretical aspects of the law of diminishing increments was to give mathematical expression to the law.

Experiments have demonstrated that the cause-result relationships are so certain that they can be shown with mathematical exactitude.

Both Mitscherlich and Spillman, working independently and unknown to each other, showed, through empirical means, that inputoutput relationships for different plant and animal production assumed a certain form which is expressed by a logarithmic curve.

This curve is so constructed that each point on the vertical axis bears the same relation to the maximum vertical rise when expressed in terms of the corresponding point on the horizontal axis as any other point on the axis.

If, for example, a unit of any input factor, horizontal axis, results in a yield, vertical axis, of one-half the possible maximum that this variant can cause, then the second unit of input will result in the production of one-half the remainder; and the addition of a third unit of the input factor will yield one half the remaining possible production which this factor can cause (Ij 19).

It is obvious that this curve represents diminishing output per unit of additional input and that exact expression can be given it.

In each of these experiments, especially those performed by Mitscherlich, productions were obtained with the variation of a single element of plant growth. Nitrogen, phosphorus, or sunlight was varied separately, but not two were varied simultaneously.

It was in connection with the variation of more than one input factor that Mitscherlich indicated his inability to show and measure results.

Baule, however, using some of Mitscherlich’s data, deductively arrived at another mathematical expression which when plotted shows a sigmoid or S curve rather than the characteristic logarithmic curve so commonly accepted as the relationship existing between added units of input of any one factor and the corresponding additional outputs.

In working on this problem Baule expressed as 100 the maximum possible yield due to the variation of any single factor (¿).

He then determined the amount of the variable element necessary to produce 50 percent of the maximum, called the Baule unit.

If x units of the variable produced 50 percent of the possible maximum, 2x units would produce 50 percent plus one-half of 50 percent (remaining production) or 75 percent of the maximum, and 3x units would produce 75 percent plus one-half of 25 percent or 87K percent, etc.

The tabular expressions of the Baule relationships of individual elements of plant growth are shown in table 2.

Author | – |

Language | English |

No. of Pages | 12 |

PDF Size | 0.5 MB |

Category | Education |

Source/Credits | naldc.nal.usda.gov |

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