# The Law of Diminishing Returns to a Factor

This law is important to understand the contribution made by different factors of production in the production process. To understand this law, you must revise production function and terms related to the concept of production, because it is a building block for the law of diminishing returns to a factor. In this post, I will be explaining this law in the following parts:

## Statement

The law of diminishing returns to a factor is also known as the law of variable proportion. This law relates to the short-run in which to increase production only variable factors can be increased.

This law states that as more and more units of a variable factor are employed with fixed factors, the Total product increases at an increasing rate, in the beginning, then total product increases, at a diminishing rate, and finally, it starts falling.

## Assumptions

There are some assumptions for the law of diminishing returns to a factor to be valid. These are:

**The technique of production does not change**– If a producer is using the capital intensive technique, then it will remain the same, and it will not change to labor-intensive technique during the production process.**All units of the variable factors are equally efficient**– If 100 labors are working in a factory, then all of them are working efficiently.**Factors of production are not a perfect substitute for each other**– Variable factors can not replace each other.**One factor is considered to be fixed which causes a change in the ratio between fixed and variable factors**. That’s why this law is termed as variable proportion.

## Stages of the law of variable proportion

There are 3 stages, let’s understand them:

### Increasing Returns to a Factor

In this stage, the total product curve increases at an increasing rate up to a point. Let that point be I, where total product stops increasing at an increasing rate and starts increasing at a diminishing rate, this point is called a point of inflection.

At the point of inflection, the Marginal product reaches its maximum and starts falling.

The average product keeps on increasing and becomes equal to the marginal product. That’s the point where the first stage gets over.

### Diminishing Returns to a Factor

In this stage, the total product curve continues to increase at a diminishing rate until it touches its maximum point M, where the second stage ends.

During this stage, the marginal product and the average product of the variable factor are diminishing, but remain positive.

At the end of this stage, when TP reaches its maximum, MP becomes 0.

### Negative Returns to a Factor

During this stage, with the increase in the variable factor, the TP declines and slopes downward.

As a result, the MP of the variable factor becomes negative. In this stage, the variable factor is more than the fixed factor.

This stage is called the stage of negative returns because MP becomes negative during this stage.

## Schedule

The following is the table of TP, MP and AP curve:

Labor | TP | AP | MP |
---|---|---|---|

0 | 0 | – | – |

1 | 2 | 2 | 2 |

2 | 5 | 2.5 | 3 |

3 | 9 | 3 | 4 |

4 | 12 | 3 | 3 |

5 | 14 | 2.8 | 2 |

6 | 15 | 2.5 | 1 |

7 | 15 | 2.14 | 0 |

8 | 14 | 1.7 | -1 |

9 | 12 | 1.3 | -2 |

## Diagrammatic Presentation

As you can see, from the diagram, the point I is the point of inflection, where MP is the maximum, and M is the point where TP reaches its maximum, and MP becomes 0.

Stage 1 ends, where MP=AP.

Stage 2 ends, where TP is maximum and MP is 0.

Stage 3 ends, where TP starts falling, and MP becomes negative.

Tips to memorize the stages of the law of variable proportion:

Make sure you write about TP, AP, and MP in all the 3 stages.

IRF- Increasing returns to factor: TP increases at an increasing rate than at a decreasing rate. At the point of inflection MP becomes maximum and then falls. AP increases, when AP = MP, this stage ends.

DRF- Diminishing returns to factor: TP reaches its maximum, MP falls and becomes 0, and AP keeps falling but remains positive.

NRF- Negative returns to factor: TP falls, MP becomes negative, and AP keeps falling but remains positive.

Thanks for reading.

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Happy Learning!

Photo by Elena Kloppenburg on Unsplash