**Law of variable proportion **

**The**

**law of variable proportion**was proposed by economist like Joan Robinson, Alfred Marshall, P.A Samuelson. This law is also known as the

**law of diminishing returns**. This law Concerns with a short-run production function. This law examines the production with one-factor variable keeping the other factors constant. When the quantity of one factor is changed, keeping the quantity of another factor constant the proportion between the variable factor and the fixed factor is changed. So, it is known as the law of variable proportion.

According to this law, as the quantity of variable factor is increased by equal amount keeping the other factors constant, initially the total product increases at an increasing rate, but after a point, it increases at a decreasing rate, becomes maximum and finally declines.

**Assumptions of the law of variable proportion: **

- The state of technology is given and constant
- At least one factor of production should be fixed.
- There must be a possibility of varying the proportion of factors of production.

**aw of variable proportion**can be explained by the help of the following table and diagram:

Units of labor (L) | Total product (TP) | Average product(AP) | Marginal product (MP) | Remarks |

0 | 0 | 0 | 0 | Stage l (no operation)(No production) |

1 | 10 | 10 | 10 | |

2 | 30 | 15 | 20 | |

3 | 60 | 20 | 30 | |

4 | 80 | 20 | 20 | Stage ll (operation point) |

5 | 90 | 18 | 10 | |

6 | 90 | 15 | 0 | |

7 | 77 | 11 | -13 | Stage lll (no operation)(No production ) |

This law can be divided into 3 stages. They are explained as follows:

**Stage 1 (stage of increasing returns)**

**In this stage, TP increases at an increasing rate unto a certain point and then it increases at a decreasing rate. In the figure, TP is increasing at an increasing rate up to point A and then it increases at a decreasing rate. This stage ends at point E where MP = AP**

**Stage 2 (stage of decreasing returns)**

**This stage begins from point B of TP. In this stage total product continues to increase at the diminishing rate until it reaches point C. The rational producer will choose to produce in this stage because the total product is maximum, AP is diminishing and MP is 0.**

**Stage 3(stage of negative returns)**

**This stage begins from point D. In this stage, TP is declining, AP is also declining and MP is negative. AP never becomes zero and negative.**

**Application/ Importance of the law of variable proportion **

**This law specially applies to agriculture because agricultural operations are carried out during short period of time, the use of technologies and machinery are very limited in agriculture. Land is taken as the fixed factor and labour, raw materials, seeds etc are taken as variable factors which satisfy the assumption of this law.**

This law does not only apply in agriculture. There are many industries, processes and business activities which operate in the short run.

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