The law of variable proportion states that keeping all other factors fixed, when the quantity of one factor increases, the marginal product of that factor will eventually decline. This means that upto the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative.

#### Definition

“As the proportion of the factor in a combination of factors is increased after a point, first the marginal and then the average product of that factor will diminish.” Benham

**Assumption**

The following assumption of law of variable proportion

- The state of technology is assumed to be constant
- Fixed amount of other factors
- The law is based upon the possibility of varying the proportions in which the various factors can be combined to produce a product.

**Illustration of the Law:**

The law of variable proportion is explained in the below given table and figure. Assume that there is a given fixed amount of land, in which more labour (variable factor) is used to produce agricultural products.

Units of labour | Total product | Marginal product | Average product |

1 | 2 | 2 | 2 |

2 | 6 | 4 | 3 |

3 | 12 | 6 | 4 |

4 | 16 | 4 | 4 |

5 | 18 | 2 | 3.6 |

6 | 18 | 0 | 3 |

7 | 14 | -4 | 2 |

8 | 8 | -6 | 1 |

In the above table we can observe that upto the use of 3 units of labour, total product increases at an increasing rate. But after the third unit the total product increases at a diminishing rate.

A marginal product is the incremental change in total product as a result of increasing the variable factor i.e labour. We can see from the table, the marginal product of labour initially rises and beyond the use of the third unit it starts diminishing. The use of 6 units does not add anything in the production. Thus marginal product of labour fell to zero. After the 6 units, total product decreases and the marginal product becomes negative.

Average product is derived by dividing the total product by the quantity of the variable unit. Till the 3 units of labour, average product increases. Whereas after the 3 units, average product is falling throughout.