**Explain in detail the Law of Variable Proportions. Give its causes **

**Ans:- Meaning of law of variable:- **Law** of variable proportions **Refers to “When one factor is increased while other factors of production are constant then total output will increase”.

**Definition of law of variable proportions:-**

**According to leftwich “The law of variable proportions states that if the input of one resource is increased while the input of other resources are constant, total output will increase”.**

**In other words:- **A single variable of inputs is increased in the production process while the other factor of inputs remains constant causing an increase in production.

On account of change in proportion of factors is called the law of variable proportions. Due to change in proportion of input factor causing change in production at first phase is increasing then after it becomes constant then beyond this it becomes diminishing in the production of process function.

Law of variable proportion | Return to a factors |

A Single Variable Factor ( Other Factors Constant ) |

It ia a Short Run Analysis |

The law of variable proportions has three different phases

**Increasing Return to a Factor****Constant Return to a Factor****Diminishing Return to a Factor**

**Increasing Return to a Factor:- I**t is a situation in which total output tends to increase at an increasing rate when more of the variable factor is combined with the fixed of production. In which marginal product is increasing and cost marginal product must be diminishing.

**Explanation**

Table shows the operations of increasing return to a factor.

Units Of Labour | Units Of Capital | Total Product | Marginal Product |

1 | 1 | 4 | 4 |

2 | 1 | 10 | 6 |

3 | 1 | 18 | 8 |

4 | 1 | 28 | 10 |

5 | 1 | 40 | 12 |

**Figure shows**

**This table shows that more and more units of labour are combined with the fixed amount of capital.**

** **Total marginal product is increasing at the increasing rate. While the total product increased in production.

Note:- Increasing to a factor leads to Diminishing cost. As a law of increasing return, When the output is increased, average cost per unit goes on diminishing |

**Causes of increasing Return to Scale**

**( I ) Fixed Factor:- **Underutilization remains of fixed factor. Its full utilisation calls for greater application of the variable factor.

**Example – **A small plant manufacturing cloth. The size of the plant is fixed in a short period. Five workers are required to get maximum output out of this plant. If a firm hires only two workers then production would be inefficient. The plant would be more efficiently utilised if more workers are added.

**( II ) Increase in efficiency :- **Due to increase in variable units of input leads to possibility of division of labour and specialisation. Division of labour increases efficiency and efficiency leads to more production.

**( lll ) Better Coordination between factors :- ** Additional application of variable factor of input tends to improve the efficiency of constant factor of input. Due to which production will be increased.

**Constant Return to a Factor:-**It is the stage when increasing application of the variable factor results no increase in the marginal product of the factor. Rather, the marginal product of the factor tends to stabilise.

**In other words:- **Constant return to a factor occurs when additional application of the variable factor increases output also increases at the constant rate.

Constant Cost :- Cost of production will remain constant at the constant Return of Law. |

**Following Table shows proper Understanding **

Units of Labour | Units of capital | Total Product | Marginal Product |

1 | 1 | 5 | 5 |

2 | 1 | 10 | 5 |

3 | 1 | 15 | 5 |

4 | 1 | 20 | 5 |

5 | 1 | 25 | 5 |

**Table **shows that as more and more units of labour are combined with the fixed amount of capital, total output increases only at the constant rate. Marginal product of the variable factor remains constant.

We can also understand the graph of constant return of factor

**Figure A. **As Total product increases at the constant rate indicated by an upward sloping straight line TO curve.

**Figure B. Shows **constant marginal product of the variable factor, indicated by horizontal straight line MP.

**Causes of Constant Return to a Factor**

**( I ) Fixed Factor :- **With the increasing of variable factor production is increased, however, a stage comes when the fixed factor gets optimally utilised. Here the marginal product of the variable factor is maximised and tends to remain constant.

**( ll ) Factor Ratio :- It is **an Ideal factor Ratio between fixed and variable factor. Hence, Marginal product of the factor stabilises at its maximum.

**( lll ) Variable Factor :- **A combination of fixed factor and variable factor a stage comes when there is best division of labour. Where variable factor is most efficiently Utilised. Here marginal product tends to be constant at its maximum.

**Diminishing Return to a Scale:-**It refers to a situation in which total output tends to increase at the diminishing rate when more variable factor is combined with the fixed factor of production. In such a situation marginal products must be diminishing.

**In other words :- **As more and more units of labour are employed on a given piece of land, the marginal product of the additional units of labour will go on diminishing.

Note Increased Cost:- The law of diminishing return gives the cost of production is increased. |

**Following Table shows proper understanding**

**Diminishing Return to a Factor**

Units of Labour | Units of capital | Total Production | Marginal Production |

1 | 1 | 5 | 5 |

2 | 1 | 8 | 3 |

3 | 1 | 10 | 2 |

4 | 1 | 11 | 1 |

5 | 1 | 11 | 0 |

6 | 1 | 10 | – 1 |

**Tables **show that as more and more units of labour are combined with fixed capital, the total capital increases only at a decreasing rate. Or it may even stop increasing at all or further start diminishing. Marginal product of the variable factor is diminishing and beyond a point it becomes zero or Even Negative.

**We can properly understand with the help of Following Figure.**

**Figure:- A Total **Product is increasing at the decreasing rate as indicated by the slope of the TP curve. At point **p **It becomes maximum and beyond that, it starts reducing.

**Figure:- B Shows** diminishing marginal product of the variable factor, indicated by downward sloping MP curve. Beyond a point it becomes zero or Even negative.

**Conclusion:- **we can understand the concept law of variable proportion or **Return to a factor. **Which includes Increasing, constant and Diminishing law of return to a factor. Here some causes of these are discussed also for the proper understanding.By Gndupapers.online law of variable proportions

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