The law of Variable Proportion

The law of variable proportion explains the relationship between proportion of fixed input and variable input on the one hand and output on the other during short period.  It is the modern Law of diminishing returns.  In the short period, if a firm wants to expand its production, it can do so by increasing its variable input keeping the fixed inputs constant.  As a result, the proportion between fixed and variable factors gets changed.  Such a situation is called the law of variable proportions.

Assumptions:

1.  Technology remains constant.

2.  One factor input is to be varied while all other factors remain constant.

3.  It is possible to change factor proportion.

4.  All the units of variable factors are equally efficient.

5.  Factors of production are not perfect substitutes.

The law of variable proportion can be understood with the help of the following example.  Let us suppose that a farmer uses a capital of Rs10, 000 on an acre of land and he uses labourers to cultivate the land.

Units of labour	Total product (in tonnes)	Average Product(in tonnes)	Marginal Product (in tones)
1	5	5	5
2	11	5.5	6
3	18	6	7
4	20	5	2
5	21	4.2	1
6	21	3.5	0
7	20	2.86	-1

There are three stages of Law of variable proportion:

1.  First stage or Increasing returns: When a firm expands its output by increasing the quantity of variable factor in proportion to fixed factor, it moves towards optimum combination of factors of production and at this stage, the marginal product increases and the total output increases at an increasing rate. 

Causes:  When more and more units of the variable factors are added to the constant quantity of the fixed factor it is more effectively and intensively used.

Output also increases due to effective and fuller utilization of the variable factor.

2.  Second Stage or Diminishing returns:  In the second stage, the total output continues to increase but at a diminishing rate and the marginal product diminishes. This stage continues till the total product reaches the maximum and the marginal product becomes zero.  The average product goes on diminishing indicating a decline in the efficiency of labour.

Causes:  The second stage occurs when the fixed factor becomes insufficient relative to the quantity of the variable factor.

The fixed indivisible factor is being worked too hard in a non-optimal proportion with variable factor.

3.  Third Stage or Negative Returns:  At this stage total product starts declining and marginal product becomes negative but Average product remains positive in spite of declining.

Causes:  The third stage operates when the number of variable factor becomes too excessive relative to the fixed factor.       

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In the above diagram, TP, from the point of origin to the point R increases at an increasing rate.  It is the first stage and MP curve rises in a part and then falls. The AP rises throughout and remains below MP.  From Point R onwards, during the stage II the total product increases at diminishing rate up to point T.  In the second stage both MP and AP are diminishing but are positive.  

In the third stage TP curve slopes downward from point T and the MP turns negative.  It moves below the X axis.