Short run production function - law of variable proportions/Law of diminishing returns

The law of variable proportions is one of the fundamental laws of economics. It is the generalized form of the law of diminishing marginal return. The law of variable proportions states that as we increase the quantity of one input which is combined with other fixed inputs, the marginal physical productivity of the variable input will eventually decline. In other words, an increase in some inputs in relation to other fixed inputs will cause the output to increase, but after a certain point, the output from the addition of inputs will become less.

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

Assumptions of the concept

• No change in technology: This law assumes that there will be no change in technology. No upgradation or no degradation will take place in terms of technology or same technology will be used throughout the process of study.
• Short - run: The law of variable proportions operates only during the short run. As a result of shortage of time, producer will be changing the proportion of only one factor and other factors are assumed to be constant.
• Identical or homogenous factors: The various factors that producer is going to use will be identical in all respects. i.e., the second unit of factor would be similar to the first factor used.
• Only three factors: Even though there are four factors of production – here, for the convenience of study we take into consideration only three factors of production. They are:- Land, Labour, Capital. Out of these land and capital will be kept as constant and labour will be the only variable factor. If the producer wants to increase the production, he has to employ more and more units of labour and vice versa.
This could be explained with the help of a numerical schedule:

 Units of Labour Total Product Average Product Marginal Product Stage 1 20 20 20 1st Stage 2 50 25 30 3 90 30 40 4 120 30 30 5 140 28 20 2nd Stage 6 150 25 10 7 150 21.42 0 8 140 17.5 -10 3rd Stage

Total product (TP)

As it could be seen from the table, when one unit of labour is employed, the total product is 20 units. When two units of labour are employed, the total product rises to 50 units. The total product goes on rising as more and more units of labour is employed. With the 7 unit of labour the total product rises to 150 units. When the 8th unit of labour is employed the total product falls to 140 units.

Average product (AP)

It is the total product per unit of variable factor {TP/Q}. As it is evident from the above table average product goes on increasing slowly as more and more labourers are employed and also decreases slowly after the appointment of 7th unit of labour.

Marginal product (MP)

It refers to the change in total product because of per unit change in the quantity of labour employed. Marginal Product = TPn – TPn-1 {Total product of the present unit minus Total product of the previous unit}. In other words, it is the addition made to the total production by an additional unit of input.

The behaviour of these three products may be better analyzed through a graph. The behaviour of these three products as a result of changing the quantity of labour is generally divided into three stages for the convenience of study. They are: -

1st Stage:
In this stage, the Total Product increases at an increasing rate, Average Product slowly increases and Marginal Product increases very rapidly but by the end of this stage, it starts diminishing rapidly. Since all the three products are increasing – this is known as “Stage of Increasing Returns”.

Explanation: The law of increasing returns operates because in the beginning the quantity of fixed factors is abundant relative to the quantity of the variable factor. As more and more variable factor is employed to the constant quantity of the fixed factors, then the fixed factors is more intensively and effectively utilised. This causes the production to increase at a rapid rate. Since the fixed factor is non divisible in nature, the factor must be employed whatever may be level of output. Hence initially it will not be put into the optimum use.

2nd Stage:
In this stage Total Product increases but at a dinishinging rate. Average Product decreases slowly and Marginal Product decreases very rapidly but is still positive. Hence it is known as “Stage of Diminishing Returns”

Explanation: As it is quite evident from the table and the diagram, after a certain amount of the variable factor has been added to the fixed quantity, land and capital, we get diminishing returns. Initially increasing return occurs because of more efficient utilisation of the fixed factors as more units of the variable factors are employed. Once the point is reached at which, the amount of variable factor is sufficient to ensure efficient utilisation of the fixed factor, then further increase in the variable factor will cause marginal and average product to decline because the fixed factor then becomes inadequate relative to the quantity of the variable factor. Hence diminishing returns occurs.

3rd Stage:
In this stage Total Product decreases, Average Product also decreases but Marginal Product will be negative. Hence this stage is known as “Stage of Negative Returns”

Explanation: As the amount of the variable factor continues to be increased to constant quantity of the fixed factor, a stage is reached, when the TP decline and Marginal Product becomes negative. This is because, the quantity of variable factor becomes too excessive relative to the quantity of fixed factor, as a result total product falls instead of rising. In such a situation a reduction in the units of the variable factor will increase the total output.

A rational producer will opt for the 2nd stage, because at this stage he will be maximizing Total product and making optimum use of the factors. So Stage 1 and 3 are non-economic regions in the production process.  