Introductory Economics

Law of Variable Proportion

Law of Variable Proportion:

• This law states that as the proportion of factors is changed, the total production at first increases more than proportionately, then equi- proportionately and finally less than proportionately.
• The classical economist called this as the Law of Diminishing Returns. They derived it by applying more and more labour to a fixed acreage of land, and thought of it as associated particularly with agriculture.
• But it is general principle that can be applied to any production operation. It is now usually called as Law of Variable proportions.

Assumptions: The law has following main assumptions

• One of the factors is variable, while others are fixed.
• All units of the variable factor are homogeneous.
• The technology of production is constant.
• The factors of production can be used in different proportions.

Explanation of the law:

• This law can be explained with the help of following table and figure.

Units of land ( Fixed input)	Units of labour (Variable input)	Total product (TP)	Marginal Product (MP)	Average Product(AP)
(1)	(2)	(3)	(4)	(5)	at increasing rate
1	1	2	-	2.0
1	2	5	3	2.5
1	3	9	4	3.0
1	4	12	3	3.0	at decreasing rate
1	5	14	2	2.8
1	6	15	1	2.5
1	7	15	0	2.1
1	8	15	0	1.8

• Suppose a farmer has one hectare farm and possess all the inputs of production. He wants to grow say tomato. He wants to decide about the number of labourers to be used, keeping other factors constant. So as the number of labourers is increased, the Total product, Marginal product and Average product is as shown in the table. Column 1 of the table shows the fixed factor i.e. land, whereas column 2 shows the variable factor labour. By using one more unit of labour whatever addition is made to the total production is called marginal product. (Column 4). Column 5 shows the average product.
• The table shows that if increasing units of labour are added to a fixed quantity of land, the total product first increases at increasing rate upto 3 units of labour afterwards it increases at decreasing rate. When 6 units of labour are used the total product is maximum. The marginal product of 7th unit of labour is zero and of 8th unit is negative. Average product of labour first increases and start the declining gradually. Average product becomes equal to marginal product, then later starts declining. The same thing is shown in the figure as below.

Three Stages of Production: From the Table as well as figure, drawn above on the assumption that production obeys the law of variable proportions, one can easily discern three stages of production as shown in the table below.

Stages	Total Product (TP)	Marginal Product (MP)	Average Product (AP)
Stage-1	Increasing	Increasing	Increasing
Stage-11	Increasing at Decreasing	Decreasing	Decreasing
Stage-111	Decreasing	Negative	Decreasing

Stage of Rational Decision: In order to achieve maximum profits, the rational decision of purely competitive firm will have to operate in stage -11. In stage-1, average returns to the variable input are increasing but the fixed input is being used uneconomically. Hence, as output increases, total profit also increases, thus the firm/farm will have an incentive to produce more through stage -1. A rational firm/farm never operates in stage -11. In this stage there is actual decline in the volume of the total production. In the words of Ferguson, “Even if the units of variable input were free, a rational producer would not employ them beyond the point of zero marginal products because their use entails a reduction in the total output.”

Causes of Application of Law: This law operates because of the indivisibility of inputs, change in their proportion and imperfect substitutes.

• Indivisibility of inputs: The main cause of the stage of increasing returns is that some inputs of production are indivisible. It means in order to produce goods up to a given limit, at least one unit of the fixed is indispensable. In the initial stages of production, fixed inputs (Land) remains underutilized and needs application of variable input (labour). Moreover additional application of variable input facilitates process based division of labour that raises the efficiency of this input. It also tends to improve the degree of co-ordination between fixed as well as variable inputs. Hence output increases at an increasing rate.
• Change in input ratio: The main cause of decreasing returns is that one of the inputs of production is variable, while other are fixed. When variable input is used with fixed inputs, their ratio compared to variable input falls. Production is the result of co-operation of all inputs. When as additional unit of variable input is combined with the fixed relatively less units of fixed inputs, the marginal return of variable input decline. For example in an area of 4 hectare 2 labourer are used to fully utilize the area. If number of labourer is increased to say 4, the land to labour ratio falls from 2:1 to 1:1. It is clear that one labour per hectare produces less as compared to 2 per hectare. Hence marginal production of labour diminishes.
• Imperfect substitutes: According to Mrs. Joan Robinson, imperfect substitution of inputs is mainly responsible for the operation of diminishing returns. Had perfect substitution among the inputs been possible then after the optimum use of fixed input, as the units of variable input are increased, the amount of fixed input could be increased by making use of substitutes. But in real life inputs are imperfect substitutes and hence one input cannot be substituted by another input indefinitely.