Law of Variable Proportion

 

Introduction:

It occupies an important role in the economic theory and also known as the law of proportionality. It is the short run production function which shows the functional relationship between the fixed and variable factors of production. In the short run, when output of a commodity is sought to be increased, the law of variable proportion comes into operation. Since, this law shows the effect on the output due to the variation in the proportions of the factor inputs i.e. the labor and capital, it is known as the law of variable proportion. This law was propounded by the economists like Joan Robinson, Alfred Marshall, P.A. Samuelson, etc.

Statement: The law of variable proportion states that when we go on adding more and more units of variable inputs i.e. labor to the given level of fixed input i.e. Capital, the total product in the initial stage increases at increasing rate, then at decreasing rate until it is maximum and finally begins to decline.

Assumptions:

a.      The state of technology remains constant.

b.     Each unit of the variable factor i.e. labor is homogeneous.

c.      Only one factor input i.e. labor is variable and another factor i.e. Capital remains constant.

d.     Prices of the factor inputs are given.

Land (L) (in Ropanies)	Units of Labor	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
10	0	0	0	0
10	1	10	10	10
10	2	30	15	20
10	3	60	20	30
10	4	80	20	20
10	5	90	18	10
10	6	90	15	0
10	7	80	11.5	-10

 

Stages of the law:

a.      Stage I

In this stage, TP increases at an increasing rate upto 3^rd unit of labor and then has started increasing at the diminishing rate. MP is increasing upto 3^rd unit of labor and then it is decreasing. AP is increasing upto the 3^rd unit of labor and becomes stable. The stage ends at point E where AP and MP are equal i.e. AP=MP. This stage is also regarded as the stage of increasing returns because the MP of labor exceeds the AP throughout this stage.

b.     Stage II

This stage ranges from 4^th unit of labor to 6^th unit of labor. The TP in this stage increases at the diminishing rate until 5^th unit of labor and remains stable at 6^th unit of labor where the second stage ends. In this stage, AP is continuously decreasing from 4^th to 6^th unit of labor. In this stage, MP continuously decreases and it is zero at 6^th unit of labor. As both AP and MP continuously fall throughout this stage, it is regarded as the stage of diminishing,

c.      Stage III

It begins from the 6^th unit of labor. In this stage, TP is declining. AP is also declining in this stage but never becomes zero and negative. MP becomes negative. In this stage, MP is negative so it is also regarded as the stage of the negative returns and a firm won’t produce anything.

Stage of Operation

A rational producer will never choose to produce in the stage III where MP of variable factor is negative because the TP declines in this stage and there is no production. A producer also never chooses to produce in the Stage I although TP increases and MP of variable factor is positive because there is an opportunity of increasing production by increasing quantity of the variable factor where AP continues to rise throughout the stage I. A producer will choose to produce at Stage II because TP is maximum and both MP and AP are diminishing.