# Solved questions to law of variable proportion

#### 1- What is law of variable proportion? Explain.

Ans: Law of variable proportion is the important law of production. It is the short-run analysis of production. In the short-run, some factors of production are fixed and some are variable. Keeping fixed factors of production constant, as variable factors are increased, the proportion of fixed and variable factors goes on varying.  Therefore, this law is called the law of variable proportion.

Law of variable proportion is also called the law of diminishing returns. It explains the impact of variation of variable factors on production of goods and services, keeping the fixed factors constant. This law is based on the following assumptions.

1-The state of technology is given and constant.

2- Some factors of production are fixed and some are variable.

3- The ratio of fixed and variable factors should be liable to vary.

4- Variable factors are homogeneous.

5- Indivisible fixed factors of production,

According to this law, when the units of a variable factor are increased to the given fixed factor, initially production increases at an increasing rate, thereafter it increases at a decreasing rate and eventually it starts to decline.

This law can be explained by the help of production schedules and figures. Suppose that the fixed factors i.e. land and capital are fixed and only a variable factor, labor is added to increase output as shown in the table.

The production schedule shows that there are three stages of production seen in the short run. They are explained below.

 Labor TP AP MP Stages 0 0 0 0 I-Stage (0 to 4th unit of labor)II-Stage (4th to 5th unit of labor)III-Stage (5th to 6th unit of labor) 1 3 3 3 2 8 4 5 3 15 5 7 4 20 5 5 5 20 4 0 6 18 3 -2

I-Stage:- TP & AP increase rapidly in this stage.  MP is maximum when the 3rd unit of labor is used and diminishes thereafter. AP is maximum when the 4th unit of labor is used & this stage ends when AP & MP are equal. This stage is called the stage of increasing returns.

#### 2-More use of variable factors increases its own efficiency through  division of labor, such as innovation, specialization etc in production.

II-Stage:- In this stage TP continues to increase at a decreasing rate.  AP & MP both decline. This stage ends when TP is maximum & MP is zero. In this schedule this happens when the 5th unit of labor is used. This stage is called the stage of diminishing returns.

#### Reasons for diminishing returns.

1-The fixed factors are over utilized and become insufficient. And the variable factors can not substitute the fixed factors.

2-The production declines due to the indivisibility of fixed factors.

III-Stage:- In this stage TP & AP both decline & MP is negative.

#### Reasons for negative MP

1-Variable factors are overcrowded & disturbs each other.

2-Difficult to coordinate among them by management.

3-Disadvantages of division of labor occurs.

It is seen in the above figure, the TP curve rises at an increasing rate in the beginning  and increases at a diminishing rate after the use of the 4th unit of  variable input. TP declines after the use of 5th units. AP & MP also increase in the beginning & decline after reaching the maximum point. The 4th unit of variable factor AP is maximum. Here AP & MP are equal. When the TP is maximum at the use of the 5th unit, MP is zero & becomes negative thereafter.

#### 2- Which stage of production is preferable?

Ans:- There are three stages of production in the short-run but which stage of production is preferable for a rational producer?

It is obvious that in the first stage of production the total product and average product are increasing, marginal product starts to decline but still positive and more than AP. So the rational producer doesn’t want to miss any opportunity for getting more benefit by postponing the production in the first stage. Hence he continues to produce up to the second stage. In the second stage TP is highest, AP is declining and MP is zero. In this stage of production, the producer can utilize his fixed factor to its fullest capacity. Any extra use of variable factors of production after this stage will bring a decline in TP and MP will be negative. It will incur losses for the producer.

So a rational producer always sticks to the second stage of production and maximizes his production and profit. He neither stops his production in the first stage nor he moves to the third stage of production.

It implies that the producer can have maximum possible production at the point where TP is highest and MP is zero. This situation of production lies in the second stage of production. So the rational producer always prefers to stay in the second stage.