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## Note on Law of Variable Proportion

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• Things to remember

### LAW OF VARIABLE PROPORTION

The Law of Variable Proportion explains how the output changes when one factor of production is made variable keeping other factors constant. In other words, it refers to the input-output relation when output is increased by varying the quantity of one input.In this law, the unit of labour change by keeping capital constant . As a number of fixed factors,capital is fixed then fixed factor and variable factor can be combined together in varying proportion. So, it is also called " The Law of Proportionality".

#### STATEMENT OF THE LAW

If we increase the quantity of variable factor keeping a number of fixed factors constant, then the total production initially increase at increasing rate, then the increase at decreasing rate becomes minimum and ultimately, the total production begins to fall. This law is also called "Short Run Production Function". The short run production function can be expressed as:

Q = f(K, L)

Where,

Q = Output

L = Variable input labour

K = Fixed input capital

According to PA Samuelson," An increase in some inputs relative to other fixed inputs will cause an output to income in a given state of technology, but after a point, the extra output resulting from the same auditions of extra inputs will become less and less."

In this law of variable proportion, we can see the changing capital labour ratio.

ASSUMPTIONS

• The technology is fixed.
• Variable inputs are homogeneous.
• Short run production
• At least one factor of production should be fixed.
• Inputs are used in varying production.

SCHEDULE ANDFIGURE

We can further explain this law by the following hypothetical table/schedule.

 Unit of Labour Total Production Marginal Product Average Product Returns 0 0 0 0 Increasing 1 5 5 5 2 15 10 10 3 30 15 15 4 50 10 15 5 60 5 10 Diminishing 6 60 0 5 7 50 -5 3 Negative

We can plot the data in graph, we obtain TP, MP and AP curve like as below;

In the above figure TP, AP and MP are shown in Y-axis and unit of labour are shown in the X-axis. In all the curves above, we can see that TP, AP, MP initially increase become maximum and fall. The point to be noted is that MP become negative but TP and APremain positive. When AP1is in its highest point,MP1has started to fall but Tp is still increasing. Again when TP reaches its highest point, MP becomes zero and AP start to fall. Finally, when TP starts to fall, MP becomes negative and AP is still falling but it remains positive. The above figure illustrates three stage of short run production process.

First Stage:

In first stage, MP starts to declines & TP increases in increasing ratio. This stage also called stage of increase in return. First stage ends when AP & MP are equal. This stage is not suitable for production decision because fixed factor are not utilized in full capicity in this stage.

Second Stage:

In second stage, TP become maximum  & stable & MP become zero. This stage is also called stage of diminishing return. Second stage is more appropriate for production decision because there is good combination of fixed & variable factor in this stage. It means fixed factor are utilized in full capacity.

Third Stage:

In third stage, MP becomes negative & TP starts to decline. This stage is also called stage of negative return. This stage also is not suitable for production decision because fixed factor are used beyond capacity in this stage.

#### APPLICATION OF LAW OF VARIABLE PROPORTION

Law of Variable Proportion is basically applicable in agriculture sector because agricultural land are fixed. This law is applied in forming under intensive cultivation, tanl or pond, fishery, etc.

Assumption:

1. All factors (inputs) are variable but enterprise is fixed.
2. Input (labour & capital) are used in fixed proportion.
3. No change in state of technology
4. There is perfect competition.
5. The product is measured in quantities (cardinal approach).

(Jha, Bhusal and Bista)(Karna, Khanal and Chaulagain)(Khanal, Khatiwada and Thapa)

Bibliography

Jha, P.K., et al. Economics II. Kalimati, Kathmandu: Dreamland Publication, 2011.

Karna, Dr.Surendra Labh, Bhawani Prasad Khanal and Neelam Prasad Chaulagain. Economics. Kathmandu: Jupiter Publisher and Distributors Pvt. Ltd, 2070.

Khanal, Dr. Rajesh Keshar, et al. Economics II. Kathmandu: Januka Publication Pvt. Ltd., 2013.

1. Short run : Period of time in which quantities of one or more production factors cannot be changed.
2. Long run: Period of time in which quantities of all factors of production are variable.
3. Amount time needed to make all production input are variable.
4. Law of variable proportion is also called short run production function.
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