# Law of Variable Proportion

### Introduction

The law of variable proportion is a widely observed law of production that takes place in the short run. The law was propounded by economists like Joan Robinson, Alfred Marshall, P.A. Samuelson, etc. This law is also known as the law of diminishing returns. The law is concerned with a short-run production function.

In the short run, production can be increased by using more of the variable factor. This law applies to all sectors of an economy. The law of variable proportion states that as we employ more and more units of a variable input, keeping other inputs fixed, the total product initially increases at an increasing rate then increases at a declining rate, and finally starts falling.

That is, the MP of a variable input initially rises when the level of employment of the input is low, but after reaching a certain level of employment, it starts falling but is positive and finally continues to fall and becomes negative.

### Assumptions

The assumptions of the law of variable proportion are:

• The state of technology remains the same.
• All units of the variable factor, labor, are homogeneous.
• There must always be some fixed input and diminishing returns results due to the fixed supply of the fixed factor.

Based on the above assumptions, the law of variable proportion can be elaborated with the three-stage of production as shown by the table and graph below.

The three phases can be identified by inspecting the behavior of MP, AP, and TP related to variable input in the above table. MP of variable input rises until 3rd units of labor employment and after that, it starts to fall but remains positive up to 6th unit and thereafter it is negative.

TP first increases at an increasing rate up to the 3rd unit of labor and then increases at decreasing rate up to the 5th unit of labor.  It is maximum at the 5th unit and remains stable at the 6th unit of labor. Thereafter it starts to decrease.

AP on the other hand increases, becomes maximum at the 3rd unit of labor, and at the 4th unit, it is stable. After this, AP is decreasing. At the 4th unit of labor AP and MP are equal.

This can be presented in the following graph.

### The Stages of Production/Stages of Law of Variable Proportion

Stage-I (Stage of Increasing Returns)

• In this stage, TP increases at an increasing rate up to a certain point and then increases at a decreasing rate. In the figure, TP increases at an increasing rate up to point A, and then it increases at decreasing rate
• MP is increasing up to point G and then it is diminishing.
• AP is increasing up to point H and at point E, it is stable.
• The equality of AP and MP ends the first stage of production. So, at point E, the first stage of production is ended.

Stage-II (Stage of Decreasing Returns)

• This sage stats at point B of the TP curve. In this stage, TP continuously increases at a decreasing rate until it reaches point C. It remains stable at point D, where the second stage ends.
• MP is continuously decreasing, and it becomes zero at point F.
• AP is also continuously decreasing throughout this stage.
• This stage ends when TP becomes maximum and stable or when MP becomes zero. So, point D or TP or point F of MP ended this stage.

Stage-III (Stage of Negative Returns)

• It covers the entire range over which the MP curve is negative. This stage begins from point D of the TP curve.
• In this stage, TP starts to decline
• AP also continually declining
• MP becomes negative

### Causes of Different Stages of Production

Stage-I (Stage of Increasing Returns)

The reasons for increasing returns to a variable factor are:

Underutilisation of Fixed Factor

The fixed factor, land, is underutilized concerning labor employed on it. This helps in better utilization of the fixed factor. It results in increasing returns.

Indivisibility of Factors

The factors employed in the production process are indivisible, i.e., they cannot be divided into smaller parts. Thus, when more units of the variable factor are combined with the fixed factor, returns are increasing.

Specialization and Division of Labour

As the number of labors is increased, specialization and division of labor will lead to increasing returns.

Stage-II (Stage of Diminishing Returns)

The reasons for diminishing returns to a variable factor are:

This stage occurs because of excessive utilization of fixed factors like land, capital, overload for management, and disadvantages of division of labor, and so on. /inadequacy of fixed factors

Inefficient utilization of variable factors. It is said that ‘too many cooks spoil the birth’. So, too many labours with fixed supplied land give negative returns.

The complexity of management/the management may feel overburden

Imperfect substitutability of the factors: If fixed factors become scarce then variable factors can be used in return/fixed factors can be substituted. However, the perfect substitution is not possible and diminishing returns occur.

Stage-III (Stage of Negative Returns)

The reasons for negative returns to a variable factor are:

If we keep on adding variable factors like labor on a given fixed factor, this will lead to overcrowding on the fixed factor. There will be a chronic shortage of tools and equipment per worker, which causes a fall in production.

The use of too many variable factors like labor also creates the problem of effective management. When there are too many workers, they may shift responsibility onto the others. It makes it difficult for management to fix the duties and responsibilities. Labor therefore can avoid the work and ultimately negative returns occur.

### Law of Variable Proportion: Stages of Production

As we discussed the three main stages of the law of variable proportion, it is important to explain which stage is the important stage of production.

In stage I, there are increasing returns till the maximum AP. There is a further possibility to increase profit beyond this stage. Thus, the producer does not want to stop production at this stage.

In stage III, there are negative returns. Operation beyond the situation causes a fall in the output with an increase in input which means losses to the producer. Therefore, production does not concur in this stage.

It means, production only occurs in stage-II, where the producer maximizes profit.

### Law of Variable Proportion: Application

The law of variable proportion is applicable in agriculture because the area of land is fixed in supply and the number of farmers that are labor- variable factor.

Initially, the total product increases become maximum and begins to decline with an increase in labor units.

Besides the agriculture sector, this law is also applied in the following sectors.

• River and tank fisheries
• Mines and brickfields
• Forest products
• Construction of buildings etc.
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