Law of Variable Proportions or Law of Diminishing Returns: Before understanding The Law of Variable proportions or Law Of Diminishing Returns we need to understand a few concepts:

Concept 1 : Total product: when we talk about total product, what exactly do we mean by total product? It is the total output resulting from the efforts of all the factors of production combined together at a time. If the inputs of all but one factor are held constant then the total product will vary with the quantity used of the variable factor.

Example: If we ask a laborer to produce 100 chocolates in a day  along with all other factors of production he produces 100 units. Now if we employ 2 laborers along with other factors of production they can produce 210 units. What do we observe? The total product keeps on rising as we employ more and more laborers. But this holds true upto a certain level after that the total product keeps on falling. The maximum output that can be achieved will be 750 units of chocolates by 9 or 10 laborers and at 10 laborers are employed the output falls to 740 units the reason being we have negative returns from 11th unit of labor. 

Concept 2: Average Product: It is the total product per unit of the variable factor. Symbolically, 

Eg: say labor is the variable factor of production. If a laborer produces 100 units of chocolates along with other factors of production in a day then his Average product will be: 100. On the other hand if there are 2 laborers and they produce 210 chocolates along with other factors of production then: Average  product will be: 105 units. 

Concept 3: Marginal Product: It is the change in total product per unit change in the quantity of variable factor. In other words, it is the addition made to the total production per unit of input. For eg: for eg: if 4 units of labor are employed along with other factors of production then the total units of chocolates produced are 440 units and when 3 units of labor are employed the number of chocolates produced are 330 units. Thus, the marginal product would be 110 units. Symbolically:

Relationship between Average Product and Marginal Product: Both Average Product and Marginal Product are derived from Total Product.

The relationship between average product and variable product can be summed up as follows:

• When the average product rises as a result of an increase in the quantity of variable input, the marginal product is more than the average product.
• When the average product is maximum , the marginal product is equal to the average product. In other words, the marginal product curve cuts the average product curve at its maximum.
• When the average product falls, the marginal product is less than the average cost.

The following table will confirm the above relationship.

Table: Product Schedule:

Law Of Variable Proportions or Diminishing Law of Returns: It examines the production function with one factor variable and keeping quantities of other factors fixed. In other words it refers to the input-output relationship where the output is increased by varying the quantity of one input. The important point to be noted in this case is that it operates in the short run where all factors of production can not be increased or decreased simultaneously. Foreg: we can not build or dismantle a plant in the short run. 

Interpretation: In short run, the Input-Output ratio is studied with one variable unit ( labor) where all other factors are held constant. The law of production under these conditions are given under different names:

• Law of Variable Proportions: The reason being the behavior of output is studied by changing the proportion in which inputs are combined. 
• Law of Returns to a Variable unit: The reason being any change in output is taken as  resulting from the additional variable unit. 
• Law of Diminishing Returns: The reason being the returns eventually diminish.

The law operates under certain assumptions which are as follows:

• The state of technology is assumed to be given and unchanged. If there is any improvement in technology, then marginal product and average product may rise instead of falling.
•  There must be some inputs whose quantity is kept fixed. This law does not apply to cases when all factors are proportionately varied. When all the factors are proportionately varied, laws of returns to scale are applicable.
• The law does not apply to those cases where the factors must be used in fixed proportions to yield output. When the various factors are required to be used in fixed proportions, an increase in one factor would not lead to any increase in output i.e., marginal product of the variable factor will then be zero and not diminishing.

Stages of Law of Variable Proportions: There are three stages of law of variable proportions:

• Stage 1: The stage of Increasing Returns:
• Stage 2: The stage of Diminishing Returns
• Stage 3: The stage of Diminishing Returns

Before understanding this concept let us understand it via a diagram and plot the Product Schedule:

Diagram: Law of Variable Proportions:

Stage 1: The stage of Increasing Returns: In this stage, the total product increases at an increasing rate ( up to point F) as per the above fig ,  Marginal Product also rises and is maximum at the point corresponding to the point of inflexion and average product goes on rising. From point F onwards during stage one, the total product goes on rising, but at a diminishing rate. Marginal Product falls, but it is positive. Stage 1 ends when the Average Product reaches its highest point. The important point to note in Stage 1 is that the Average Product curve rises throughout, whereas the marginal product curve first rises and then starts falling once it reaches its maximum. The marginal product, though starts  to decline, remains greater than the average product throughout the stage, so the average product continues to rise. 

Explanation of Law of Increasing Returns:  The combination of fixed factors of production and variable factors of production plays a key role while calculating the returns. In the beginning, fixed factors can be used more intensively and effectively. The law of increasing returns operates because in the beginning the quantity of fixed factors is abundant as compared to the quantity of variable factors. As an increasing number of variable factor units have been added to the constant quantity of the fixed factor, production is increasing rapidly. For e.g.: A machine will be highly efficient if 4 workers were working on the machine as compared to only three workers working on the machine. Now if we employ the 4th worker the efficiency would definitely increase. Now the question arises why the fixed factors were not taken into consideration while determining the quantity that suits the available quantity of the variable factor. The answer to the above is generally the fixed factors are indivisible. The indivisibility of factor means due to technological requirements a minimum amount of factor must be employed, whatever be the level of output. The second reason why we get increasing returns is that at the initial stage, as more and more units of variable factors will be employed for that, then the efficiency of the variable factor of production increases. This is mainly because of division of labor and specialization becomes possible with sufficient quantities of the variable factors, thereby resulting in higher productivity.  

Stage 2: The stage of Diminishing Returns: In stage 2the total product continues to increase at a diminishing rate until it reaches its maximum point, i.e. point H as per the above figure, where the second stage ends. In this stage, the important point to be noted is that both marginal product and average product of the variable factor are diminishing but are positive. At the end of this stage, i.e. at point  M (corresponding to the highest  point H of the total product curve) , the marginal product of the variable factor is zero. The rationale for calling stage 2 as the stage of diminishing returns is that both the average and the marginal products of the variable factors continuously fall during this stage, thus it becomes a significant stage because the firm will seek to produce within the range.

Explanation of Law of Diminishing Returns:  As we know, we get increasing returns because of more efficient use of fixed factors as more units of the variable factor are combined to work for it. However, once the point is reached at which the amount of variable factor is sufficient to ensure efficient utilization of the fixed factor. Any further increase in the variable factor will cause the marginal and average product to decline because the fixed factor then becomes inadequate as compared to the variable factor. For eg: if 4 men are employed to work on a machine in order to achieve the optimum combination was achieved and in case if 5th person is employed his contribution will be nil. In other words, the marginal product will start diminishing. The phenomenon of diminishing returns just like that of increasing returns just like that of increasing returns depends upon the invisibility of the fixed factor. Just as the average product of the variable factor increases in the first stage due to better utilization of the indivisible factor, the average product of the variable factor diminishes in the second stage when the fixed indivisible factor is being worked too hard. Another reason for the law of diminishing returns  is the imperfect substitutability of one factor for another. If perfect substitutes for scarce fixed factors would have been available, then the paucity of scarce fixed factors during the second stage would have been made up by increasing the supply of its perfect substitute, with the result that output would have been expanded without diminishing returns.

Stage 3: The stage of Negative  Returns: In stage 3, the total product declines, marginal product is negative and average product is diminishing. This stage is also called the stage of negative returns since the marginal product of the variable factor is negative during this stage.

Explanation of Law of Diminishing Returns:  As the variable factor continues to be increased to a constant quantity of another, a stage is reached when the total product declines and the marginal product becomes negative. The reason being the quantity of the variable factor becomes too expensive relative to the fixed factor so that they can get in each other’s ways and as a result the total output falls instead of rising. In such a situation, a reduction in the units of the variable factor will increase the total output.

Stage Of Operation: Now, the most important question in this stage is when will a rational producer produce? A rational producer would never produce in stage 3 as the marginal product of the variable factor is negative. A producer can always increase its output by reducing the amount of variable factor even if the variable factor is free of cost, a rational producer steps before the beginning of the third stage. A rational producer won’t be producing in stage 1 too as he will not be making the use of fixed factors as he will not be utilizing fully the opportunities of increasing production by increasing the quantity of the variable factor, whose average product continues to rise throughout stage 1. Even if the fixed factor is free in this stage, a rational producer will continue adding more variable factors. Thus, one thing is clear from the above discussion that a rational producer will not produce in stage 1 and stage 3 and hence, the stages are also called stages of ‘ economic absurdity’ or ‘ economic nonsense’. A rational producer will always produce in stage 2 where both marginal product and average product of the variable factor are diminishing. The producer’s decision to produce at a particular stage also depends upon the price of the factors. The optimum level of the variable factor (here labor) will be determined by applying the principle of marginalism in such a way that the marginal revenue product of labor is equal to the marginal wages.

Returns to Scale: We’ll now look at how output varies when all components of production in a given production function are increased at the same time. In other words, we’ll look at how output changes in reaction to a change in scale. When a scale is changed, it indicates that all production factors are increased or decreased in the same amount. Changes in factor proportions are not the same as changes in scale. As previously stated, the law of variable proportions deals with changes in output as a result of changes in factor proportions. Returns to scale, on the other hand, is the study of changes in output as a result of changes in scale, which is described further below. It should be preserved. It’s important to remember that a firm’s returns to scale are exclusively driven by technological factors and are not influenced by the economic decisions taken by the firm or by  market conditions. Returns to scale might be:

•  Constant 
• Increasing or 
• Decreasing

Let us understand each one of these points:

Constant Return to Scales: The question arises when can we say that returns to scale are constant? Returns to scale are considered to be constant if we increase all factors in a certain proportion and output increases in the same proportion. Returns to scale are constant if all factors are doubled or tripled, resulting in a doubling or trebling of output.  Constant returns to scale imply that as the scale is increased in some proportion, production grows in the same proportion. Constant returns to scale, often known as the “Linear Homogeneous Production Function,” can be written as:

When all of the inputs are increased by a particular amount (say k), the output grows in the same proportion (k). It has been found that an individual firm passes through a long phase of constant returns over its lifetime.

Increasing Return to Scales:  Returns to scale are considered to be increasing if an increase in all components leads to a greater than proportionate increase in production. Returns to scale are considered to be growing if all factors are doubled and output increases more than double, then the returns to scale are considered to be increasing. Increasing returns to scale indicates that output grows at a faster rate than inputs grow. Increasing returns to scale are obtained in the early stages of a company’s expansion. A three-foot-cube wooden box, for example, holds nine times the amount of wood as a one-foot-cube wooden box. The capacity of the three-foot-cube box, on the other hand, is 27 times that of the one-foot-cube box. Many examples like these can be discovered in the actual world. Another reason for increasing returns to scale is the indivisibility of factors. Some factors are available in huge, lumpy units and can thus be used with utmost efficiency at large output. Increasing returns may not be possible if all of the elements are perfectly divisible. Returns to scale may also increase because of greater possibilities of specialization of land and machinery. 

Decreasing Return to Scales:  Returns to scale are said to be diminishing when all components rise but output increases less than proportionately.  When output grows at a slower rate than all other inputs, decreasing returns to scale is said to be the case. When a company continues to grow by increasing all inputs, falling returns to scale occur. Because of the rising difficulty of management, coordination, and control, decreasing returns to scale eventually arise. It is tough to manage a company that has grown to a large size with the same efficiency as before. The Cobb-Douglas production function is used to explain production “returns to scale.” Cobb and Douglas first thought that returns to scale are constant. The exponents of the function were created in such a way that they added up to a+1-a=1. The criterion was later reduced, and the equation was rewritten as follows:

Where ‘Q’ stands for output, ‘L’ for labor, and ‘C’ for capital, and ‘K’, ‘a’, and ‘b’ stand for positive constants.

Interpretation:

If a + b > 1, Increasing Returns to Scale result, i.e., increase in output is more than proportionate increase in the use of factors.

If a+b=1, Constant Returns to Scale result, i.e., the output increases in the same proportion in which factors are increased.

If a + b< 1, Decreasing Returns to Scale result, i.e., the output increases less than proportionate increase in the labor and capital.

Thanks for Reading, always Welcome. Stay tuned for more……