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Updated on 13th January, 2023 , 8 min read
The Law of Variable Proportions, often known as the Law of Returns to a Factor, is an essential concept in the study of the Theory of Production. It is recognized as a significant economic theory that states that increasing the quantity of one element of production while keeping all other variables constant causes the marginal product of that factor to decrease. The Law of Variable Proportion is another term for the Law of Proportionality.
When the variable component increases, the marginal product may have a negative value. When a variable factor is raised while all other elements remain constant, the total result will initially grow at an increasing pace, then decrease at a decreasing rate, and finally, drop at a decreasing rate.
The Law of Variable Proportions is concerned with how the output varies when the number of units of a variable component is increased. As a result, it relates to the effect of altering the factor ratio on output. In other words, the rule depicts the short-term relationship between the units of a variable element and the amount of output. This assumes that all other variables remain constant. This is also known as the return to a variable factor relationship. The rule indicates that when you raise the variable component while leaving other elements constant, the total product initially climbs at an increasing pace, then decreases at a reducing rate, and ultimately begins to decline. In other words, when one of the components in production varies in amount while the other factors remain constant, the ratio between the factors begins to shift, influencing the level of output.
This rule illustrates short-run production functions in which one element fluctuates while the rest remains constant. Furthermore, when you acquire extra output by applying an additional unit of input, this output is either equal to or less than the output obtained from the prior unit.
For Example:- Imagine you're standing in line at your favorite ice cream shop, anxious to dig in, and you start eating the scoops one after the other. Your pleasure level is at its height at first, and after 3 or 4 scoops, your level is still growing, but at a slower rate. Eventually, you'll reach a point when you're practically content and full, and you'll be less likely to take another scoop. This is what the Law of Variable Proportions entails.
As one input varies and all others remain constant, the factor ratio or the factor proportion varies. To better comprehend this, consider the following example below-
Assume you have 10 acres of land and 1 unit of labor to produce. As a result, the land-labor ratio is 10:1. If you maintain the land unchanged but raise the labor units to two, the land-labor ratio becomes 5:1. As can be seen, the law examines the consequences of a change in the factor ratio on the quantity of out and is hence known as the Law of Variable Proportions.
The law of variable proportion remains true under specific conditions, which are described below-
The phrases that will be used in the Law of Variable Proportion are explained in the table below-
Terminologies |
Description |
Marginal Product (MP) |
When a producer uses more units of input in variable components, he or she derives a marginal product or output. That is, it is the pace at which the TP increases. |
Average Product (AP) |
Total Product (TP) divided by Total Number of Variable Inputs = Average Product. To put it another way, AP is the output per unit. |
Total Product (TP) |
Total Product (TP) is another term for total production. This method returns the value of TP after varying the values of the physical variables input and a set quantity of input. |
Product Function |
Production, as we all know, entails the transformation of physical inputs into physical outputs. As a result, the production function illustrates the interdependence of the factors' input and output. |
The Law of Variable Proportions is divided into three stages, which are explained below-
1. Stage 1 (Stage of Growing Returns):- The first stage occurs when the overall product grows at an increasing pace. This occurs because the efficiency of the fixed elements rises as the product's variable inputs grow. The TPP expands at an increasing rate, as does the MPP. The MPP grows as the variable factor's units increase. As a result, it is also known as the stage of growing returns. In this case, Stage I of the statute allows for up to three units of labor (between the points of O and L).
2. Stage 2 (Stage of Diminishing Returns):- The second stage occurs when the total product rises at a decreasing pace until it reaches its maximum value. The TPP continues to grow, although at a slower pace. The growth, though, is positive. Furthermore, as the number of units of the variable component increases, so does the MPP. As a result, it is known as the stage of decreasing returns. In this case, Stage II requires four to six units of labor (between the points L and M). This stage reaches a point when TPP is at its maximum (18 in the preceding example) and MPP is zero (point R). The marginal and average products are both positive, but they are rapidly declining.
3. Stage 3 (Stage of Negative Returns):- The third stage occurs when the overall product drops and the marginal product becomes negative. The TPP now begins to decline, and the MPP drops and becomes negative. As a result, it is known as the "stage of negative returns." In this case, Stage III requires seven to eight units of labor (from point M onwards).
The following are the significance of the three stages-
The law of variable proportions can be postponed under the following conditions-
The following are the causes of the law of variable proportion-
The below details are an explanation of TPP and MPP-
The law of variable proportions demonstrates the link between units of a variable element and the overall physical product. Also, if we hold all other variables constant while increasing the units of the variable component, the TPP grows at first at a rising pace, then at a falling rate, and eventually falls.
As a result, it has three distinct stages-
I - TPP is growing at a rapid pace.
II - The TPP's expansion is slowing.
III - TPP decline exemplification of the Law of Variable Proportions in terms of TPP.
The law also indicates that if all other factors are held constant and the units of a variable component are increased, the marginal physical product initially increases, then drops, and ultimately becomes negative.
As a result, it has three stages-
I – MPP is rising.
II - MPP is dropping but still positive.
III - MPP continues to fall and becomes negative.
The three factors that are connected to one another are explained below-
The following are the reasons for the law's application-
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