Understanding the Law of Variable Proportion: Concepts and Applications

Law of Variable Proportion: Meaning and Explanation

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. 

Why is it Called the Law of Variable Proportion?

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.

 Historical Background of the Law of Variable Proportion

The Law of Variable Proportion was recognized to have its roots back in classical economics. While the early insight was remarkably well spotted by economists like Adam Smith and David Ricardo, way back in 18th and 19th centuries respectively, Adam Smith's discussions on the division of labor and specialization already indicated that indeed production may vary with variable inputs. Indeed, it was more formally initiated by David Ricardo through his work on diminishing returns in agriculture.

The law further improved with the contributions from economists Thomas Malthus and John Stuart Mill, who expanded on how changes in one factor of production, keeping others constant, would eventually lead to varying levels of output. In the early 20th century, this idea became more refined as the Law of Variable Proportion, encapsulating how output first increases then diminishes, then becomes negative with the addition of variable inputs beyond a certain point.

This development characterizes the change from more generalistic agricultural examples to more diversified applications in manufacturing, services, and modern industries, hence being a basic principle of contemporary microeconomics.

Assumptions to the Law of Variable Proportion

The law of variable proportion remains true under specific conditions, which are described below- 

1. A constant state of technology: The first assumption is that the situation's technological condition remains unaltered. If technology improves, the marginal product may increase rather than decrease.
2. Variable Factor Proportions: This presupposes that production factors are variable. The legislation is invalid if the factors of production are fixed. 
3. Homogeneous factor units: These are units that have the same quality, quantity, and price. In other words, the units are all the same.
4. Brief Run:This suggests that this law applies to systems that are only operational for a short period of time and where it is not possible to change all factor inputs.

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Terminologies and Description for Law of Variable Proportion

The phrases that will be used in the Law of Variable Proportion are explained in the table below-

3 Stages of Law of Variable Proportion

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).

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Law of Variable Proportion: Significance of Three Stages

The following are the significance of the three stages-

1. In Stage I, a producer does not work. At this level, as the variable factor grows, so does the marginal product. As a result, the producer can use more units of the variable to make better use of the fixed components. As a result, the producer would prefer not to stop at Stage I and will endeavor to grow further.
2. Any logical manufacturer will avoid both the first and third stages of production. As a result, producers choose Stage II, which is the stage of declining returns. According to the rule of changing proportions, this is the most important stage of operation for a producer.
3. Producers dislike working at Stage III as well. At this moment, the total product is dropping, and the marginal product is negative. Producers minimize the number of variable components in order to boost output. However, in Stage III, he incurs larger expenditures and receives less income, resulting in lower earnings.

Delay of the Law

The law of variable proportions can be postponed under the following conditions-

1. Improvement in Production Techniques: The law's implementation might be delayed if variable factor production techniques are improved.
2. Perfect Substitute: The law of variable proportion can also be postponed if production elements are made perfect replacements—that is when one ingredient can be swapped for the other.

Causes for Law of Variable Proportion

The following are the causes of the law of variable proportion- 

1. Causes of growth factors return I Fuller usage of the fixed factor: In the early stages, the fixed factor is underutilized. Its increased use leads to higher use of the variable component. As a result, initially, more units of the variable factor add more and more to the overall output.
2. Increased variable factor efficiency: Additional application of the variable factor results in the process-based division of labor, which increases the variable factor's efficiency. As a result, the factor's MP tends to rise.
3. Imperfect factor substitutability: Production factors are imperfect equivalents to one another. More and more labor cannot be employed in place of greater capital indefinitely.

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Law of Variable Proportion in terms of TPP and MPP

The below details are an explanation of TPP and MPP- 

a. TPP and the Law of Variable Proportions

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.

b.   MPP and the Law of Variable Proportions

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.

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TP vs MP vs AP

The three factors that are connected to one another are explained below- 

1. When TP rises at a faster pace, the MP and AP increase as well. However, at this point, MP > AP.
2. When TP rises at a slower rate, the MP and AP begin to plummet. 
3. When MP begins to plummet dramatically while AP falls at a slow rate, it signifies that MPAP is currently.
4. When TP decreases, MP decreases, and AP decreases while remaining above the x-axis.
5. MP intersects AP when the latter is at its maximum. This is where MP = AP.

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Law of Variable Proportion: Reasons

The following are the reasons for the law's application-

1. We cannot change all production variables in the near term.
2. There is just one changeable factor in this example, while the rest are fixed.
3. All other components work together ideally to deliver the best results.
4. If the units of a variable component grow before the point of optimal combination, the factor proportion becomes more suited, resulting in more effective exploitation of the fixed factors. As a result, the marginal physical product rises.
5. When the producer applies additional units of a variable element to the fixed factors in the early stages, the total product tends to grow at a rising pace.
6. As a result, if the producer uses additional units of the variable factor beyond the point of optimal combination, the factor proportion becomes inefficient. As a result, the variable factor's marginal product decreases.
7. In addition, when the producer raises the units of the variable component, the quantity of the fixed factor input per unit of the variable decreases.
8. As a result of having fewer fixed inputs to work with, consecutive units of variable input add diminishing quantities to the overall output.

Significance of The Law Of Variable Proportion

The law of variable proportion is very important for knowing the relationship between the variable factors and the fixed factors. There are many kinds of importance of the law of variable proportion. A few of the major importance are written below, 

• The law of variable proportion is useful for the understanding of the production process.
• It helps clear up the relation between input and output. This explains why there is a change in output as caused by changes in input.
• Laws of Variable Proportion: This law states that when the variable factor is increased, the total product increases at a diminishing rate.
• The law of variable proportions essentially means that increasing returns exist only up to a certain point in each sector of the economy, beyond which diminishing returns are found.
• This aids in proper usage of resources.

Limitations of Law of Variable Proportion

The Law of Variable Proportion is very wide in its applicability but at the same time, has certain limitations where it may not be valid for:

1. Short Run Application Only: This law is only valid for short run where at least one factor of production is fixed. It does not hold true for long run conditions when all factors of production are variable.
2. Assumed Constant Technology: The law presumed that the technology factor is constant; however, in the real world, it experiences frequent inventions capable of changing the production results making the law inapplicable.
3. Homogeneous Units of Variable Factor: The law presumed that one unit of the variable factor was as effective as the other, but in the actual world, workers are distinct from one another in terms of ability and productivity.
4. Disregards the Outside Influence: The law pays no consideration to the impact of outside influence such as government policy, environmental changes, or market. This can differ the output of production regardless of whether there's a change in the variable factor.
5. It Does Not Apply to Industries: The theory applies to most industries and whose practice involves variable factors in conjunction with fixed factors. Sometimes, it does not apply to those heavy-edge reliance sectors on highly volatile inputs or products whose production process is highly mechanized.

Practical Uses of the Law of Variable Proportion

The uses are bulleted and explained below:

• In farming, when more fertilizers or labor is supplied to a given piece of land, initially, crop yield increases very steeply (Stage 1). Even more is provided then the gain in yield goes on increasing slowly (Stage 2). And when excessive is supplied then it might harm the crop also and the total output will start decreasing (Stage 3).
• In a factory, putting more workers on a limited number of machines may increase the production. This would be due to the aspect of specialization that occurs during Stage 1. With time, an increased number of workers added to the given machines has the effect where each extra worker would contribute less to output. At this point, overcrowding may lead to inefficiencies and decreased productivity. Service Industry:
• In a call center, the curve begins with an upward slope: more agents translate to more calls at Stage 1. Once it exceeds the optimal scale, however, agents will begin to compete for scarce resources like computers or phone lines, and service efficiency begins to decline at Stage 2. Too many agents would even result in confusion and delays, forcing this decline in overall service quality at Stage 3.

The following examples indicate how the law applies to different sectors. Therefore, they indicate practical applicability of the law in many sectors, thereby becoming an excellent means of elaborating on how factors of variable inputs affect output in various sectors.