Law of Variable Proportion: Meaning, Phases, Assumptions & Examples

The law of variable proportions is also known as the law of diminishing returns, is a fundamental concept in economics that explains how the output of a production process changes when the quantity of one input is varied while keeping all other inputs constant. It is most relevant in the short run, a period during which at least one factor of production (like land or machinery) is fixed. This concept is crucial for students preparing for competitive exams like UGC NET Commerce, as it not only appears frequently in papers but also aids in understanding how businesses manage resources efficiently.

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What is the Law of Variable Proportion?

The law of variable proportion in economics refers to the effect on output when only one input is varied, keeping others fixed. It shows how the marginal product (additional output from one extra unit of input) behaves as more units of a variable factor are added to fixed factors.The law of variable proportion is also known as the law of proportionality in some textbooks.

Technical Definition:

“The law of variable proportion is a short-run production law stating that as more and more units of a variable input are combined with fixed inputs, the marginal product initially increases, then decreases, and eventually becomes negative.” This law is also known as the law of diminishing returns because it shows how returns (output) start to decline after a certain level of input usage.

Assumptions of the Law of Variable Proportion

In explaining the law of variable proportion, one must understand the conditions under which it holds. These are known as the assumptions of the law: 

• One Factor is Variable: Changes only in one input (for example labor or some raw material) while all other factors remain fixed. This facilitates the isolation of the effect of that variable input on production.
• Constant Technology: The technology used in production remains unchanged during the analysis. If technology changes, output might rise due to better machines or tools, not because of an increase in the variable input.
• Short-Run Production: The law applies only to the short run, where some inputs (like land or machinery) are fixed. In the long run, all inputs can change, so this law doesn't apply.
• Homogeneous Units: The variable input being added is uniform in quality. This means that all additional workers or raw materials are assumed to be equally productive.
• Efficient Input Usage: Inputs are assumed to be used efficiently. Any inefficiency (like idle labor or faulty machinery) is not considered under this law.

To further explain the law of variable proportion, we need to look into how output behaves across its three distinct stages. The law of variable proportion consists of three distinct phases that describe how total output (Total Product), average output (Average Product), and marginal output (Marginal Product) change as input increases.

Stage 1: Increasing Returns to the Variable Factor

• Total Product (TP): Increases at an increasing rate
• Marginal Product (MP): Increases
• Average Product (AP): Also increases

This phase occurs because the variable factor (e.g., labor) complements the fixed factor (e.g., land or machine), resulting in more efficient production.

Example: A factory has five machines (fixed), but initially only one worker. As more workers are added, machines are better utilized, increasing output rapidly.

Stage 2: Diminishing Returns to the Variable Factor

• TP: Continues to increase but at a diminishing rate
• MP: Declines but remains positive
• AP: Reaches its peak and then starts decreasing

This is the most efficient stage of production. Though marginal returns are decreasing, the output is still growing. Firms usually operate in this stage because it's the rational zone for resource allocation.

Example: The factory adds more workers, but space and machines start becoming limited. Output grows slowly.

Stage 3: Negative Returns to the Variable Factor

• TP: Starts to decline
• MP: Becomes negative
• AP: Continues to decline

In this phase, the fixed inputs become overcrowded, and inefficiencies increase. Additional input causes total output to fall.

Example: The farm becomes so crowded with workers that they start getting in each other’s way. Productivity drops.

Example of Law of Variable Proportion

Let's consider a farm with fixed land and an increasing number of workers.To understand the practical application of the law of variable proportion in economics, consider the following data. A common example of the law of variable proportion in economics is seen when labor is added to a fixed farm area

Interpretation:

• Stage 1 (1–3 workers): TP and MP increase.
• Stage 2 (3–5 workers): TP increases slowly, MP decreases.
• Stage 3 (6th worker): TP declines, MP is negative.

This real-world example of the law of variable proportion demonstrates how productivity changes as labor is added.

Graphical Representation

TP Curve: 

• -risks sharply upward in Stage I
• -rises gingerly in Stage II
• -falls off in Stage III

MP and AP Curve:

• -Rises at first in Stage I, then falls after a peak
• -It rises at first, then falls afterward for AP too
• -In Stage III, MP becomes negative

These curves augment the visual representation of the law of variable proportion and the stages of production. 

Conclusion

The law of variable proportions is a very important law that helps in understanding the terms of input and output in the short-run mode of production processes.. By studying the relationship between Total Product (TP), Marginal Product (MP), and Average Product (AP) across the three stages of production, businesses can make smarter decisions about resource allocation and efficiency.

Law of Variable Proportion are available in Testbook, so download theTestbook App now. This concept is essential not just in theory but in real-world applications—from farming and factories to service industries—and forms a critical part of the UGC NET Commerce syllabus.