Law of Variable Proportion Diagram and Its Three Stages Explained
The Law of Variable Proportions is a core concept in economics within the commerce stream. It explains how output responds when more units of one input are added, while other inputs are kept constant in the short run. This principle is fundamental for understanding short-term production decisions in business and economics.
According to the law, when the quantity of one input (for example, labour) increases and the quantity of other inputs (like land or machinery) stays the same, the overall increase in output (total product) occurs in three distinct stages.
The output will initially increase rapidly, then the rate of increase will slow down, and finally, the total output may decline. This behaviour demonstrates that there is an optimal level of the variable input for maximum productivity.
Meaning and Key Principles
The Law of Variable Proportions describes how total production (output) changes when only one input varies, and all others are kept fixed.
This law helps businesses find the point where adding more resources is efficient and when it becomes wasteful or even counterproductive. It is also known as the law of diminishing returns.
Stages of Production
| Stage | Description | Key Feature |
|---|---|---|
| Increasing Returns to a Factor | Total output rises rapidly as more units of the variable input are used. Each additional unit gives a larger increase in output due to better use of the fixed inputs. | High efficiency, output grows faster with each input. |
| Diminishing Returns to a Factor | Total output continues to rise but at a decreasing rate. Although adding more of the variable input still increases production, each unit adds less than the previous one. | Efficiency starts to fall, but total output rises. |
| Negative Returns to a Factor | Total output starts to decrease even though more input is added. The extra input actually lowers productivity because too many variable factors cause crowding or inefficiency. | Adding more reduces total output. |
Practical Example
Imagine a farm with a fixed amount of land (constant input). If the farmer keeps adding more labourers (the variable input), the amount of crops harvested changes as shown in the table below:
| Number of Workers | Total Output (Units) |
|---|---|
| 1 | 30 |
| 2 | 65 |
| 3 | 105 |
| 4 | 140 |
| 5 | 160 |
| 6 | 170 |
| 7 | 165 |
At first, the increase in output is large as more workers are added. Then, each additional worker adds less to output, and finally, further increases actually reduce total output, showing all three stages of the law.
Essential Formulas
| Formula | What it Means |
|---|---|
| Marginal Product (MP) = Change in Total Output / Change in Input | Extra output produced by one more unit of variable input |
| Average Product (AP) = Total Output / Number of Units of Input | Output per unit of variable input |
Step-by-Step Analysis
- Identify which input is variable and which are kept constant for the scenario.
- Collect data on total output as the variable input increases (like in the example table above).
- Calculate Marginal Product and Average Product using the formulas.
- Observe the changes in total, marginal, and average product to find the three stages.
- Stage 2: MP and AP fall but are still positive; TP increases at a decreasing rate.
- Stage 3: MP is negative; TP falls.
Applications in Commerce
- This law helps firms decide the optimal level of resources to use for maximum profit.
- It helps avoid overusing labour or materials, saving cost and improving efficiency.
- Managers use this principle to allocate tasks and plan production.
Key Takeaways
- The law applies only in the short run, when at least one input remains fixed.
- It is relevant in agriculture, manufacturing, and service industries whenever production factors are not fully flexible.
Further Learning and Practice
- Explore practice questions and detailed lessons on the Law of Variable Proportion at the Vedantu resources.
- Keep practicing with numerical examples and tables to improve your understanding of short-run production laws.
Mastering the law of variable proportions gives you a strong base for further topics in economics, accounting, and business studies. Revisit examples and solve step-by-step problems to prepare for exams and real-world situations.
FAQs on Law of Variable Proportion: Meaning, Diagram, Stages & Uses
1. What is the Law of Variable Proportion?
The Law of Variable Proportion states that as additional units of a variable input (such as labour) are combined with fixed inputs (like land), the resulting total output increases at first at an increasing rate, then at a diminishing rate, and may eventually decline if more units are added. This law helps explain how production behaves in the short run when not all factors of production can be varied.
2. Who gave the Law of Variable Proportion?
The Law of Variable Proportion was first introduced by Turgot and later developed by economists like David Ricardo. It is a fundamental principle in classical and modern economics.
3. What are the assumptions of the Law of Variable Proportion?
Major assumptions of the Law of Variable Proportion include:
- Technology remains unchanged during production
- At least one input is fixed
- Inputs (like labour and capital) are divisible and homogenous
- The law operates only in the short run
- There must be the possibility of varying the proportions of inputs
4. What are the three stages of the Law of Variable Proportion?
The three stages are:
Stage I (Increasing Returns): Marginal Product (MP) rises, Total Product (TP) increases rapidly.
Stage II (Diminishing Returns): MP falls but stays positive, TP increases at a decreasing rate.
Stage III (Negative Returns): MP becomes negative, TP starts to decline.
5. What is the difference between Law of Variable Proportion and Returns to Scale?
Law of Variable Proportion operates in the short run where only one input is variable and others are fixed, affecting output through marginal changes. Returns to Scale applies in the long run when all inputs change together in equal proportion, measuring the resulting effect on output. In short:
- Variable Proportion: Short run, one input varied, others fixed
- Returns to Scale: Long run, all inputs changed simultaneously
6. Why is the Law of Variable Proportion also called the Law of Diminishing Returns?
The law is also known as the Law of Diminishing Returns because after a certain point, adding more of the variable input leads to a less than proportionate increase in output, and eventually, marginal returns decrease. This diminishing effect occurs after the optimum combination of inputs has been reached.
7. How do you illustrate the Law of Variable Proportion with a diagram?
The law is represented using TP (Total Product), MP (Marginal Product), and AP (Average Product) curves:
- TP curve initially rises quickly, then slows, and may decline.
- MP curve rises, reaches a peak, then falls, and can become negative.
- AP curve increases, then falls.
The three stages correspond to changes in the slopes of these curves as variable input increases.
8. Give a real-life example of the Law of Variable Proportion.
A classic example is agriculture: If a farmer increases the number of workers on a fixed piece of land, initially output increases rapidly due to better teamwork (increasing returns). After a point, adding more workers causes overcrowding so each adds less to total output (diminishing returns), and eventually, output may decrease if too many workers are employed (negative returns).
9. What are Marginal Product (MP) and Average Product (AP)?
Marginal Product (MP): Additional output from adding one more unit of variable input (MP = ΔTP / ΔL).
Average Product (AP): Output per unit of variable input (AP = TP / L).
Both concepts help identify in which stage of production a business is operating.
10. What are the applications of the Law of Variable Proportion in business and management?
Managers use the law to find the most efficient level of input use. Applications include:
- Deciding the optimum number of workers to employ
- Planning resource allocation in the short run
- Avoiding wastage from overuse of variable resources
- Making cost and output decisions for maximum profitability
11. Why does the Law of Variable Proportion not apply in the long run?
The law does not apply in the long run because all inputs are variable in the long run. It only applies when at least one input is fixed, which is characteristic of short-run production.
12. How can I avoid calculation errors in numerical questions on the Law of Variable Proportion?
To avoid calculation errors:
- Write clear step-by-step workings for each stage
- Use the correct formula for MP (MP = Change in TP / Change in input) and for AP (AP = TP / Number of input units)
- Watch for signs (positive and negative values), especially for MP
- Practice with tables and diagrams regularly
Following these steps improves accuracy and clarity in exams.
