Law of Variable Proportions
Class 11 Microeconomics — The most important law of production in the short run
Statement of the Law
Key Takeaways
- LVP is one of the most important laws of production.
- It shows the nature of rate of change in output due to a change in only one variable factor of production.
The Three Phases — Watch the Graph Unfold
Instead of a long page, step through the story below. With each step, the graph on the right unfolds to show exactly what is happening to TP and MP.
Set the Stage
Fix one input — land — and add labour one worker at a time. Watch how Total Product (TP) and Marginal Product (MP) respond on the graph as each worker joins.
TP & MP under the Law of Variable Proportions
Numerical Example
| Fixed Factor (Land) | Variable Factor (Labour) | TP (units) | MP (units) | Phase |
|---|---|---|---|---|
| 1 | 1 | 10 | 10 | Phase I: Increasing Returns |
| 1 | 2 | 30 | 20 | Phase I: Increasing Returns |
| 1 | 3 | 45 | 15 | Phase II: Diminishing Returns |
| 1 | 4 | 52 | 7 | Phase II: Diminishing Returns |
| 1 | 5 | 52 | 0 | Phase II: Diminishing Returns |
| 1 | 6 | 48 | -4 | Phase III: Negative Returns |
Key Graph Points
- Point of Inflexion (Q): Point where curvature of TP changes. Till this point, TP increases at an increasing rate. From this point onwards, TP increases at a diminishing rate. Marks the beginning of Phase II.
- Point M: TP is Maximum (at 52 units, 5th unit of labour).
- Point P: MP is Maximum.
- Point S: MP = 0.
- Phase I: O to Q — TP increases at increasing rate, MP rises.
- Phase II: Q to M — TP increases at decreasing rate, MP falls but positive.
- Phase III: Beyond M — TP falls, MP negative.
Assumptions
It operates in the short run, as factors are classified as variable and fixed factor.
The law applies to all fixed factors including land.
Under Law of Variable Proportions, different units of variable factor can be combined with fixed factor.
This law applies to the field of production only.
The effect of change in output due to change in variable factor can be easily determined.
It is assumed that factors of production become imperfect substitutes of each other beyond a certain limit.
The state of technology is assumed to be constant during the operation of this law.
It is assumed that all variable factors are equally efficient.
Rational Producer's Perspective
Why Phase II?
- •Phase I has scope for more output — MP is still rising, so profit can be increased by producing more.
- •Phase III is technically inefficient — MP is negative, so producing more actually reduces total output.
- •Phase II is where TP is maximum and MP is positive — this is the rational operating zone.
Key Takeaways
- A rational producer operates in Phase II only.
- Phase I has scope for more output (MP still rising).
- Phase III is technically inefficient (MP negative).
- Phase II is where TP is maximum and MP is positive.