Explain the law of variable proportion.

Question

Accepted Answer

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> [!TLDR]
> The law of variable proportions (short-run law of production) says that as additional units of a variable factor are combined with a fixed factor, marginal product first rises (increasing returns), then falls while staying positive (diminishing returns), and finally becomes negative (negative returns). Production is carried on in Stage II, where total product is maximised at the margin that matters.
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> **Meaning**
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> The law of variable proportions operates in the short run, when at least one factor (say land or plant) is fixed and only one factor (say labour) is varied. As the proportion between the variable and the fixed factor changes, output changes in a definite pattern.
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> **Assumptions**
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> - The state of technology is given and unchanged.
> - Only one factor is varied; others are held fixed.
> - All units of the variable factor are equally efficient (homogeneous).
> - It is a short-run analysis.
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> **The three stages** (illustrated with labour applied to a fixed piece of land):
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> | Stage | Total Product (TP) | Marginal Product (MP) | Average Product (AP) |
> | --- | --- | --- | --- |
> | I — Increasing returns | Rises at an increasing rate | Rises, reaches maximum | Rises |
> | II — Diminishing returns | Rises at a diminishing rate to its maximum | Falls but stays positive, becomes 0 at the end | Falls after its peak |
> | III — Negative returns | Falls | Becomes negative | Falls |
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> - Stage I (Increasing returns): The fixed factor is under-utilised; adding the variable factor makes better use of it, so MP rises and TP increases quickly.
> - Stage II (Diminishing returns): The fixed factor is now used more fully; further units of the variable factor add less and less, so MP falls though it is still positive. TP rises at a slowing rate and reaches its maximum where MP = 0.
> - Stage III (Negative returns): Too many units of the variable factor crowd the fixed factor; MP becomes negative and TP actually falls.
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> **Operational stage**

Number of Workers	Total Output (kg wheat)	Marginal Product (kg per worker)
0	0	—
1	10	10
2	24	14
3	39	15
4	50	11
5	58	8
6	63	5
7	63	0
8	60	–3

Q.Explain the law of variable proportion.

Concept understanding — Law of Variable Proportions

The Law of Variable Proportions: Why Adding More of One Thing Eventually Backfires

The Everyday Intuition

The Precise Meaning (NCERT Style)

The Three Stages in Detail

Why It Matters

Stage	Total Product (TP)	Marginal Product (MP)	Average Product (AP)
I — Increasing returns	Rises at an increasing rate	Rises, reaches maximum	Rises
II — Diminishing returns	Rises at a diminishing rate to its maximum	Falls but stays positive, becomes 0 at the end	Falls after its peak
III — Negative returns	Falls	Becomes negative	Falls

Q.Explain the law of variable proportion.

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