What is the law of variable proportions?

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Q. What is the law of variable proportions?

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Concept understanding — Law of Variable Proportions

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

The Everyday Intuition

Imagine you're making chai for your family. You have one stove, one kettle, and one burner. You start with one person making tea — that's fine. Now you add a second person to help. Things speed up: one boils water, the other gets cups ready. Add a third person — maybe they help with sugar and milk. Still good.

Now add a fourth person. They're standing around, bumping elbows. A fifth? They're just getting in the way. The sixth person? They're actually slowing down the whole process because there's no space, no extra stove, no extra work to do.

That's the Law of Variable Proportions in a nutshell: as you keep adding more of one input (like labour) to a fixed input (like the stove), the extra output you get from each additional worker first rises, then stays constant, and eventually falls — even turning negative.

The Precise Meaning (NCERT Style)

In economics, production requires factors of production — land, labour, capital, and entrepreneurship. The Law of Variable Proportions (also called the Law of Diminishing Returns) applies when:

One factor is variable (you can change its quantity, e.g., labour)
All other factors are fixed (e.g., land, machinery, factory size)

The law states that as you increase the variable factor, keeping others constant, the marginal product (extra output from one more unit of the variable factor) will eventually decline.

Important

The law has three stages:

Increasing returns — Marginal product rises (each new worker adds more than the previous one)
Diminishing returns — Marginal product falls but remains positive
Negative returns — Marginal product becomes negative (adding more workers actually reduces total output)

The Three Stages in Detail

Let's use a concrete example from NCERT: a farmer with a fixed plot of land (1 acre) who hires more and more workers.

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

Stage 1 (Increasing Returns): Workers 1 to 3. Each new worker adds more than the last. Why? Because with few workers, they can specialise — one digs, one sows, one waters. The fixed land is underutilised, so each extra worker makes fuller use of it.

Stage 2 (Diminishing Returns): Workers 4 to 7. Each new worker still adds output, but less and less. The land is now being used more intensively, but there's only so much space. Workers start getting in each other's way.

Stage 3 (Negative Returns): Worker 8. Total output actually falls. Too many workers on the same plot — they trample crops, waste time coordinating, and create chaos.

Note

A rational producer will never operate in Stage 3 (negative returns) and will stop before Stage 2 ends — because once marginal product becomes zero, adding more workers reduces total output.

Why It Matters

This law is the foundation of production theory in economics. It explains:

Why firms don't just keep hiring more workers — at some point, the extra cost of a worker exceeds the extra revenue they generate.
Why agriculture in densely populated countries faces limits — you can't keep adding labour to the same land and expect proportional increases in food. …

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The law of variable proportions describes how output changes when one input is varied while keeping all other inputs fixed. It states that as we increase the quantity of the variable input (say, labor) while holding other inputs (say, land or capital) constant, the marginal product of that input initially rises, then eventually falls.

This law operates in the short run, where at least one factor of production is fixed. The production function exhibits three distinct phases:

Phase	Marginal Product	Total Product	Reason
I	Rising (MP increases)	Increases at increasing rate	Better utilization of fixed factor
II	Falling but positive (MP decreases)	Increases at decreasing rate	Optimal combination passed; fixed factor becoming inadequate
III	Negative (MP < 0)	Falls	Variable factor excessively large relative to fixed factor

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The law of variable proportions explains how output changes when one input is varied while others remain fixed — initially rising at an increasing rate, then at a decreasing rate, and eventually falling — reflecting the three stages of production.

Every production process combines inputs: land, labor, capital, and entrepreneurship. In the short run, at least one of these factors is fixed. A farmer cannot instantly acquire more land; a factory cannot overnight double its machinery. The law of variable proportions describes what happens to output when you keep changing the quantity of one variable input (usually labor) while holding all other inputs constant.

The economic intuition is straightforward. Imagine a workshop with ten machines (fixed capital) and you start hiring workers. The first worker operates all ten machines poorly, running between them. Add a second worker and productivity jumps — they can specialize, coordinate, use the machines more efficiently. Output rises faster than the increase in labor. This is the phase of increasing returns.

But this cannot continue indefinitely. As you keep adding workers — say the twentieth, thirtieth worker — each additional person contributes less because the fixed capital is now being stretched thin. Machines are fully utilized, workers wait for their turn, coordination becomes harder. Output still rises, but at a diminishing rate. This is diminishing returns.

Push further still. The fiftieth worker in a workshop built for ten machines may actually get in the way, cause accidents, create bottlenecks. Total output can actually fall. This is the stage of negative returns.

The law unfolds in three distinct stages:

Stage I: Increasing Returns to the Variable Factor

Total product rises at an increasing rate. Marginal product (the addition to output from one more unit of the variable input) rises, and average product also rises. The fixed factor is underutilized relative to the variable factor. Better division of labor and fuller use of the fixed input drive efficiency up.

Stage II: Diminishing Returns to the Variable Factor

Total product continues to rise, but at a decreasing rate. Marginal product falls but remains positive. Average product also declines. The variable factor is now being added to a relatively fixed quantity of other inputs, so each additional unit contributes less. This is the rational zone of production — a producer operates here, balancing input cost against diminishing marginal gains.

Stage III: Negative Returns to the Variable Factor

Total product actually falls. Marginal product becomes negative. The variable factor is now excessive relative to the fixed factors — overcrowding, inefficiency, and coordination failures dominate. No rational producer operates in this stage.

Note

The law assumes technology, quality of the variable input, and quantities of other inputs remain constant. It is a short-run phenomenon because in the long run all factors can be varied, and the law of returns to scale applies instead. …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

Showing the 12 most recent of 16 on this concept.

CA Foundation 2026Set jan-20261 markMCQ
$Q. Which of the following is not true with regard to stage of diminishing returns? (A) Total product continues to decrease (B) Both marginal product and average product of the variable factor are diminishing but are positive (C) A rational producer will seek to produce within the range of this stage (D) By the end of this stage, total product reaches its maximum$
›Reveal solutionSolution
During diminishing returns (Stage II) total product still increases at a diminishing rate; it does not decrease, so statement (A) is not true.

The three stages of the Law of Variable Proportions

Stage I (increasing returns): MP rises then AP rises; TP increases at an increasing rate.

Stage II (diminishing returns): both MP and AP are falling but remain positive; TP continues to increase but at a diminishing rate, and by the end of this stage TP reaches its maximum (where MP = 0). A rational producer operates in this stage.

Stage III (negative returns): MP becomes negative and TP actually falls.

Applying it

(B), (C) and (D) are all correct features of Stage II.

(A) — 'Total product continues to decrease' — describes Stage III, not the diminishing-returns stage, and is therefore the untrue statement. …
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CA Foundation 2026Set may-20261 markMCQ
$Q. The three stages of the law of variable proportion can be referred to as the stages of __________. (A) Increasing returns, optimum returns & nil returns (B) Positive returns, diminishing returns & nil returns (C) Increasing returns, diminishing returns & negative returns (D) Negative returns, nil returns & positive returns$
›Reveal solutionSolution
The three stages of the law of variable proportions are increasing returns, diminishing returns and negative returns.

Step 1 — The law

As successive units of a variable input are added to fixed inputs, the marginal product first rises, then falls, and finally becomes negative. This gives three stages:

Step 2 — The three stages

Stage I — Increasing returns: total product increases at an increasing rate; marginal product rises.

Stage II — Diminishing returns: total product increases at a decreasing rate; marginal product falls but stays positive. (A rational producer operates here.)

Stage III — Negative returns: additional input reduces total product; marginal product becomes negative.

Step 3 — Why the other options are wrong …
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CA Foundation 2025Set jan-20251 markMCQ
$Q. What will be the average product when quantity of labour is 6 ? (A) 9 (B) 10 (C) 11 (D) 12$
›Reveal solutionSolution
Reconstruct the schedule: at L = 6, TP = 60, so AP = 60/6 = 10.

Step 1 — Rules linking TP, AP and MP
$AP = \frac{TP}{L}, \qquad MP_n = TP_n - TP_{n-1}$
Step 2 — Fill the product schedule step by step

Starting from the given entries (TP₁ = 10, MP₂ = 11, AP₃ = 11, MP₄ = 11, TP₅ = 52, MP₆ = 8):

Labour (L) Total Product (TP) Average Product (AP) Marginal Product (MP)
1 10 10 –
2 21 10.5 11
3 33 11 12
4 44 11 11
5 52 10.4 8
6 60 10 8

TP₂ = 10 + 11 = 21; TP₃ = AP₃ × 3 = 33; TP₄ = 33 + 11 = 44; TP₅ = 52 (given); TP₆ = 52 + 8 = 60.

Step 3 — Read off AP at L = 6

$AP_6 = \frac{TP_6}{6} = \frac{60}{6} = 10$ …
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CA Foundation 2025Set jan-20251 markMCQ
$Q. What will be the total product when quantity of labour is 4 ? (A) 38 (B) 40 (C) 42 (D) 44$
›Reveal solutionSolution

Cumulate the schedule: TP₄ = TP₃ (33) + MP₄ (11) = 44.

Step 1 — Relationship used
$TP_n = TP_{n-1} + MP_n, \qquad AP = \frac{TP}{L}$
Step 2 — Reconstruct up to L = 4

Labour (L) Total Product (TP) How obtained
1 10 given
2 21 10 + MP₂(11)
3 33 AP₃(11) × 3
4 44 33 + MP₄(11)

Step 3 — State the answer
$TP_4 = 33 + 11 = 44$
We can cross-check: AP₄ = 44/4 = 11, consistent with the schedule's pattern. …
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CA Foundation 2025Set jan-20251 markMCQ
$Q. What will be the marginal product when quantity of labour is 5 ? (A) 8 (B) 9 (C) 10 (D) 11$
›Reveal solutionSolution

$MP_5 = TP_5 - TP_4 = 52 - 44 = \mathbf{8}$ .

Step 1 — Definition of marginal product
$MP_n = TP_n - TP_{n-1}$
MP is the extra output produced by employing one additional unit of labour.

Step 2 — Get the two TP values

From the reconstructed schedule (see Q18/Q19):

Labour (L) Total Product (TP)
4 44
5 52 (given)

Step 3 — Compute MP at L = 5
$MP_5 = 52 - 44 = 8$
So the marginal product when the quantity of labour is 5 equals 8. …
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CA Foundation 2025Set may-20251 markMCQ
$Q. Which of the following is not true about relationship between average product and marginal product ? (A) When average product rises as a result of an increase in the quantity of variable input marginal product is more than the average product. (B) When average product is maximum, marginal product is equal to average product. (C) When average product falls, marginal product is less than the average product. (D) When average product is negative, marginal product becomes zero.$
›Reveal solutionSolution
Average product can never be negative, so statement (D) is the one that is not true.

Step 1 — AP–MP relationships that ARE true

(A) When AP is rising (as variable input increases), MP > AP — true (MP pulls AP up).

(B) When AP is at its maximum, MP = AP — true (MP cuts AP at AP's peak).

(C) When AP is falling, MP < AP — true (MP pulls AP down).

Step 2 — Why (D) is false
$AP = \frac{TP}{L}$
As long as total product (TP) is positive and the number of units of the variable input (L) is positive, AP is always positive — it cannot become negative. Marginal product can become negative (when TP falls), but average product cannot. So a statement premised on "average product is negative" is impossible, making (D) not true. …
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CA Foundation 2025Set may-20251 markMCQ
$Q. Total product starts declining in which stage of production ? (A) Stage 1 : The stage of increasing returns (B) Stage 2 : The stage of diminishing returns (C) Stage 3 : The stage of negative returns (D) It may decline in any stage of production$
›Reveal solutionSolution
Total product actually declines only in Stage 3 (negative returns), where marginal product is negative → (C).

Step 1 — The three stages (law of variable proportions)

Stage 1 — increasing returns: TP rises at an increasing rate; MP rising.

Stage 2 — diminishing returns: TP rises at a decreasing rate and reaches its maximum at the end of this stage; MP positive but falling to zero.

Stage 3 — negative returns: MP becomes negative, so TP actually falls.

Step 2 — Locate where TP declines

TP is still increasing (or at its peak) through Stages 1 and 2. It starts declining only when MP turns negative — that is Stage 3.

Step 3 — Reject the others

(A) Stage 1 — TP rising fast.

(B) Stage 2 — TP still rising, then at maximum. …
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CA Foundation 2025Set may-20251 markMCQ
$Q. Use the following data to answer question 24-25 : Output (Q) 012345 Total cost (TC) ₹ 200 ₹ 310 ₹ 410 ₹ 500 ₹ 604 ₹ 710 Diminishing marginal returns start to occur between units : (A) 1 and 2 (B) 2 and 3 (C) 3 and 4 (D) 4 and 5$
›Reveal solutionSolution

Diminishing marginal returns begin where marginal cost stops falling and starts rising — here between the 3rd and 4th units.

Step 1 — Compute marginal cost for each unit

$MC$ = change in TC per extra unit:

Unit TC MC (ΔTC)
1 310 110
2 410 100
3 500 90
4 604 104
5 710 106

Step 2 — Link MC to marginal returns

Falling MC ⇔ rising marginal product (increasing marginal returns); rising MC ⇔ falling marginal product (diminishing marginal returns). MC declines 110 → 100 → 90 through the 3rd unit, then RISES to 104 at the 4th unit.

Step 3 — Locate the turning point

The reversal — MC's minimum at unit 3, then upward — occurs between units 3 and 4, so diminishing marginal returns start there.

Why the other options are wrong …
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CA Foundation 2025Set sep-20251 markMCQ
$Q. When average product rises as a result of an increase in the quantity of variable input, marginal product is : (A) less than the average product (B) minimum (C) equal to the average product (D) more than the average product$
›Reveal solutionSolution
AP rises only when MP is above AP; so a rising AP ⇒ MP > AP.

Step 1 — Recall the MP–AP relationship

Marginal product pulls the average up or down like a running average:

When $MP > AP$ , AP is rising.

When $MP = AP$ , AP is at its maximum.

When $MP < AP$ , AP is falling.

Step 2 — Apply to the stated case

We are told AP rises as the variable input increases. From the relationship above, AP can only rise while marginal product exceeds average product. Hence MP is more than AP. …
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CA Foundation 2025Set sep-20251 markMCQ
$Q. Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product Schedule Quantity of labour Total Product (TP) Average Product (AP) Marginal Product (MP) 00 - - 1 - - 20 2 - - 26 366 - - 4 - 19 - 5 - - 4 What will be the average product when the quantity of labour is 3 ? (A) 22 (B) 24 (C) 20 (D) 18$
›Reveal solutionSolution

AP at L = 3 is TP ÷ L = 66 ÷ 3 = 22.

Step 1 — Read the total product at L = 3

The schedule directly gives $TP = 66$ when the quantity of labour is 3.

Step 2 — Apply the average product formula
$AP = \frac{TP}{L} = \frac{66}{3} = 22$
For completeness, filling the whole schedule: TP is 0, 20, 46, 66, 76, 80 for L = 0…5 (using the given MP and AP values), which confirms $AP_3 = 22$ . …
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CA Foundation 2025Set sep-20251 markMCQ
$Q. Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product Schedule Quantity of labour Total Product (TP) Average Product (AP) Marginal Product (MP) 00 - - 1 - - 20 2 - - 26 366 - - 4 - 19 - 5 - - 4 What will be the total product when the quantity of labour is 5 ? (A) 86 (B) 84 (C) 80 (D) 92$
›Reveal solutionSolution

TP₄ = AP₄ × 4 = 76; add MP₅ = 4 ⇒ TP₅ = 76 + 4 = 80.

Step 1 — Find TP at L = 4

Average product at L = 4 is given as 19, so
$TP_4 = AP_4 \times L = 19 \times 4 = 76$
Step 2 — Add the marginal product of the 5th unit

Marginal product at L = 5 is given as 4, so
$TP_5 = TP_4 + MP_5 = 76 + 4 = 80$
The completed TP column (0, 20, 46, 66, 76, 80) confirms this. …
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CA Foundation 2025Set sep-20251 markMCQ
$Q. Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product Schedule Quantity of labour Total Product (TP) Average Product (AP) Marginal Product (MP) 00 - - 1 - - 20 2 - - 26 366 - - 4 - 19 - 5 - - 4 What will be the marginal product when the quantity of labour is 4 ? (A) 26 (B) 20 (C) 10 (D) 19$
›Reveal solutionSolution
MP₄ = TP₄ − TP₃ = 76 − 66 = 10.

Step 1 — Get the two total products

At L = 3: $TP_3 = 66$ (given).

At L = 4: $AP_4 = 19$ , so $TP_4 = 19 \times 4 = 76$ .

Step 2 — Compute the marginal product
$MP_4 = TP_4 - TP_3 = 76 - 66 = 10$
Marginal product is the extra output from the 4th unit of labour, which is 10. …
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Labour (L)	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
1	10	10	–
2	21	10.5	11
3	33	11	12
4	44	11	11
5	52	10.4	8
6	60	10	8

Labour (L)	Total Product (TP)	How obtained
1	10	given
2	21	10 + MP₂(11)
3	33	AP₃(11) × 3
4	44	33 + MP₄(11)

Labour (L)	Total Product (TP)
4	44
5	52 (given)

Output (Q)	0	1	2	3	4	5
Total cost (TC)	₹ 200	₹ 310	₹ 410	₹ 500	₹ 604	₹ 710

Unit	TC	MC (ΔTC)
1	310	110
2	410	100
3	500	90
4	604	104
5	710	106

Quantity of labour	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
0	0	–	–
1	–	–	20
2	–	–	26
3	66	–	–
4	–	19	–
5	–	–	4

Quantity of labour	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
0	0	–	–
1	–	–	20
2	–	–	26
3	66	–	–
4	–	19	–
5	–	–	4

Quantity of labour	Total Product (TP)	Average Product (AP)	Marginal Product (MP)
0	0	–	–
1	–	–	20
2	–	–	26
3	66	–	–
4	–	19	–
5	–	–	4

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Q.What is the law of variable proportions?

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