Q.State the Law of Variable Proportions. Why does the marginal product of the variable factor eventually diminish, even though nothing about the fixed factor itself changes?
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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.
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.
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. …
State the law in terms of what happens to Marginal Product, then explain the diminishing phase through the fixed factor becoming relatively scarcer.
MP first rises, then falls, then turns negative, as more of the variable factor is added to an unchanged fixed factor.
As successive units of labour are added, each new worker has a progressively SMALLER share of the SAME fixed capital/land to work with — the fixed factor becomes relatively scarcer per worker, which is exactly why MP eventually falls even though the fixed factor's own quantity never changes. …
Statement of the law: the Law of Variable Proportions states that when successive units of a variable factor (such as labour) are combined with a fixed factor (such as capital), technology remaining unchanged, the marginal product of the variable factor initially RISES, then FALLS while still remaining positive, and eventually becomes NEGATIVE.
Why marginal product eventually diminishes: although the fixed factor's own physical QUANTITY never changes, the amount of the fixed factor AVAILABLE PER UNIT of the variable factor keeps shrinking as more units of the variable factor are added. Early workers benefit from a generous share of the fixed capital/land and may even allow useful specialisation and teamwork (raising MP at first, in Stage I), but once the fixed factor has been fully and efficiently combined with an optimal number of workers, every ADDITIONAL worker must share an increasingly crowded workplace with a smaller and smaller effective share of machinery, floor space, or land. Because the fixed factor genuinely cannot expand to keep pace, the CONTRIBUTION each new worker can add necessarily starts to shrink — not because the workers themselves become less skilled, but purely because they have proportion …
A common misconception is attributing diminishing MP to the variable factor's workers becoming "less skilled" or "lazier" as more are hired — the correct economic reason is purely proportional: the FIXED factor becomes scar …
Showing the 12 most recent of 16 on this concept.
- CA Foundation 2026Set jan-20261 markMCQQ.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. …
- CA Foundation 2026Set may-20261 markMCQQ.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 …
- CA Foundation 2025Set jan-20251 markMCQQ.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=LTP,MPn=TPn−TPn−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
AP6=6TP6=660=10 …
- CA Foundation 2025Set jan-20251 markMCQQ.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
TPn=TPn−1+MPn,AP=LTP
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
TP4=33+11=44
We can cross-check: AP₄ = 44/4 = 11, consistent with the schedule's pattern. …
- CA Foundation 2025Set jan-20251 markMCQQ.What will be the marginal product when quantity of labour is 5 ? (A) 8 (B) 9 (C) 10 (D) 11
›Reveal solutionSolution
MP5=TP5−TP4=52−44=8.
Step 1 — Definition of marginal product
MPn=TPn−TPn−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
MP5=52−44=8
So the marginal product when the quantity of labour is 5 equals 8. …
- CA Foundation 2025Set may-20251 markMCQQ.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=LTP
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. …
- CA Foundation 2025Set may-20251 markMCQQ.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. …
- CA Foundation 2025Set may-20251 markMCQQ.Use the following data to answer question 24-25 :Diminishing marginal returns start to occur between units : (A) 1 and 2 (B) 2 and 3 (C) 3 and 4 (D) 4 and 5
Output (Q) 0 1 2 3 4 5 Total cost (TC) ₹ 200 ₹ 310 ₹ 410 ₹ 500 ₹ 604 ₹ 710 ›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 …
- CA Foundation 2025Set sep-20251 markMCQQ.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. …
- CA Foundation 2025Set sep-20251 markMCQQ.Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product ScheduleWhat will be the average product when the quantity of labour is 3 ? (A) 22 (B) 24 (C) 20 (D) 18
Quantity of labour Total Product (TP) Average Product (AP) Marginal Product (MP) 0 0 – – 1 – – 20 2 – – 26 3 66 – – 4 – 19 – 5 – – 4 ›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=LTP=366=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 AP3=22. …
- CA Foundation 2025Set sep-20251 markMCQQ.Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product ScheduleWhat will be the total product when the quantity of labour is 5 ? (A) 86 (B) 84 (C) 80 (D) 92
Quantity of labour Total Product (TP) Average Product (AP) Marginal Product (MP) 0 0 – – 1 – – 20 2 – – 26 3 66 – – 4 – 19 – 5 – – 4 ›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
TP4=AP4×L=19×4=76
Step 2 — Add the marginal product of the 5th unit
Marginal product at L = 5 is given as 4, so
TP5=TP4+MP5=76+4=80
The completed TP column (0, 20, 46, 66, 76, 80) confirms this. …
- CA Foundation 2025Set sep-20251 markMCQQ.Based on the information given in the following table, answer the Questions Nos. 18 to 20 : Product ScheduleWhat will be the marginal product when the quantity of labour is 4 ? (A) 26 (B) 20 (C) 10 (D) 19
Quantity of labour Total Product (TP) Average Product (AP) Marginal Product (MP) 0 0 – – 1 – – 20 2 – – 26 3 66 – – 4 – 19 – 5 – – 4 ›Reveal solutionSolution
MP₄ = TP₄ − TP₃ = 76 − 66 = 10.
Step 1 — Get the two total products
- At L = 3: TP3=66 (given).
- At L = 4: AP4=19, so TP4=19×4=76.
Step 2 — Compute the marginal product
MP4=TP4−TP3=76−66=10
Marginal product is the extra output from the 4th unit of labour, which is 10. …
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