Q.Using the same schedule as Worked Example 1, state at which level of labour Average Product is maximum, and verify the relationship between Marginal Product and Average Product at that point.
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.
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.
- The shape of the total product curve — it first rises steeply, then flattens, then bends downward.
A common mistake: students think the law says "output always falls after some point." No — it says marginal product eventually falls. Total output can still rise (Stage 2), but at a decreasing rate.
The Diagram (Describe It in Words)
Draw a graph with labour (units) on the x-axis and output on the y-axis.
- Total Product (TP) curve: Starts at origin, rises steeply (Stage 1), then rises more slowly (Stage 2), then peaks and starts falling (Stage 3).
- Marginal Product (MP) curve: Rises in Stage 1, peaks at the end of Stage 1, then falls through Stage 2, crosses zero at the start of Stage 3, and becomes negative.
The point where MP = 0 is exactly where TP is maximum.
The Bottom Line
The Law of Variable Proportions is not a theory — it's an observed fact about production. It tells us that there is no free lunch from endlessly adding one input. Every production process has a fixed factor, and that fixed factor eventually becomes a bottleneck.
Marginal Product = ΔVariable InputΔTotal Product
Where Δ means "change in." The law says that beyond some point, each successive Δ in variable input yields a smaller Δ in total product.
For your exams: remember the three stages, the shape of the TP and MP curves, and the reason — the fixed factor becomes over-utilised. That's the core.
Average product is highest where adding another worker no longer raises the per-worker output; at that point marginal product equals average product.
AP is maximum (13) at L=4, and there MP=AP=13 — MP crosses AP at AP's peak.
AP is maximum at L=4 (AP=13), where MP=AP=13; before this MP>AP (AP rising), after it MP<AP (AP falling).
Given: the AP and MP columns computed in Worked Example 1.
Step 1 — Locate the maximum AP: the AP values are 10,12,13,13,12,10,8. The highest value is 13, reached at L=3 and L=4; the last level at which AP is at its peak before it starts to fall is L=4.
Step 2 — Read MP at that point: at L=4, MP=13, which equals AP=13.
Step 3 — Check the relationship on both sides:
- Before the peak, at L=3: MP=15, AP=13, so MP>AP — and indeed AP was still rising (from 13 towards its peak).
- At the peak, L=4: MP=AP=13.
- After the peak, at L=5: MP=8, AP=12, so MP<AP — and indeed AP is now falling (from 13 to 12).
This confirms the general rule: AP rises while MP>AP, is maximum where MP=AP, and falls while MP<AP.
Check (independent method — averaging logic): average product is a running average of the marginal products. A new marginal value above the current average must pull the average up; one below it pulls the average down; the two are equal exactly at the turning point of the average — which is why MP=AP coincides with the maximum of AP, matching the table.
AP is maximum (13) at L=4, where MP=AP=13; MP lies above AP while AP rises and below AP once AP falls.
Claiming AP is maximum where MP is maximum — MP peaks much earlier (at L=3, in Stage I), whereas AP peaks later, exactly where the falling MP curve crosses it.
Showing the 12 most recent of 20 on this concept.
- CBSE 2026Set MARCH1 markMCQQ.Product obtained from additional factors of production is termed as(a) Marginal product(b) Total product(c) Average product(d) Annual product
›Reveal solutionSolution
The product from an additional factor unit is the marginal product — option (a).
In production analysis (law of variable proportions), three product concepts are used:
- Total product (TP) — the total output produced by all units of the variable factor together.
- Marginal product (MP) — the addition to total product when one more unit of the variable factor is employed, other factors held constant. MP = change in TP / change in the variable input.
- Average product (AP) — total product divided by the number of units of the variable factor (TP / units).
The phrase "product obtained from additional factors of production" describes the extra output from an added unit, which is precisely the marginal product. "Annual product" is not a standard economic term.
✓Final answerOption (a) Marginal product — the output added by employing one additional unit of the variable factor.
- CBSE 2026Set ANNUAL1 markMCQQ.Read the following both statements and choose the correct option : Assertion (A) : When the marginal product is zero, the total product is constant. Reason (R) : The marginal product measures the change in total product.(a) Both A and R are correct and R is the correct explanation of A.(b) Both A and R are correct but R is not the correct explanation of A.(c) A is correct but R is incorrect.(d) Both A and R are incorrect.(a) Both A and R are correct and R is the correct explanation of A.(b) Both A and R are correct but R is not the correct explanation of A.(c) A is correct but R is incorrect.(d) Both A and R are incorrect.
›Reveal solutionSolution
Both statements are true, and the definitional link between MP and the change in TP directly explains why MP = 0 implies TP is (momentarily) constant.
Assertion: 'When the marginal product is zero, the total product is constant' — TRUE at that specific point: since MP = ΔTP/ΔL (the change in Total Product per additional unit of the variable factor), MP = 0 means ΔTP = 0, i.e., Total Product has stopped changing at exactly that unit of input — this is the single point where TP is at its maximum (neither rising nor about to fall from that exact unit's addition).
Reason: 'The marginal product measures the change in total product' — TRUE; this is the precise definition of Marginal Product (MP = ΔTP/ΔInput).
Logical link: the Reason directly and correctly explains the Assertion — it is PRECISELY BECAUSE MP measures the change in TP that an MP value of zero necessarily means TP is not changing (is constant) at that point.
✓Final answerBoth A and R are correct, and R is the correct explanation of A (Option 1) — because MP is defined as the change in TP, MP = 0 directly means TP is momentarily constant, at its maximum point.
- CBSE 2025Set ANNUAL1 markMCQQ.Which of the following laws explains the short-run production function? (A) Law of demand (B) Law of variable proportion (C) Law of returns to scale (D) Elasticity of demand
›Reveal solutionSolution
The short-run production function is explained by the Law of Variable Proportions, so the answer is (B).
In the short run some factors (like land or plant) are fixed while others (like labour) are variable, so the factor proportions change as more of the variable factor is applied to the fixed factor. The Law of Variable Proportions describes exactly this: as successive units of a variable factor are added to a fixed factor, total product first rises at an increasing rate, then at a diminishing rate, and may finally fall. The Law of Returns to Scale (C) applies to the long run when all factors vary, and the laws of demand and elasticity concern demand, not production. Hence the short-run production function is governed by the Law of Variable Proportions.
✓Final answer(B) Law of variable proportion.
- CBSE 2025Set ANNUAL1 markMCQQ.In which stage of production a rational producer likes to operate in the condition short-run production? (A) First stage (B) Second stage (C) Third stage (D) None of these
›Reveal solutionSolution
A rational producer operates in the second stage of production, so the answer is (B).
The Law of Variable Proportions has three stages. In Stage I (increasing returns) the average product keeps rising, meaning the fixed factor is under-utilised, so it is not optimal to stop here. In Stage III (negative returns) marginal product becomes negative and total product falls, so producing here is irrational. In Stage II (diminishing but positive returns) total product is still increasing and marginal product, though declining, is positive until it reaches zero at the peak of total product. A rational producer therefore operates in Stage II, where resources are used most efficiently. Hence the answer is the second stage.
✓Final answer(B) Second stage.
- CBSE 2025Set ANNUAL1 markMCQQ.Which factors among the following we find in short-run production process? (A) Fixed factors (B) Variable factors (C) Both (A) and (B) (D) None of these
›Reveal solutionSolution
Short-run production uses both fixed and variable factors, so the answer is (C).
The short run is a time period too short to change all inputs. In it, at least one factor (such as plant, machinery or land) is fixed, while other factors (such as labour, raw material and power) can be varied to change output. This co-existence of fixed and variable factors is exactly why the Law of Variable Proportions operates in the short run. In the long run, by contrast, all factors become variable. Therefore, in short-run production both fixed and variable factors are found.
✓Final answer(C) Both (A) and (B).
- CBSE 2025Set ANNUAL1 markMCQQ.Which of the following factors are there in short-run production process? (A) Fixed factors (B) Variable factors (C) Both (A) and (B) (D) None of these
›Reveal solutionSolution
In the short run a firm has both fixed factors and variable factors, so the answer is (C) Both (A) and (B).
Economists classify the production period by how freely inputs can be changed. In the short run, the quantity of some inputs cannot be altered — these are the fixed factors (for example, plant, building, heavy machinery). Other inputs can be freely increased or decreased with the level of output — these are the variable factors (for example, labour, raw material, power).
Because production in the short run always takes place with at least one fixed factor combined with variable factors, both kinds of factors are present. (Only in the long run do all factors become variable.) This is the basis of the Law of Variable Proportions studied in the BSEB Class-12 / Bihar Inter commerce syllabus, which aligns with the NCERT microeconomics curriculum.
✓Final answer(C) Both (A) and (B) — the short-run production process uses both fixed and variable factors.
- CBSE 2024Set MARCH1 markMCQQ.Formula for calculating AP is :(a) TP/MP(b) ΔTP/N(c) TP/N(d) ΔTP/ΔN
›Reveal solutionSolution
The correct option is (c) TP/N: AP = total product ÷ units of the factor.
Average product (AP) is the output per unit of the variable factor. It is found by dividing total product (TP) by the number of units (N) of the variable factor employed: AP = TP/N.
Why the others are wrong: (a) TP/MP and (b) ΔTP/N are not the AP formula; (d) ΔTP/ΔN is the formula for marginal product, the change in total product from one more unit of the factor.
✓Final answerOption (c) TP/N — average product equals total product divided by the number of units of the factor.
- CBSE 2024Set ANNUAL1 markMCQQ.Which factor(s) among the following do we find in short-run production process? (A) Fixed factor (B) Variable factor (C) Both (A) and (B) (D) None of these
›Reveal solutionSolution
The short-run production process has both fixed and variable factors, so the answer is (C).
In the BSEB Inter Class-12 Economics syllabus, the short run is defined as the period in which at least one factor of production is fixed (e.g. plant, machinery) while others are variable (e.g. raw material, labour). Production in the short run therefore involves both fixed and variable factors together — this coexistence is what gives rise to the law of variable proportions. (In the long run, by contrast, all factors are variable.) Hence the answer is (C).
✓Final answer(C) Both (A) and (B)
- CBSE 2024Set ANNUAL1 markMCQQ.Law of variable proportion is related to (A) Long-run (B) Short-run (C) Both (A) and (B) (D) Very long-run
›Reveal solutionSolution
The law of variable proportions operates in the short run, so the answer is (B).
In the BSEB Inter Class-12 Economics syllabus, the law of variable proportions (returns to a variable factor) describes how total, average and marginal product change when one factor is increased while other factors are kept fixed. This is possible only in the short run, where at least one factor is fixed. In the long run all factors are variable, so returns to scale apply instead. Hence the law of variable proportions is a short-run concept.
✓Final answer(B) Short-run
- CBSE 2024Set ANNUAL1 markMCQQ.Labour is an example of:(a) A fixed factor(b) A variable factor(c) demand(d) supply
›Reveal solutionSolution
Labour is an example of a variable factor — option (b).
In the short run, factors of production are of two kinds:
- Fixed factors – whose quantity cannot be changed in the short run (e.g., plant, machinery, factory building).
- Variable factors – whose quantity can be readily changed with the level of output (e.g., labour, raw materials, power).
Labour can be hired or reduced quickly as output changes, so it is a variable factor. (It is this that drives the law of variable proportions.)
✓Final answerCorrect option: (b) A variable factor.
- CBSE 2023Set ANNUAL1 markMCQQ.The value of Change in output / Change in input is-(a) Total Product(b) Average product(c) Marginal Product(d) None of these(a) Total Product(b) Average product(c) Marginal Product(d) None of these
›Reveal solutionSolution
Marginal Product = Change in output ÷ Change in input.
Total Product (TP) is the overall quantity of output produced by all units of the variable factor together. Average Product (AP) = TP ÷ number of units of the variable factor. Marginal Product (MP), by contrast, specifically measures the ADDITIONAL output from the LAST unit of the variable input added, calculated as MP = ΔTP/ΔL (change in total product divided by change in labour/input units). It is this measure — the ratio of change in output to change in input — that is being described in the question, and it is distinct from both TP (the total) and AP (the average per unit).
✓Final answerMarginal Product is the value of Change in output ÷ Change in input.
- CBSE 2023Set ANNUAL1 markQ.What the factor is called, which the firm can vary in the short run?
›Reveal solutionSolution
The factor a firm can change in the short run is the Variable Factor.
In the short run, a firm operates with a given plant/capital size that cannot be altered quickly — this is the Fixed Factor. However, the firm CAN change the quantity of certain other inputs — most commonly labour and raw materials — within this same short period to adjust its output level; such an input is called the Variable Factor. The behaviour of output as the variable factor is changed, with the fixed factor held constant, is precisely what the Law of Variable Proportions describes.
✓Final answerThe factor a firm can vary in the short run is called the Variable Factor (e.g., labour).
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