Concepts of Production: ISC Class 12 Economics, Law of Variable Proportions
Updated 14 October 2026 · Fact-checked
Production is the process of converting inputs into output. ISC Class 12 Economics tests the production function (short run and long run), total, average and marginal physical product and their relationships, the law of variable proportions with its assumptions, diagram and three stages, and the meaning of returns to scale.
What Concepts of Production is about
A firm turns inputs (land, labour, capital, entrepreneurship) into output. The technical relation between them is the production function: Q = f(L, K), the maximum output obtainable from given inputs with a given technology. In the short run at least one input (usually capital: the factory, machines) is fixed and output changes only by changing the variable input; in the long run all inputs can be varied.
In the short run, as more units of a variable factor are added to a fixed factor, output behaves in a predictable way described by the law of variable proportions (returns to a factor). Measured by total product (TP), average product (AP) and marginal product (MP), output first rises at an increasing rate (Stage I: increasing returns), then at a diminishing rate (Stage II: diminishing returns) until TP is maximum, and then falls (Stage III: negative returns). A rational producer operates in Stage II. The point of inflexion on the TP curve is where MP is maximum.
In the long run, when all inputs change in the same proportion, the response of output is called returns to scale, which the syllabus asks for in meaning only. Examiners have warned about confusing returns to a factor with returns to scale, reading "NOT" carefully, and answering only the stage asked. The LVP schedule is for understanding, not for testing; the diagram and explanation of the three stages are tested.
Weightage: Concepts of Production is part of the unit Microeconomic Theory: Market Mechanism, Concepts of Production, Cost and Revenue, which carries 12 of the 80 theory marks, shared with 2 other chapters. Questions on it can appear in any section of the paper.Source: CISCE ISC Economics syllabus, examination year 2027, distribution of marks
Key concepts
- Production function: short run and long run
A production function shows the functional relationship between physical inputs and physical output of a firm, for a given state of technology: Q = f(L, K).
- Short-run production function: some factors are fixed (plant, machinery) and some variable (labour, raw material). Output is changed by changing only the variable factor; this gives returns to a factor.
- Long-run production function: all factors are variable; the firm can change its scale of production; this gives returns to scale.
The short run and long run are not fixed periods of time; they depend on whether all inputs can be changed.
Worked example
Suppose a bakery has one oven and can hire more bakers. Within a month it cannot buy another oven. Is this short run or long run? Which law describes the effect of adding bakers? [2 marks]
Try it first, then show the solutionSolution
- The oven is fixed and bakers are variable: short run.
- Adding variable bakers to a fixed oven: law of variable proportions (returns to a factor).
Answer: Short run; law of variable proportions.
- Total, average and marginal product
- Total product (TP): total output from all units of the variable factor, with fixed factors constant.
- Average product (AP) = TP ÷ units of the variable factor (L).
- Marginal product (MP) = change in TP from one more unit of the variable factor: MPn = TPn − TPn−1 (or ΔTP ÷ ΔL).
- TP = ΣMP.
Relationships:
- TP and MP: when MP rises, TP rises at an increasing rate; when MP falls but is positive, TP rises at a diminishing rate; when MP = 0, TP is maximum; when MP is negative, TP falls. MP is maximum at the point of inflexion of TP.
- AP and MP: when MP > AP, AP rises; when MP = AP, AP is maximum (MP cuts AP at its highest point); when MP < AP, AP falls. MP can be zero or negative; AP is always positive.
- TP and AP: AP rises as long as TP rises faster than labour; AP is maximum where a line from the origin is tangent to TP; AP falls but stays positive even when TP falls.
Worked example
Suppose TP from 1 to 4 labourers is 10, 24, 42 and 56 units. Calculate AP and MP. [2 marks]
Try it first, then show the solutionSolution
- MP = 10, 14, 18, 14.
- AP = 10, 12, 14, 14.
Answer: MP rises to 18 (3rd labourer) then falls; AP rises to 14 and equals MP at 14 for the 4th labourer.
- Law of variable proportions: statement and assumptions
Statement: when more and more units of a variable factor are employed with a given quantity of fixed factors, the total product initially increases at an increasing rate, then at a diminishing rate, and finally starts falling. In terms of MP: MP first rises, then falls, and eventually becomes negative.
Assumptions:
- At least one factor is fixed (short run).
- All units of the variable factor are homogeneous (equally efficient).
- Technology remains unchanged.
- Factors can be combined in varying proportions.
- Prices of factors are constant (output is measured in physical units).
The law does not apply when all factors are increased in the same proportion: that is returns to scale.
Worked example
Suppose a factory doubles its workers, machines and floor space together. Does the law of variable proportions apply? Why? [1 mark]
Try it first, then show the solutionSolution
- No factor is fixed; all are increased in the same proportion.
Answer: No: this is a change in scale (returns to scale), not returns to a factor.
- Three stages of the law
Stage I: increasing returns to a factor: TP rises at an increasing rate up to the point of inflexion, then at a diminishing rate; MP rises then starts falling; AP rises and the stage ends where AP is maximum and AP = MP.
*Reasons*: better utilisation of the fixed factor (it was under-used); division of labour and specialisation; indivisibility of fixed factors.
Stage II: diminishing returns to a factor: TP rises at a diminishing rate and is maximum at the end; MP falls and becomes zero; AP falls.
*Reasons*: the fixed factor becomes scarce relative to the variable factor; imperfect substitutability of factors.
Stage III: negative returns to a factor: TP falls; MP is negative; AP continues to fall.
*Reasons*: overcrowding of the variable factor; the fixed factor is overused; poor coordination.
Rational stage: a producer operates in Stage II: not Stage I (the fixed factor is under-used, adding labour raises AP) and never Stage III (more labour reduces output).
Worked example
Suppose the schedule below shows a farm with a fixed plot of land. Identify the three stages and give the stage where a rational farmer will operate. [4 marks]
Schedule (for understanding only)
Labour (units) TP AP MP Stage 1 10 10 10 I: increasing returns 2 24 12 14 I: increasing returns 3 42 14 18 I: increasing returns 4 56 14 14 II: diminishing returns 5 65 13 9 II: diminishing returns 6 70 11.67 5 II: diminishing returns 7 70 10 0 II: diminishing returns 8 66 8.25 −4 III: negative returns Try it first, then show the solutionSolution
- Stage I: 1 to 3 labourers (MP rising, AP rising) up to where AP = MP = 14 (4th unit).
- Stage II: from 4 to 7 labourers: MP falling, TP rising at a diminishing rate, reaching maximum 70 when MP = 0.
- Stage III: 8th labourer: MP negative (−4), TP falls.
- Rational: Stage II.
Answer: Stages I, II and III as above; operate in Stage II.
- Returns to scale (meaning only)
Returns to scale describe how output responds in the long run when all inputs are changed in the same proportion:
- Increasing returns to scale: output increases in a greater proportion than inputs (inputs double, output more than doubles).
- Constant returns to scale: output increases in the same proportion.
- Diminishing returns to scale: output increases in a smaller proportion.
Returns to a factor versus returns to scale:
Basis Returns to a factor Returns to scale Period Short run Long run Factors changed One variable, others fixed All, in the same proportion Factor ratio Changes Remains the same Scale of production Unchanged Changes Worked example
Suppose a company doubles all its inputs and output rises from 1,000 to 2,500 units. Which kind of returns to scale is this? [1 mark]
Try it first, then show the solutionSolution
- Inputs × 2; output × 2.5: output rises in a greater proportion.
Answer: Increasing returns to scale.
Concepts of Production in real life
Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.
Diminishing returns in a kitchen
Suppose a small restaurant kitchen with two stoves adds cooks one by one during the lunch rush.
Why might the fifth or sixth cook add little or even reduce output?
Try it first, then show the solutionSolution
- The stoves and space are fixed; each extra cook has less equipment to work with, so MP falls (Stage II).
- Too many cooks crowd the kitchen and get in each other's way: MP becomes negative (Stage III).
Answer: Fixed equipment makes extra cooks less productive and, beyond a point, counter-productive.
Memory hook: Too many cooks spoil the broth: Stage III.
Increasing returns from specialisation
Imagine a tailoring shop with a large cutting table run by one person, who must measure, cut, stitch and finish every garment.
Why might adding a second and third worker raise output more than proportionately?
Try it first, then show the solutionSolution
- The fixed table and machines were under-used by one worker.
- Workers can specialise (one cuts, one stitches), so MP rises: Stage I.
Answer: Better use of fixed factors and division of labour give increasing returns.
Memory hook: Specialise to multiply.
Returns to scale
Suppose a car maker builds an identical second plant next to the first, doubling all its inputs.
If output exactly doubles, what are the returns to scale?
Try it first, then show the solutionSolution
- All inputs changed in the same proportion: a long-run change in scale.
- Output changed in the same proportion: constant returns to scale.
Answer: Constant returns to scale.
Memory hook: Double everything, double output: constant returns.
Topics in this chapter
Concepts of Production: key facts
- Production function
- Q = f(L, K)
- Average product
- AP = TP ÷ L
- Marginal product
- MPn = TPn − TPn−1 = ΔTP ÷ ΔL
- Total product
- TP = ΣMP
How the board asks Concepts of Production
The question patterns to expect, and the method that works for each.
| Question type | How it is asked | Method |
|---|---|---|
| Objective (Q1) | What is maximum at the point of inflexion; when the law does NOT apply; TP/AP/MP from a schedule. | Read "NOT" carefully; MP is maximum at the point of inflexion. |
| Short answer (Section B, 4 marks) | Relationship of AP and TP (or MP and TP) with a diagram; behaviour of TP, AP, MP in one stage with a reason. | Diagram with TP above and AP/MP below; answer only the stage asked. |
| Long answer (Section C, 8 marks) | Law of variable proportions: statement, assumptions, diagram, three stages with reasons. | Statement → assumptions → diagram → stages with reasons → rational stage. |
Tricks to remember Concepts of Production
Short memory aids. Say each one aloud once, then use it on a question the same day.
Stage boundaries: "AP max, then MP zero"
Stage I ends where AP is maximum (AP = MP); Stage II ends where MP = 0 (TP maximum).
Use it when: Marking stages on a diagram.
MP leads, AP follows
MP rises first and falls first; AP follows and is cut by MP at its peak.
Use it when: AP-MP relationship.
Concepts of Production: board-level solved questions
Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.
Example 1: Point of inflexion · 1 mark · MCQBoard level
The point of inflexion on the total product curve corresponds to the maximum of:
(a) total product
(b) average product
(c) marginal product
(d) total cost
Try it first, then show the solutionSolution
- TP changes from increasing at an increasing rate to increasing at a diminishing rate where MP stops rising.
Answer: (c) marginal product
Example 2: When the law does not apply · 1 mark · MCQHarder board level
The law of variable proportions does NOT apply when:
(a) one factor is fixed
(b) technology is constant
(c) all factors are varied in the same proportion
(d) units of the variable factor are homogeneous
Try it first, then show the solutionSolution
- (a), (b) and (d) are assumptions of the law. Changing all factors proportionately is returns to scale.
Answer: (c)
Example 3: AP and MP from TP · 2 marks · Short answerHarder board level
TP of 4, 5, 6 and 7 workers is 56, 65, 70 and 70 units. Calculate MP and AP for the 5th to 7th workers and state where AP is falling while TP is still rising.
Try it first, then show the solutionSolution
- MP: 9, 5, 0. AP: 13, 11.67, 10.
- From the 5th worker AP falls (MP < AP) while TP still rises until the 7th worker, where MP = 0.
Answer: MP 9, 5, 0; AP 13, 11.67, 10; AP falls while TP rises from 5 to 7 workers.
Example 4: Increasing returns to a factor only · 2 marks · Short answerHarder board level
How do TP, AP and MP behave under increasing returns to a factor? Give one reason for this stage.
Try it first, then show the solutionSolution
- TP rises at an increasing rate (and then at a diminishing rate towards the end of the stage); MP rises and later starts falling; AP rises throughout and reaches its maximum at the end of the stage.
- Reason: better utilisation of the indivisible fixed factor, which was under-used.
Answer: TP and AP rise, MP rises then falls; reason: fuller use of the fixed factor.
Example 5: AP and TP relationship · 4 marks · Short answerHarder board level
Workers are added one by one to a fixed plant. Using a diagram, show how average product behaves as total product rises, peaks and then declines.
Try it first, then show the solutionSolution
- Diagram: TP curve in the upper panel; AP (and MP) curves in the lower panel against units of labour.
- AP is the slope of a ray from the origin to a point on TP. As TP rises steeply, AP rises.
- AP is maximum where the ray from the origin is tangent to TP.
- Beyond that AP falls; it falls but stays positive even after TP reaches its maximum and starts falling.
Answer: AP rises, reaches a maximum at the tangency of a ray from the origin with TP, and then falls but remains positive.
Example 6: Full law with stages · 6 marks · Long answerHOTS / competency
State the law of variable proportions and its assumptions. Explain its three stages with a diagram description and reasons, and identify the stage in which a rational producer operates.
Try it first, then show the solutionSolution
- Statement: adding units of a variable factor to fixed factors, TP first rises at an increasing rate, then at a diminishing rate, and finally falls.
- Assumptions: one factor fixed; homogeneous variable units; constant technology; variable factor proportions possible.
- Diagram: TP with point of inflexion and maximum; MP rising, cutting AP at its maximum, reaching zero below TP's maximum and becoming negative.
- Stage I (to AP max): better use of fixed factor, specialisation. Stage II (to MP = 0): fixed factor scarce, imperfect substitutes. Stage III (MP < 0): overcrowding.
- Rational stage: II.
Answer: Three stages as explained; producer operates in Stage II.
Case-study practice (Section C style)
Read the situation, then answer every part. In the board paper this is a 8-mark question split into 2 + 2 + 2 + 2 marks.
Hiring pickers on a tea estate
Suppose a tea estate with a fixed 20-hectare garden hires pickers. With 10, 20, 30, 40 and 50 pickers, daily output of leaf is 500, 1,200, 1,650, 1,800 and 1,750 kg.
(i) · 2 marks
Calculate MP of each additional batch of 10 pickers and AP at each level.
Answer
Answer: MP per batch: 500, 700, 450, 150, −50. AP (kg per picker): 50, 60, 55, 45, 35.
1 mark MP, 1 mark AP.
(ii) · 2 marks
Identify the stages.
Answer
Answer: Stage I up to 20 pickers (AP rising to its maximum of 60); Stage II from 20 to 40 (MP falling but positive); Stage III beyond 40 (MP negative).
2 marks.
(iii) · 2 marks
How many pickers should the estate hire and why?
Answer
Answer: Between 20 and 40 (Stage II): output is still rising and the garden is well used; never beyond 40.
1 mark range, 1 mark reason.
(iv) · 2 marks
If the estate doubled both garden area and pickers, which concept would apply?
Answer
Answer: Returns to scale (all inputs changed in the same proportion).
2 marks.
Where the marks are
How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.
Increasing returns to a factor (2 marks) (2 marks)
| Step | Marks |
|---|---|
| Behaviour of TP, AP and MP in Stage I only | 1 |
| One reason explained | 1 |
AP-TP relationship with diagram (4 marks) (4 marks)
| Step | Marks |
|---|---|
| Correct diagram with labelled TP and AP | 2 |
| Explanation of rising, maximum and falling AP | 2 |
Law of variable proportions (6 marks) (6 marks)
| Step | Marks |
|---|---|
| Statement and assumptions | 1 |
| Diagram with three stages marked | 2 |
| Explanation of each stage with a reason | 2 |
| Rational stage identified | 1 |
Where students lose marks in Concepts of Production
The slips examiners see most often, and what to write instead.
Mistake: Confusing MP and AP at the point of inflexion
CISCE examiners' comments, 2024: "Confused marginal product with average product".
Do this: Point of inflexion → MP maximum; AP is maximum later, where MP = AP.
Usually costs: 1 mark.
Mistake: Explaining in words when a diagram is asked
CISCE examiners' comments, 2024: "Lacked clarity on concepts of total product and average product"; "Explained TP–MP relationship in words instead of using a diagram".
Do this: Draw TP above and AP/MP below on the same horizontal scale and refer to the diagram.
Usually costs: 2 marks.
Mistake: Mixing up returns to a factor and returns to scale; missing "NOT"
CISCE examiners' comments, 2025: "Overlooked the word NOT in the question"; "Confused Law of Returns to Scale with Law of Variable Proportions".
Do this: Underline negatives in the question; one factor varied → variable proportions; all factors → scale.
Usually costs: 1 mark.
Mistake: Writing all three stages when one is asked
CISCE examiners' comments, 2025: "Explained the entire Law of Variable Proportions with all three stages instead of only increasing returns"; "Failed to give a reason for the occurrence of increasing returns".
Do this: Answer only the stage asked and give its reason.
Usually costs: 1 mark.
Practice questions on Concepts of Production
Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.
Q1 · 1 mark · MCQBoard level
When TP is maximum, MP is:
(a) maximum
(b) zero
(c) negative
(d) equal to APHint
Top of the hill.
Answer
(b) zero
Q2 · 1 mark · Very short answerBoard level
Define marginal product.
Hint
One more unit.
Answer
The change in total product from employing one more unit of the variable factor.
Q3 · 2 marks · Short answerBoard level
TP of 5 workers is 65 and of 6 workers is 70. Find MP of the 6th worker and AP at 6 workers.
Hint
Difference and division.
Answer
MP = 5; AP = 70 ÷ 6 = 11.67.
Q4 · 2 marks · Short answerHarder board level
Give two differences between returns to a factor and returns to scale.
Hint
Time and factors.
Answer
Returns to a factor: short run, one factor varied. Returns to scale: long run, all factors varied in the same proportion.
Q5 · 2 marks · Short answerHarder board level
Why does MP become negative in Stage III?
Hint
Overcrowding.
Answer
Too many units of the variable factor crowd the fixed factor and obstruct one another, so an extra unit reduces total output.
Q6 · 2 marks · Short answerHOTS / competency
Explain why AP can never be negative though MP can.
Hint
TP is positive.
Answer
AP = TP ÷ L, and TP (total output) is always positive, so AP is positive; MP is a change in TP, which can be negative when TP falls.
Q7 · 2 marks · Short answerHOTS / competency
Why would a rational producer not operate in Stage I?
Hint
AP still rising.
Answer
In Stage I the fixed factor is under-used and AP is rising, so adding more of the variable factor increases efficiency; the producer gains by expanding into Stage II.
Q8 · 1 mark · Very short answerBoard level
State the meaning of increasing returns to scale.
Hint
Proportions.
Answer
When all inputs are increased in a given proportion, output increases in a greater proportion.
Test your recall
Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.
1.MP at maximum TP?Show answer
Zero.
2.Where does MP cut AP?Show answer
At the maximum point of AP.
3.Rational stage of production?Show answer
Stage II.
4.Returns to scale is a short-run or long-run concept?Show answer
Long run.
Best order to study it
- Production function: short and long run.
- TP, AP, MP and their relationships.
- Law of variable proportions: statement and assumptions.
- Three stages with reasons and diagram.
- Returns to scale (meaning only).
Quick revision checklist
The night before the exam: can you do each of these without looking?
- Q = f(L, K); short run: some factors fixed.
- AP = TP/L; MP = ΔTP/ΔL; TP = ΣMP.
- Stage I ends at AP max; Stage II at MP = 0; Stage III MP < 0.
- Point of inflexion: MP maximum.
- Returns to scale: all inputs, same proportion, long run.
Concepts of Production: frequently asked questions
Do I need to remember the LVP schedule?
No. The syllabus says the schedule is for understanding and not for testing; the statement, assumptions, diagram and stages are tested.
How much of returns to scale is needed?
Only its meaning and the three types (increasing, constant, diminishing).
Is the law also called diminishing returns?
The law of variable proportions describes all three phases; "diminishing returns" refers to its second stage, which is the most common phase in practice.
Based on: CISCE ISC 2027 Economics syllabus; CISCE ISC 2027 Economics specimen question paper and answer key; CISCE Analysis of Pupil Performance, ISC Economics, 2025; CISCE Analysis of Pupil Performance, ISC Economics, 2024