Production and Costs Class 11: Returns to a Factor and Short-Run Cost Curves

What Production and Costs is about

Weightage: This chapter is part of Unit 6, Producer Behaviour and Supply, which carries 14 of the 80 theory marks in the school annual exam.Source: CBSE Economics (030) syllabus 2026-27, Class XI course structure, Unit 6 Producer Behaviour and Supply

Key concepts

Production function; short run and long run

NCERT section 3.1 and 3.2

The production function shows the relationship between inputs and the maximum output that can be produced from them with given technology:

q = f(L, K), where L = labour and K = capital.

• Fixed factors: inputs that cannot be changed in the short run (building, heavy machinery).
• Variable factors: inputs that can be changed (labour, raw materials, power).

Short run: at least one factor is fixed; output changes by changing variable factors only. Long run: all factors can be varied, including plant size. The short and long run are not fixed calendar periods; they depend on how quickly the firm can change its fixed inputs.

A production function assumes efficient use: it gives the maximum possible output, not output from wasteful use.

Worked example

A bakery can hire more workers in a week but needs a year to build a second oven. Which is the variable factor and what is the short run here?

Try it first, then show the solutionSolution

1. Workers can be changed quickly: variable factor
2. The oven cannot be changed within a year: fixed factor
3. Any period less than a year, with one oven, is the short run

Answer: Labour is variable; with one fixed oven, periods under a year are the short run.

Total, average and marginal product

NCERT section 3.3

With capital fixed and labour variable:

• Total product (TP): total output from a given amount of labour.
• Average product (AP) = TP ÷ L: output per worker.
• Marginal product (MP) = ΔTP ÷ ΔL: change in TP from one more worker. Also TP = ΣMP.

Labour (L)	TP	MP = ΔTP	AP = TP ÷ L
0	0	-	-
1	10	10	10
2	24	14	12
3	39	15	13
4	52	13	13
5	62	10	12.4
6	68	6	11.33
7	70	2	10
8	68	-2	8.5

Relations:

• When MP is positive, TP rises; when MP = 0, TP is maximum; when MP is negative, TP falls.
• When MP > AP, AP rises; when MP = AP, AP is at its maximum; when MP < AP, AP falls.

Here AP reaches its maximum (13) at L = 3 and stays there at L = 4, because the 4th worker's MP (13) exactly equals AP: MP = AP at the maximum of AP. TP is maximum (70) at L = 7, where MP has fallen to 2 and the next worker's MP is negative.

Worked example

From the table, find MP of the 5th worker and AP at 5 workers. Is AP rising or falling there?

Try it first, then show the solutionSolution

1. MP₅ = 62 − 52 = 10
2. AP₅ = 62 ÷ 5 = 12.4
3. MP (10) < AP (12.4): AP is falling

Answer: MP = 10, AP = 12.4; AP is falling because MP is below it.

Law of variable proportions (returns to a factor)

NCERT section 3.4

Law of diminishing marginal product: if more and more units of a variable input are applied to a fixed input, the marginal product of the variable input eventually falls.

Law of variable proportions (returns to a factor) describes the full pattern as the ratio of the variable factor to the fixed factor rises:

Phase	TP	MP	Reason
I: Increasing returns to a factor	Rises at an increasing rate	Rises	Better use of the fixed factor; division of labour
II: Diminishing returns to a factor	Rises at a diminishing rate, up to its maximum	Falls but stays positive (up to 0)	Fixed factor becomes scarce relative to labour
III: Negative returns to a factor	Falls	Negative	Too many workers on the fixed factor; overcrowding

In the schedule above: Phase I is from 0 to 3 workers (MP rises to 15); Phase II from the 4th to the 7th worker (MP falls from 13 to 2, TP rises to its maximum); Phase III after 7 workers (MP = −2, TP falls).

A rational producer operates in Phase II: in Phase I it pays to add workers (MP is rising), and in Phase III extra workers reduce output.

Worked example

Why will a rational farmer never employ labour in Phase III?

Try it first, then show the solutionSolution

1. In Phase III, MP is negative: an extra worker reduces total output
2. The farmer would pay wages and get less output

Answer: Because extra workers lower total output; the farmer can produce more with fewer workers.

Shapes of TP, AP and MP curves

NCERT section 3.5

• TP curve: rises at an increasing rate (Phase I), then at a decreasing rate (Phase II) until its maximum, then falls (Phase III). It is S-shaped at first and then bends over.
• MP curve: inverse U-shaped: rises, reaches a maximum, falls, cuts the x-axis where TP is maximum, and becomes negative.
• AP curve: also inverse U-shaped but flatter; it rises while MP > AP and falls when MP < AP. MP cuts AP at the maximum of AP (from above).
• AP is always positive as long as TP is positive.

The point of inflexion of TP (where it stops rising at an increasing rate) is where MP is at its maximum.

Worked example

Where does the MP curve cut the AP curve and the x-axis?

Try it first, then show the solutionSolution

1. MP cuts AP at the maximum point of AP
2. MP cuts the x-axis (MP = 0) where TP is maximum

Answer: At AP's maximum, and at the level of labour where TP is maximum.

Short-run costs: TFC, TVC and TC

NCERT section 3.7

In the short run a firm has two kinds of costs:

• Total fixed cost (TFC): costs of fixed factors, which do not change with output and must be paid even at zero output (rent, salaries of permanent staff, interest on loans, insurance). The TFC curve is a horizontal line.
• Total variable cost (TVC): costs of variable factors, which change with output and are zero at zero output (raw materials, wages of casual workers, power). TVC first rises at a falling rate and then at a rising rate (inverse of TP's shape).
• Total cost (TC) = TFC + TVC. TC starts from TFC (not the origin) and is parallel in shape to TVC; the vertical gap between TC and TVC is always TFC.

(Costs include explicit costs paid out and implicit costs such as the normal return on the owner's own resources, as NCERT treats cost as including opportunity cost.)

Worked example

A firm's TC at zero output is ₹60 and at 4 units is ₹180. Find TFC and TVC at 4 units.

Try it first, then show the solutionSolution

1. At zero output only fixed cost exists: TFC = ₹60
2. TVC at 4 units = TC − TFC = 180 − 60 = ₹120

Answer: TFC = ₹60; TVC = ₹120.

Average and marginal costs and their relationships

NCERT section 3.7.1

• AFC = TFC ÷ Q: falls continuously as output rises (the same fixed cost is spread over more units); the AFC curve is a rectangular hyperbola (AFC × Q = TFC), never touching either axis.
• AVC = TVC ÷ Q: U-shaped.
• AC (SAC) = TC ÷ Q = AFC + AVC: U-shaped; the gap between AC and AVC (= AFC) narrows as output rises but never disappears.
• MC = ΔTC ÷ ΔQ = ΔTVC ÷ ΔQ (fixed cost does not change): U-shaped. ΣMC = TVC.

Output (Q)	TFC	TVC	TC	MC	AFC	AVC	AC
0	60	0	60	-	-	-	-
1	60	40	100	40	60	40	100
2	60	70	130	30	30	35	65
3	60	90	150	20	20	30	50
4	60	124	184	34	15	31	46
5	60	160	220	36	12	32	44
6	60	220	280	60	10	36.67	46.67

Relationships:

• When MC < AC (or AVC), AC (AVC) falls; when MC > AC, AC rises; MC = AC at the minimum of AC. The same holds for AVC.
• MC cuts AVC first (at its minimum) and then AC (at its minimum), so the minimum of AVC lies at a lower output than the minimum of AC.

Here AVC is lowest (₹30) at Q = 3 and AC is lowest (₹44) at Q = 5: MC stays below AC up to the 5th unit (MC₅ = 36 < AC₄ = 46) and rises above it with the 6th (MC₆ = 60 > AC₅ = 44). In a smooth curve, MC would cut AC exactly at its minimum.

Why U-shaped? AVC and MC first fall because of increasing returns to the variable factor, then rise because of diminishing returns (law of variable proportions). AC is U-shaped because AFC falls and AVC is U-shaped.

Worked example

From the cost table, show that AC = AFC + AVC at Q = 6, and explain why AC rises between Q = 5 and Q = 6.

Try it first, then show the solutionSolution

1. AFC₆ = 60 ÷ 6 = 10; AVC₆ = 220 ÷ 6 = 36.67; sum = 46.67 = AC₆ (280 ÷ 6 = 46.67)
2. MC of the 6th unit = 60 > AC at Q = 5 (44), so AC rises

Answer: AC₆ = 46.67; it rises because MC (₹60) is above AC.

Production and Costs 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.

Topics in this chapter

• Law of Variable Proportions: TP, AP and MP
• Short-run Costs and Cost Curves

Production and Costs: key facts

Average product

AP = \frac{TP}{L}

Output per unit of the variable factor.

Marginal product

MP = \frac{\Delta TP}{\Delta L};\ TP = \sum MP

TP maximum where MP = 0.

Total cost

TC = TFC + TVC

TVC = 0 at zero output.

Average costs

AFC = \frac{TFC}{Q},\ AVC = \frac{TVC}{Q},\ AC = \frac{TC}{Q} = AFC + AVC

AFC curve is a rectangular hyperbola.

Marginal cost

MC = \frac{\Delta TC}{\Delta Q} = \frac{\Delta TVC}{\Delta Q};\ TVC = \sum MC

Fixed cost does not affect MC.

Relationships

MC < AC ⇒ AC falls; MC = AC at min AC; MC > AC ⇒ AC rises

Same for AVC; and MP vs AP similarly.

How the school exam asks Production and Costs

The question patterns to expect, and the method that works for each.

Tricks to remember Production and Costs

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Phases of the law

  "I-D-N": Increasing, Diminishing, Negative returns; a rational producer stays in D.

  Use it when: Law of variable proportions.

• Marginal pulls average

  If marginal is above average, average rises; if below, it falls; if equal, the average is at its turning point.

  Use it when: MP-AP and MC-AC relations.

• Cost family

  TC = TFC + TVC; AC = AFC + AVC; MC from TVC only.

  Use it when: Cost tables.

Production and Costs: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section E style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 4-mark question split into 1 + 1 + 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.

Where students lose marks in Production and Costs

The slips examiners see most often, and what to write instead.

• ✗Mistake: Starting the TVC curve at TFC

  Confusing TVC with TC.

  ✓Do this: TVC starts from the origin (zero at zero output); TC starts from TFC.

  Usually costs: 1 mark in a diagram.

• ✗Mistake: Including fixed cost in MC

  MC computed from TC sounds like it includes everything.

  ✓Do this: MC = ΔTC = ΔTVC; fixed cost does not change, so it never affects MC.

  Usually costs: 1 mark.

• ✗Mistake: Saying "MC is falling, so AC must be falling"

  Looking at MC's direction instead of its level.

  ✓Do this: AC falls when MC is below AC and rises when MC is above AC, whatever MC's own direction.

  Usually costs: 1 mark in reasoning questions.

• ✗Mistake: Calling the three phases "returns to scale"

  Similar names.

  ✓Do this: Phases of the law of variable proportions are returns to a factor (short run). Returns to scale (all factors changing) is not in the 2026-27 CBSE content.

  Usually costs: 1 mark.

• ✗Mistake: Drawing MC cutting AC before AVC

  Order of the minimum points is forgotten.

  ✓Do this: MC cuts AVC at its minimum first (lower output), then AC at its minimum.

  Usually costs: 1 mark.

NCERT exercise guide: Production and Costs

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on Production and Costs

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   In the short run, which cost remains the same at all levels of output?
   (a) TVC
   (b) TC
   (c) TFC
   (d) MC

   Hint

   Rent, insurance.

   Answer

   (c) TFC

2. Q2 · 1 mark · MCQExam level

   MP cuts AP at:
   (a) maximum of MP
   (b) maximum of AP
   (c) minimum of AP
   (d) where TP is maximum

   Hint

   Like MC and AC, but for products.

   Answer

   (b) maximum of AP

3. Q3 · 1 mark · Very short answerExam level

   Give two examples of fixed costs.

   Hint

   Paid even at zero output.

   Answer

   Rent of the factory; salary of permanent staff (also insurance, interest on loans).

4. Q4 · 3 marks · Short answerExam level

   Find MP and AP: L = 1, 2, 3, 4, 5; TP = 8, 20, 30, 36, 38.

   Hint

   Differences and ratios.

   Answer

   MP: 8, 12, 10, 6, 2. AP: 8, 10, 10, 9, 7.6.

5. Q5 · 4 marks · Short answerHarder exam level

   TC at outputs 0 to 4 is ₹50, 80, 100, 130, 180. Find TFC, TVC, AVC and MC.

   Hint

   TFC = TC at zero output.

   Answer

   TFC = 50. TVC: 0, 30, 50, 80, 130. AVC: -, 30, 25, 26.67, 32.5. MC: 30, 20, 30, 50.

6. Q6 · 6 marks · Long answerHarder exam level

   State the law of variable proportions and explain its three phases with a schedule.

   Hint

   Increasing, diminishing, negative.

   Answer

   When more units of a variable factor are added to a fixed factor, MP first rises (increasing returns), then falls but stays positive (diminishing returns), then becomes negative (negative returns). Schedule: L 1-6, TP 10, 24, 39, 52, 62, 68 ... MP 10, 14, 15, 13, 10, 6, then 2 and −2. Reasons: better use of the fixed factor; then scarcity of the fixed factor; then overcrowding.

7. Q7 · 3 marks · Short answerHarder exam level

   Why is the AFC curve a rectangular hyperbola?

   Hint

   AFC × Q = constant.

   Answer

   AFC × Q = TFC, a constant, at every output. A curve on which the product of the two coordinates is constant is a rectangular hyperbola. AFC keeps falling but never reaches zero.

8. Q8 · 3 marks · Short answerHarder exam level

   Explain the relationship between AVC and MC.

   Hint

   Below, equal, above.

   Answer

   When MC < AVC, AVC falls; when MC = AVC, AVC is at its minimum; when MC > AVC, AVC rises. MC cuts AVC at the minimum of AVC from below.

9. Q9 · 3 marks · Short answerHarder exam level

   Distinguish between the short run and the long run in production.

   Hint

   Fixed factors.

   Answer

   Short run: at least one factor is fixed; output changes only by varying variable factors; there are fixed and variable costs. Long run: all factors can be changed; no fixed costs; plant size can change.

10. Q10 · 3 marks · Short answerHarder exam level

    AC at 5 units is ₹40 and at 6 units is ₹42. Find the MC of the 6th unit.

    Hint

    TC = AC × Q.

    Answer

    TC₅ = 200; TC₆ = 252; MC₆ = ₹52 (above AC, so AC rises).

11. Q11 · 3 marks · Short answerHarder exam level

    Explain why the gap between AC and AVC narrows as output rises but they never meet.

    Hint

    The gap is AFC.

    Answer

    AC − AVC = AFC, which falls as output rises, so the gap narrows. AFC never becomes zero (TFC > 0), so the curves never meet.

12. Q12 · 4 marks · Long answerHOTS / competency

    Suppose a firm's MC is falling but its AC is rising. Is this possible? Explain with numbers.

    Hint

    Compare MC with AC, not with its own past.

    Answer

    Yes, if MC is falling but still above AC. Example: AC of 4 units = 40 (TC 160). If the 5th unit's MC = 50, AC₅ = 42 (rising). If the 6th unit's MC = 48 (falling MC), AC₆ = 258/6 = 43 (still rising) because MC (48) > AC (42). AC depends on whether MC is above or below AC, not on MC's direction.

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. 1.Define marginal product.Show answer

   The change in total product from one more unit of the variable factor.

2. 2.In which phase does a rational producer operate?Show answer

   Phase II (diminishing returns to a factor).

3. 3.What is TVC at zero output?Show answer

   Zero.

4. 4.Formula for AC?Show answer

   TC ÷ Q = AFC + AVC.

5. 5.Shape of the AFC curve?Show answer

   Rectangular hyperbola.

6. 6.Where does MC cut AC?Show answer

   At the minimum point of AC.

7. 7.What is ΣMC equal to?Show answer

   TVC.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you define a production function and the short run?
• ☐Can you compute MP and AP from TP?
• ☐Can you state the relation between AP and MP?
• ☐Can you identify the three phases in a schedule?
• ☐Can you give reasons for each phase?
• ☐Can you complete a cost table from TC?
• ☐Can you explain why AFC is a rectangular hyperbola?
• ☐Can you explain why AVC, AC and MC are U-shaped?
• ☐Can you describe the MC-AC and MC-AVC relationships?

Production and Costs: frequently asked questions