NCERT Solutions for Class 12 Economics Chapter 3: Production and Costs (NCERT 2026–27)

These Class 12 Economics Chapter 3 solutions cover Production and Costs from the NCERT textbook Introductory Microeconomics, updated for the 2026–27 session. The chapter explains how a firm transforms inputs into output through a production function, the concepts of Total Product (TP), Average Product (AP) and Marginal Product (MP), the law of variable proportions, returns to scale, and the firm’s short-run and long-run cost structure (TFC, TVC, TC, AFC, AVC, SAC, SMC, LRAC, LRMC). Below you get verbatim NCERT exercise questions with step-by-step answers — every theory question explained and every numerical solved with full working — plus extra practice, MCQs, Assertion–Reason and FAQs.

Class: 12 Subject: Economics Book: Introductory Microeconomics Chapter: 3 Chapter Name: Production and Costs Session: 2026–27
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Class 12 Economics Chapter 3 – Overview

Chapter 3, Production and Costs, studies the behaviour of a producer (firm). Production is the process by which inputs (labour, capital, land, raw materials) are transformed into output. The production function shows the maximum output obtainable from given input combinations for a given technology, usually written q = f(L, K). In the short run at least one factor is fixed; in the long run all factors are variable. Holding all inputs but one constant gives us the Total Product of the variable input, and from it the Average Product (AP = TP/L) and Marginal Product (MP = ΔTP/ΔL). The law of variable proportions states that MP first rises and then falls, so the TP, MP and AP curves take their characteristic shapes (MP and AP inverse ‘U’-shaped, MP cutting AP from above at AP’s maximum). When all inputs change together we get returns to scale (constant, increasing or decreasing). On the cost side, TC = TVC + TFC, SAC = AVC + AFC, and SMC = ΔTC/Δq; the AFC curve is a rectangular hyperbola, while SMC, AVC and SAC are ‘U’-shaped, with SMC cutting AVC and SAC from below at their minimum points. In the long run there are no fixed costs and both LRAC and LRMC are ‘U’-shaped.

Key Concepts & Terms

Production function: the relationship between inputs used and the maximum output a firm can produce with a given technology; q = f(L, K). It deals only with the efficient use of inputs.

Isoquant: the set of all input combinations (of L and K) that yield the same maximum level of output; like an indifference curve but for output. Isoquants are negatively sloped when marginal products are positive.

Short run / long run: in the short run at least one factor is fixed (the fixed factor) and only the variable factor can be changed; in the long run all factors are variable, so there is no fixed factor. The distinction is about whether all inputs can be varied, not about calendar time.

Total Product (TP): the relationship between a variable input and output when all other inputs are held constant; also called total return or total physical product. TP is the sum of the marginal products of every preceding unit.

Average Product (AP): output per unit of variable input, APL = TPL / L.

Marginal Product (MP): the change in output per unit change in the variable input, MPL = ΔTPL / ΔL = (TP at L units) − (TP at L − 1 unit). MP is undefined at zero input.

Law of variable proportions (law of diminishing marginal product): as the variable factor is increased (other factors fixed), its MP first rises and then, after a point, falls, because factor proportions become first more and then less suitable.

Returns to scale: a long-run concept where all inputs change in the same proportion — Constant (CRS) if output rises in the same proportion, Increasing (IRS) if output rises more than proportionately, and Decreasing (DRS) if output rises less than proportionately. For a Cobb–Douglas function q = x1αx2β: α+β=1 ⇒ CRS, α+β>1 ⇒ IRS, α+β<1 ⇒ DRS.

Cost function: the least cost of producing each level of output, given factor prices and technology. For every output level the firm chooses the least-cost input combination.

TFC, TVC, TC: total fixed cost (independent of output), total variable cost (rises with output), and total cost TC = TVC + TFC.

AFC, AVC, SAC, SMC: average fixed cost (TFC/q, a rectangular hyperbola), average variable cost (TVC/q), short-run average cost SAC = AVC + AFC = TC/q, and short-run marginal cost SMC = ΔTC/Δq (= ΔTVC/Δq in the short run).

Long-run costs: in the long run there are no fixed costs, so TC and TVC coincide; LRAC = TC/q and LRMC = (TC at q units) − (TC at q − 1 units). Both are ‘U’-shaped, with LRMC cutting LRAC from below at LRAC’s minimum.

Important Formulas (Chapter 3)

Production function: q = f(L, K).

Average Product: APL = TPL ÷ L.

Marginal Product: MPL = ΔTPL ÷ ΔL = (TP at L) − (TP at L−1). Also TP = sum of all MPs up to that level.

Total cost: TC = TVC + TFC.

Average costs: AFC = TFC ÷ q  •  AVC = TVC ÷ q  •  SAC = TC ÷ q = AVC + AFC.

Marginal cost: SMC = ΔTC ÷ Δq = (TC at q) − (TC at q−1). Also TVC = sum of all SMCs up to that level.

Long run: LRAC = TC ÷ q  •  LRMC = (TC at q) − (TC at q−1).

NCERT “Exercises” — Full Solutions

All questions below are reproduced verbatim from the NCERT textbook’s end-of-chapter Exercises. Answers are original; all numerical problems are solved with complete working and verified.

1. Explain the concept of a production function.

ANSWER A production function expresses the technological relationship between the inputs a firm uses and the output it can produce. For any combination of inputs, it gives the maximum quantity of output that can be produced with a given technology. If a firm uses two factors — labour (L) and capital (K) — the production function is written as q = f(L, K), where q is the maximum output. Because it always takes the maximum output for any input level, the production function deals only with the efficient use of inputs. It is defined for a given technology; if technology improves, we get a new production function.

2. What is the total product of an input?

ANSWER When we vary a single input and keep all other inputs constant, we obtain different levels of output for different levels of that input. This relationship between the variable input and output, holding all other inputs fixed, is called the Total Product (TP) of the variable input (also called total return or total physical product). For any level of employment of the input, the sum of the marginal products of every preceding unit gives the total product at that level.

3. What is the average product of an input?

ANSWER Average Product (AP) is the output produced per unit of the variable input. It is calculated by dividing total product by the quantity of the variable input: APL = TPL ÷ L. The average product at any level of employment is also the average of all the marginal products up to that level.

4. What is the marginal product of an input?

ANSWER Marginal Product (MP) of an input is the change in output per unit change in that input, when all other inputs are held constant: MPL = ΔTPL ÷ ΔL = (TP at L units) − (TP at L − 1 unit). For example, if TP rises from 10 to 24 when labour rises from 1 to 2, the MP of the 2nd unit of labour is (24 − 10) ÷ 1 = 14. MP is undefined at zero input.

5. Explain the relationship between the marginal products and the total product of an input.

ANSWER The total product is the sum of the marginal products of all the units of the variable input employed up to that level. So TP at any level = MP1 + MP2 + … + MPL. As long as MP is positive, TP keeps rising. While MP is rising, TP increases at an increasing rate; when MP starts falling (but is still positive), TP increases at a decreasing rate; when MP becomes zero, TP is maximum; and if MP becomes negative, TP falls.

6. Explain the concepts of the short run and the long run.

ANSWER Short run: a period in which at least one factor of production (say capital) cannot be varied and remains fixed; output can be changed only by varying the other (variable) factor. The fixed factor is the fixed factor and the one that can be changed is the variable factor. Long run: a period in which all factors of production can be varied; there is no fixed factor and the firm can change all inputs simultaneously. The short run and long run are defined by whether all inputs can be varied, not in terms of days, months or years.

7. What is the law of diminishing marginal product?

ANSWER The law of diminishing marginal product states that if we go on increasing the quantity of a variable input while keeping other inputs fixed, the marginal product of that input eventually begins to decline after a certain level of employment. This happens because, as the variable input is increased relative to the fixed input, the factor proportions become less and less suitable for production — the production process becomes ‘too crowded’ with the variable input, so each additional unit adds proportionally less to output.

8. What is the law of variable proportions?

ANSWER The law of variable proportions states that the marginal product of a variable factor first rises with its level of employment and, after reaching a certain level, begins to fall. Hence the MP curve is inverse ‘U’-shaped. It arises because, as one factor is held fixed and the other is increased, the factor proportions change — first becoming more suitable for production (MP rises) and then, after a point, less suitable as the process becomes overcrowded with the variable input (MP falls).

9. When does a production function satisfy constant returns to scale?

ANSWER A production function satisfies constant returns to scale (CRS) when a proportional increase in all inputs results in an increase in output by the same proportion. If all inputs are doubled and output exactly doubles, CRS holds. Formally, with q = f(x1, x2), CRS holds if f(tx1, tx2) = t·f(x1, x2) for t > 1.

10. When does a production function satisfy increasing returns to scale?

ANSWER A production function satisfies increasing returns to scale (IRS) when a proportional increase in all inputs results in an increase in output by a larger proportion. If all inputs are doubled and output more than doubles, IRS holds. Formally, IRS holds if f(tx1, tx2) > t·f(x1, x2) for t > 1.

11. When does a production function satisfy decreasing returns to scale?

ANSWER A production function satisfies decreasing returns to scale (DRS) when a proportional increase in all inputs results in an increase in output by a smaller proportion. If all inputs are doubled and output less than doubles, DRS holds. Formally, DRS holds if f(tx1, tx2) < t·f(x1, x2) for t > 1.

12. Briefly explain the concept of the cost function.

ANSWER A given level of output can usually be produced by more than one combination of inputs. With input prices given, a profit-maximising firm chooses, for every level of output, the least-cost input combination. The cost function therefore describes the least cost of producing each level of output, given the prices of the factors of production and the technology.

13. What are the total fixed cost, total variable cost and total cost of a firm? How are they related?

ANSWER Total Fixed Cost (TFC): the cost a firm incurs to employ the fixed inputs; it remains the same at every level of output (including zero output). Total Variable Cost (TVC): the cost incurred to employ the variable inputs; it is zero at zero output and rises as output increases. Total Cost (TC): the sum of total fixed and total variable cost. Relationship: TC = TVC + TFC. At zero output TC equals TFC; as output rises, TC rises only because TVC rises (since TFC is constant).

14. What are the average fixed cost, average variable cost and average cost of a firm? How are they related?

ANSWER Average Fixed Cost (AFC): fixed cost per unit of output, AFC = TFC ÷ q. Average Variable Cost (AVC): variable cost per unit of output, AVC = TVC ÷ q. Short-run Average Cost (SAC): total cost per unit of output, SAC = TC ÷ q. Relationship: SAC = AVC + AFC, since dividing TC = TVC + TFC by q gives TC/q = TVC/q + TFC/q.

15. Can there be some fixed cost in the long run? If not, why?

ANSWER No, there can be no fixed cost in the long run. By definition, the long run is a period in which all factors of production are variable — there is no fixed factor. Since fixed cost is the cost of employing fixed factors, and no factor is fixed in the long run, there is no fixed cost. Consequently, in the long run total cost and total variable cost coincide.

16. What does the average fixed cost curve look like? Why does it look so?

ANSWER The AFC curve is downward sloping throughout and takes the shape of a rectangular hyperbola. This is because AFC = TFC ÷ q, and TFC is a constant. As output q rises, the same fixed cost is spread over more units, so AFC falls continuously — very large when output is near zero and approaching zero (but never touching the axis) as output becomes very large. Since AFC × q = TFC (a constant) at every point, the curve is a rectangular hyperbola.

17. What do the short run marginal cost, average variable cost and short run average cost curves look like?

ANSWER All three — SMC, AVC and SAC — are ‘U’-shaped curves: they first fall, reach a minimum, and then rise. The SMC curve cuts both the AVC and SAC curves from below at their minimum points. The SAC curve lies above the AVC curve, with the vertical gap between them equal to AFC; since AFC keeps falling, the minimum point of SAC lies to the right of the minimum point of AVC.

18. Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?

ANSWER AVC is the average of all the marginal costs up to a given output. As long as SMC is less than AVC, it pulls the average down, so AVC keeps falling. When SMC is greater than AVC, it pulls the average up, so AVC rises. AVC therefore stops falling and starts rising exactly where SMC equals AVC — the minimum point of AVC. Hence the SMC curve cuts the AVC curve from below at AVC’s minimum.

19. At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.

ANSWER The SMC curve cuts the SAC curve from below at the minimum point of the SAC curve. Reason: SAC falls as long as SMC is less than SAC (the marginal pulls the average down) and rises when SMC is greater than SAC (the marginal pulls the average up). So SAC is at its minimum precisely where SMC = SAC, and there the SMC curve intersects the SAC curve from below.

20. Why is the short run marginal cost curve ‘U’-shaped?

ANSWER SMC is ‘U’-shaped because of the law of variable proportions. Initially, as employment of the variable factor increases, its marginal product rises, so the additional input needed to produce one more unit of output falls — with the factor price given, SMC falls. After a certain point, the marginal product of the factor falls, so producing each extra unit needs more and more of the factor, and SMC rises. Thus SMC first falls and then rises, giving the ‘U’ shape.

21. What do the long run marginal cost and the average cost curves look like?

ANSWER Both LRAC and LRMC are ‘U’-shaped. The LRAC curve falls initially (the firm enjoys increasing returns to scale, so average cost falls), reaches a minimum (constant returns to scale), and then rises (decreasing returns to scale). The LRMC curve also first falls and then rises; it cuts the LRAC curve from below at the minimum point of LRAC. To the left of the minimum, LRMC is below LRAC; to the right, LRMC is above LRAC.

22. The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.L : 0, 1, 2, 3, 4, 5  |  TPL : 0, 15, 35, 50, 40, 48

ANSWER Working: APL = TP ÷ L; MPL = (TP at L) − (TP at L−1). AP: at L=1, 15/1=15; L=2, 35/2=17.5; L=3, 50/3=16.67; L=4, 40/4=10; L=5, 48/5=9.6. MP: at L=1, 15−0=15; L=2, 35−15=20; L=3, 50−35=15; L=4, 40−50=−10; L=5, 48−40=8.
LTPLAPLMPL
00––
1151515
23517.520
35016.6715
44010−10
5489.68
Note: the negative MP at L=4 (TP falls from 50 to 40) and the small rise again at L=5 simply reflect the data in the schedule.

23. The following table gives the average product schedule of labour. Find the total product and marginal product schedules. It is given that the total product is zero at zero level of labour employment.L : 1, 2, 3, 4, 5, 6  |  APL : 2, 3, 4, 4.25, 4, 3.5

ANSWER Working: TP = AP × L; MP = (TP at L) − (TP at L−1), with TP at L=0 equal to 0. TP: L=1, 2×1=2; L=2, 3×2=6; L=3, 4×3=12; L=4, 4.25×4=17; L=5, 4×5=20; L=6, 3.5×6=21. MP: L=1, 2−0=2; L=2, 6−2=4; L=3, 12−6=6; L=4, 17−12=5; L=5, 20−17=3; L=6, 21−20=1.
LAPLTPLMPL
0–0–
1222
2364
34126
44.25175
54203
63.5211

24. The following table gives the marginal product schedule of labour. It is also given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.L : 1, 2, 3, 4, 5, 6  |  MPL : 3, 5, 7, 5, 3, 1

ANSWER Working: TP = sum of MPs up to that level (TP at L=0 is 0); AP = TP ÷ L. TP: L=1, 0+3=3; L=2, 3+5=8; L=3, 8+7=15; L=4, 15+5=20; L=5, 20+3=23; L=6, 23+1=24. AP: L=1, 3/1=3; L=2, 8/2=4; L=3, 15/3=5; L=4, 20/4=5; L=5, 23/5=4.6; L=6, 24/6=4.
LMPLTPLAPL
1333
2584
37155
45205
53234.6
61244

25. The following table shows the total cost schedule of a firm. What is the total fixed cost schedule of this firm? Calculate the TVC, AFC, AVC, SAC and SMC schedules of the firm.Q : 0, 1, 2, 3, 4, 5, 6  |  TC : 10, 30, 45, 55, 70, 90, 120

ANSWER Working: TFC = TC at Q=0 = Rs 10 (same at every output). TVC = TC − TFC; AFC = TFC/Q; AVC = TVC/Q; SAC = TC/Q; SMC = (TC at Q) − (TC at Q−1). Sample (Q=4): TVC = 70−10 = 60; AFC = 10/4 = 2.5; AVC = 60/4 = 15; SAC = 70/4 = 17.5; SMC = 70−55 = 15. (TVC + TFC = 60 + 10 = 70 = TC ✓)
QTCTFCTVCAFCAVCSACSMC
010100––––
130102010203020
2451035517.522.515
35510453.331518.3310
47010602.51517.515
59010802161820
6120101101.6718.332030

26. The following table gives the total cost schedule of a firm. It is also given that the average fixed cost at 4 units of output is Rs 5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output.Q : 1, 2, 3, 4, 5, 6  |  TC : 50, 65, 75, 95, 130, 185

ANSWER Finding TFC: AFC = TFC ÷ Q. At Q=4, AFC = Rs 5, so TFC = AFC × Q = 5 × 4 = Rs 20 (constant for all output). Working: TVC = TC − 20; AFC = 20/Q; AVC = TVC/Q; SAC = TC/Q; SMC = (TC at Q) − (TC at Q−1) [taking TC at Q=0 = TFC = 20, so SMC at Q=1 = 50−20 = 30].
QTCTFCTVCAFCAVCSACSMC
150203020305030
26520451022.532.515
37520556.6718.332510
4952075518.7523.7520
5130201104222635
6185201653.3327.530.8355

27. A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the TVC, TC, AVC and SAC schedules of the firm.Q : 0, 1, 2, 3, 4, 5, 6  |  SMC : –, 500, 300, 200, 300, 500, 800

ANSWER Working: TVC = sum of all SMCs up to that level of output (TVC at Q=0 = 0); TC = TVC + TFC = TVC + 100; AVC = TVC/Q; SAC = TC/Q. TVC: Q=1, 500; Q=2, 500+300=800; Q=3, 800+200=1000; Q=4, 1000+300=1300; Q=5, 1300+500=1800; Q=6, 1800+800=2600.
QSMCTVCTFCTCAVCSAC
0–0100100––
1500500100600500600
2300800100900400450
320010001001100333.33366.67
430013001001400325350
550018001001900360380
680026001002700433.33450

28. Let the production function of a firm be Q = 5 L1/2 K1/2. Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.

ANSWER Working: Q = 5 × L1/2 × K1/2, with L = 100, K = 100. L1/2 = √100 = 10 and K1/2 = √100 = 10. Q = 5 × 10 × 10 = 500 units.

29. Let the production function of a firm be Q = 2 L2 K2. Find out the maximum possible output that the firm can produce with 5 units of L and 2 units of K. What is the maximum possible output that the firm can produce with zero unit of L and 10 units of K?

ANSWER (i) With L = 5, K = 2: Q = 2 × L2 × K2 = 2 × (5)2 × (2)2 = 2 × 25 × 4 = 200 units. (ii) With L = 0, K = 10: Q = 2 × (0)2 × (10)2 = 2 × 0 × 100 = 0 units. Since labour is essential here, output is zero when L = 0 (no production is possible without both inputs being positive).

30. Find out the maximum possible output for a firm with zero unit of L and 10 units of K when its production function is Q = 5 L + 2 K.

ANSWER Working: Q = 5 L + 2 K, with L = 0 and K = 10. Q = (5 × 0) + (2 × 10) = 0 + 20 = 20 units. Here labour and capital are perfect substitutes in a linear (additive) function, so the firm can still produce output using capital alone.

Extra Practice Questions

Short Answer Type Questions

Q1. Define an isoquant.

ANSWERAn isoquant is the set of all possible combinations of two inputs (labour and capital) that yield the same maximum level of output. It is an alternative way of representing the production function and, like an indifference curve, is negatively sloped when marginal products are positive.

Q2. Why is marginal product undefined at zero level of input?

ANSWERMarginal product is the change in output per unit change in the input. To calculate the MP of the first unit we compare it with the ‘previous’ unit, but inputs cannot take negative values and there is no unit before the zeroth one. Hence MP is undefined at zero level of input employment.

Q3. State the relationship between AP and MP.

ANSWERWhen MP > AP, AP rises; when MP < AP, AP falls; and when MP = AP, AP is at its maximum. Therefore the MP curve cuts the AP curve from above at the maximum point of AP. AP is the average of all marginal products up to that level.

Q4. Why is the AFC curve never touching the axes?

ANSWERAFC = TFC/q. As q increases, AFC keeps falling and moves towards zero but never becomes zero (TFC is positive), so it never touches the horizontal axis. As q approaches zero, AFC becomes arbitrarily large, so it never touches the vertical axis. Hence the AFC curve is a rectangular hyperbola that approaches but never meets either axis.

Q5. Distinguish between returns to a factor and returns to scale.

ANSWERReturns to a factor (law of variable proportions) is a short-run concept where only one factor is varied while others are held fixed, so factor proportions change. Returns to scale is a long-run concept where all factors are varied in the same proportion, so factor proportions remain unchanged while the scale of production changes.

Long Answer Type Questions

Q1. Explain the three phases of the law of variable proportions with reference to TP, MP and AP.

ANSWERThe law of variable proportions operates in three phases as the variable factor is increased while the fixed factor is held constant. Phase I (increasing returns): MP rises, AP rises, and TP increases at an increasing rate; factor proportions become more suitable as the fixed factor is more fully used. Phase II (diminishing returns): after a point MP falls (but remains positive) and AP falls, so TP increases at a diminishing rate and reaches its maximum at the end of this phase, when MP becomes zero; the production process becomes increasingly crowded with the variable input. Phase III (negative returns): MP becomes negative and TP actually falls; using more of the variable factor reduces output, so a rational producer never operates here. Production is normally carried on in Phase II, where MP and AP are positive but falling.

Q2. Explain why the SAC curve is ‘U’-shaped and why its minimum lies to the right of the AVC minimum.

ANSWERSAC is the sum of AVC and AFC. Initially both AVC and AFC fall as output rises, so SAC falls steeply. After a certain output, AVC begins to rise (because of the law of variable proportions) while AFC continues to fall. As long as the fall in AFC outweighs the rise in AVC, SAC keeps falling; but beyond a point the rise in AVC outweighs the fall in AFC, and SAC begins to rise. This gives SAC its ‘U’ shape. Because SAC keeps falling for a while even after AVC has started rising (thanks to the continuing fall in AFC), the minimum point of SAC lies to the right of the minimum point of AVC. The vertical gap between SAC and AVC equals AFC and keeps narrowing as output rises.

Q3. Discuss how returns to scale determine the shape of the long-run average cost curve.

ANSWERIn the long run all inputs are variable, so cost behaviour depends on returns to scale. Under increasing returns to scale (IRS), output rises more than proportionately to inputs, so to increase output by a given proportion, inputs (and hence cost) rise by less; LRAC therefore falls. Under constant returns to scale (CRS), inputs and output rise in the same proportion, so cost rises in the same proportion as output and LRAC remains constant (at its minimum). Under decreasing returns to scale (DRS), output rises less than proportionately, so cost rises more than proportionately and LRAC rises. A typical firm experiences IRS first, then CRS, then DRS, so the LRAC curve is ‘U’-shaped — its falling part corresponds to IRS, its minimum to CRS, and its rising part to DRS. The LRMC curve cuts LRAC from below at the minimum of LRAC.

MCQs & Assertion–Reason

1. A production function shows the:

(a) minimum cost of producing output    (b) maximum output obtainable from given inputs    (c) price of inputs    (d) profit of the firm

2. In the short run, a firm can change its output only by varying the:

(a) fixed factor    (b) variable factor    (c) technology    (d) scale of plant

3. Marginal product of labour is calculated as:

(a) TP ÷ L    (b) ΔTP ÷ ΔL    (c) TP × L    (d) AP × L

4. The MP curve cuts the AP curve from above at the point where:

(a) AP is minimum    (b) MP is zero    (c) AP is maximum    (d) MP is maximum

5. According to the law of variable proportions, the marginal product of a variable factor:

(a) keeps rising    (b) keeps falling    (c) first rises and then falls    (d) stays constant

6. If all inputs are doubled and output more than doubles, the production function shows:

(a) constant returns to scale    (b) increasing returns to scale    (c) decreasing returns to scale    (d) diminishing returns

7. Which cost remains the same at all levels of output in the short run?

(a) Total variable cost    (b) Total cost    (c) Average variable cost    (d) Total fixed cost

8. The average fixed cost curve is a:

(a) horizontal straight line    (b) rectangular hyperbola    (c) ‘U’-shaped curve    (d) vertical line

9. The SMC curve cuts the AVC curve from below at the point where AVC is:

(a) maximum    (b) minimum    (c) zero    (d) equal to AFC

10. In the long run, the total cost of a firm equals its:

(a) total fixed cost    (b) total variable cost    (c) average cost    (d) marginal cost

Answer key: 1-(b), 2-(b), 3-(b), 4-(c), 5-(c), 6-(b), 7-(d), 8-(b), 9-(b), 10-(b).

For each Assertion–Reason question, choose: (A) Both true and the Reason correctly explains the Assertion; (B) Both true but the Reason is not the correct explanation; (C) Assertion true, Reason false; (D) Assertion false, Reason true.

A-R 1. Assertion: Total product is the sum of the marginal products of all units employed up to that level.

Reason: Marginal product measures the change in total product when one more unit of the variable input is employed.

A-R 2. Assertion: The average fixed cost curve is downward sloping throughout.

Reason: AFC = TFC ÷ q, and since TFC is constant, AFC falls continuously as output rises.

A-R 3. Assertion: There can be fixed costs in the long run.

Reason: In the long run all factors of production are variable, so there is no fixed factor.

A-R 4. Assertion: The minimum point of the SAC curve lies to the right of the minimum point of the AVC curve.

Reason: After AVC starts rising, AFC continues to fall, so SAC keeps falling for a while.

A-R 5. Assertion: The short-run marginal cost curve is ‘U’-shaped.

Reason: Because of the law of variable proportions, the marginal product of the variable factor first rises and then falls.

Answer key: 1-(A), 2-(A), 3-(D), 4-(A), 5-(A).

Exam Tips & Common Mistakes

How to score full marks in this chapter

For numericals, always show the formula first, then the substitution, then the answer — and present cost/product schedules as neat tables. Remember the two ways to build a schedule: TP = sum of MPs, and TVC = sum of SMCs. Learn the key relationships (MP cuts AP from above at AP’s max; SMC cuts AVC and SAC from below at their minima; SAC’s minimum is to the right of AVC’s). When asked “why” a curve is ‘U’-shaped, link it to the law of variable proportions (short run) or returns to scale (long run). State that fixed cost exists only in the short run, never in the long run.

Common mistakes to avoid

  • Confusing returns to a factor (one input varied, short run) with returns to scale (all inputs varied, long run).
  • Writing MP = TP ÷ L — that is AP; MP = ΔTP ÷ ΔL.
  • Forgetting that TFC is constant, so SMC = ΔTC = ΔTVC in the short run.
  • Calculating AFC, AVC or SAC at zero output — they are undefined there.
  • Saying SAC and AVC reach their minimum at the same output — SAC’s minimum is to the right of AVC’s.
  • Forgetting that √100 = 10 (not 50) when solving Q28, or treating L2K2 as 2LK in Q29.
  • Claiming output is positive at L = 0 for a multiplicative function (Q29) — it is zero; only additive functions (Q30) give positive output with one input zero.

Frequently Asked Questions

What is Chapter 3 of Class 12 Economics (Introductory Microeconomics) about?

Chapter 3, Production and Costs, explains the production function, Total, Average and Marginal Product, the law of variable proportions, returns to scale, and the firm’s short-run and long-run cost structure (TFC, TVC, TC, AFC, AVC, SAC, SMC, LRAC, LRMC), including the shapes of all the product and cost curves.

How do you calculate marginal product and marginal cost?

Marginal product is the change in total product per extra unit of input: MP = ΔTP ÷ ΔL = (TP at L) − (TP at L−1). Marginal cost is the change in total cost per extra unit of output: SMC = ΔTC ÷ Δq = (TC at q) − (TC at q−1). In the short run SMC equals the change in TVC, since TFC is constant.

Why is there no fixed cost in the long run?

The long run is defined as a period in which all factors of production are variable, so there is no fixed factor. Since fixed cost is the cost of employing fixed factors, there can be no fixed cost in the long run; total cost and total variable cost therefore coincide.

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