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← Introductory Microeconomics — all chapters

Class 12EconomicsIntroductory MicroeconomicsChapter 3

Production and Costs

≈ 45 min read · 1 Prelims and 0 Mains questions from this chapter

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Start here: why this chapter matters

In simple wordsA tea stall owner with one stove can hire a second helper and serve many more customers. A fifth helper in the same tiny stall mostly gets in the way. And whatever the number of helpers, the stall's rent is the same. This chapter turns those two ideas — crowding and fixed costs — into the cost curves every firm faces.

This is Chapter 3 of Introductory Microeconomics: 16 pages (36–52) in seven sections — 3.1 the production function; 3.2 short run and long run (with an isoquant box); 3.3 total, average and marginal product; 3.4 the law of variable proportions; 3.5 shapes of the product curves; 3.6 returns to scale (with a Cobb-Douglas box); 3.7 costs, short run and long run — three tables, nine figures and 30 exercise questions, nine of them numerical. Every schedule below is recomputed and every curve drawn from computed points; one NCERT sentence contradicts its own table, and we flag it.

Builds on Chapter 1 (leec201 — scarcity, opportunity cost) and Chapter 2 (leec202 — indifference curves, which isoquants mirror). Leads into Chapter 4 (the firm's supply decision: price = marginal cost, shut-down at minimum AVC) and Chapter 5 (market equilibrium).
Pairs with live chapters: Indian Economic Development keec106 (disguised unemployment — labour with zero marginal product) and keec102/103 (industrial policy, scale); Introductory Macroeconomics leec102 (factor incomes); Class 12 Geography legy207/208 on industry location and scale.
UPSC, honestly: production theory is rarely asked directly. Prelims has used marginal productivity in defining disguised unemployment (2013). The ideas — diminishing returns, economies of scale, fixed versus variable cost — recur in GS3 answers on MSMEs, farm fragmentation, manufacturing and infrastructure.

Word	What it means here
Production function	Maximum output from each combination of inputs, for a given technology
Isoquant	All input combinations giving the same maximum output
Fixed / variable factor	Cannot / can be varied in the short run
Short run / long run	At least one factor fixed / all factors variable
TP, AP, MP	Output from the variable input; output per unit of it; extra output from one more unit
Law of variable proportions	With other inputs fixed, MP of a factor first rises, then falls
Returns to scale	Response of output when all inputs rise in the same proportion: constant, increasing, decreasing
Cost function	Least cost of producing each output, given input prices and technology
TFC, TVC, TC	Cost of fixed inputs; cost of variable inputs; their sum
AFC, AVC, SAC	Each total divided by output; SAC = AVC + AFC
SMC / LRMC	Change in total cost from one more unit of output, short run / long run
LRAC	Long-run cost per unit, when all inputs can be varied

Reading the chapter opening ‘A Firm Effort’ (page 36)The opening lists producers — a tailor (sewing machine, cloth, thread, labour), a farmer (land, labour, tractor, seed, fertiliser, water), a car maker, a rickshaw puller producing rides, a domestic helper producing cleaning services — and states the assumptions: production is instantaneous, production and supply are used interchangeably, and the firm maximises profit = revenue − cost. The point: ‘production’ includes services, and the chapter studies inputs → output → cost as steps towards the profit-maximising output (Chapter 4).

At a glance — the six ideas to carry away

Production function q = f(L, K): maximum output for each input mix, for given technology. Isoquant: equal-output combinations (Table 3.1: q = 10 at (4,1), (2,2), (1,4)).
Short run: at least one factor fixed; long run: all variable — defined by flexibility, not by calendar time.
Table 3.2 (K = 4): TP 10, 24, 40, 50, 56, 57 → MP 10, 14, 16, 10, 6, 1; AP peaks 13.33 at L = 3. Law of variable proportions: MP rises, then falls.
MP and AP are inverse-U; MP cuts AP from above at AP's maximum. TP = sum of MPs.
Returns to scale (all inputs ×t): CRS / IRS / DRS; Cobb-Douglas α + β = 1 / > 1 / < 1.
Costs (Table 3.3): TC = TFC + TVC; AFC a rectangular hyperbola; SMC, AVC, SAC U-shaped; SMC cuts AVC (min at q = 6) and SAC (min at q = 7) from below; LRAC U-shaped from IRS → CRS → DRS.

1. The production function and isoquants

In simple wordsA recipe card that says ‘with this much flour and this many hours in the kitchen, the most rotis you can make is …’ — and lists that number for every combination — is a production function. Better technique (a new recipe) gives a new card.

The production function relates inputs to output: for each quantity of inputs it gives the maximum output. NCERT's farmer example: 2 hours of labour a day on 1 hectare yields at most 2 tonnes of wheat; one possible form is q = K × L (land K in hectares, labour L in hours), and indeed 1 × 2 = 2. Because it shows the maximum, the production function concerns only the efficient use of inputs. It is defined for a given technology; better technology gives a new production function. With two factors, labour and capital, we write q = f(L, K).

Table 3.1, with two isoquants and the capital-4 column highlighted.

In Table 3.1, 1 unit each of labour and capital give at most 1 unit of output; 2 and 2 give 10; 3 labour and 2 capital give 18. Both inputs are necessary — zero of either gives zero output — and output rises with either input. An isoquant (the box on page 38) is the set of input combinations giving the same maximum output — an alternative way of representing the production function, like an indifference curve for a producer. Output 10 comes from (4L, 1K), (2L, 2K) and (1L, 4K). With positive marginal products, using more of one input means less of the other is needed for the same output, so isoquants slope downward; reaching more output means moving to a higher isoquant.

Isoquants for outputs 10, 24 and 50, plotted from Table 3.1.

Reading Table 3.1 and the isoquant box with its figure (pages 37–38)Table 3.1 gives outputs for labour 0–6 (rows) and capital 0–6 (columns); the box's figure shows three isoquants q₁ < q₂ < q₃, with (L₁, K₂) and (L₂, K₁) on q₁ and a move from L₁ to L₃ at fixed K₁ reaching q₂. The point: a table, a set of curves and a formula are three ways to write one production function. We checked the table: it is symmetric (f(L, K) = f(K, L)), and the combinations NCERT names for outputs 10 and 50 are correct.

Beyond NCERT

The slope of an isoquant is the marginal rate of technical substitution (MRTS) — the producer's version of the MRS — equal to MP_L/MP_K. The least-cost combination is where an isoquant touches an isocost line (MRTS = wage/rental), the producer's version of the consumer's optimum.
NCERT's ‘q = K × L’ is only an illustration; the Cobb-Douglas form (section 4) is the usual teaching example.

Exam traps

The production function gives the maximum output (efficiency), not any output.
A change in technology changes the production function itself.
Isoquants slope down only while marginal products are positive.

2. Short run and long run; total, average and marginal product

In simple wordsA wedding caterer can call in extra cooks tonight (variable), but cannot build a bigger kitchen by tonight (fixed). ‘Short run’ is whatever period the kitchen stays the same size — not a fixed number of days.

In the short run at least one factor is fixed and output can be changed only through the variable factor; in the long run all factors can vary. The long run is generally longer, but it differs between processes; NCERT defines the periods by whether all inputs can vary, not in days, months or years. Fixing capital at 4 in Table 3.1 and varying labour gives the total product (TP) of labour — also called total return or total physical product of the variable input. Average product AP_L = TP_L/L. Marginal product MP_L = ΔTP/ΔL = TP at L − TP at L − 1 (e.g. TP rises from 10 to 24 as L goes from 1 to 2, so MP of the 2nd worker = 14). MP is undefined at zero input; TP is the sum of MPs, and AP at any level is the average of the MPs up to it.

Labour	TP (NCERT)	MP (NCERT)	AP (NCERT)	Our check
0	0	–	–	—
1	10	10	10	MP = 10 − 0 = 10; AP = 10/1 = 10
2	24	14	12	MP = 24 − 10 = 14; AP = 24/2 = 12
3	40	16	13.33	MP = 40 − 24 = 16; AP = 40/3 = 13.33
4	50	10	12.5	MP = 50 − 40 = 10; AP = 50/4 = 12.5
5	56	6	11.2	MP = 56 − 50 = 6; AP = 56/5 = 11.2
6	57	1	9.5	MP = 57 − 56 = 1; AP = 57/6 = 9.5

Table 3.2 is correct, and the MPs add up: 10 + 14 + 16 + 10 + 6 + 1 = 57 = TP at 6 workers.

Table 3.2 to scale: TP, MP and AP of labour.

Reading Table 3.2 (page 40)The table lists TP, MP_L and AP_L for labour 0–6 with capital at 4. The point: three views of the same column of Table 3.1. Slip: the text on the same page says that raising labour from 1 to 2 adds 10 units and from 2 to 3 adds 12; the table (and the worked example two paragraphs later) gives 14 and 16. Safe line: use the table — MP of the 2nd worker is 14, of the 3rd 16.

Exam traps

Short run vs long run is about which inputs can vary, not calendar time.
MP is undefined at zero input; TP = sum of MPs.
AP is the average of MPs — so AP and MP of the first unit are equal (10 here).

3. The law of variable proportions and the shapes of TP, MP and AP

In simple wordsOne person alone on four hectares can't keep up — a second and third worker make the land far more productive. By the fifth and sixth, they are stepping on each other's toes. Each extra worker still adds something, but less and less.

TP rises with labour, but not at a constant rate: MP rises up to the 3rd worker (10 → 14 → 16) and then falls (10, 6, 1). The law of variable proportions (or of diminishing marginal product): the MP of a factor initially rises with its employment and, beyond a certain level, falls. The reason is factor proportions — the ratio in which inputs are combined. Holding one factor fixed and adding the other changes the proportion: at first it becomes more suitable and MP rises; after a point the process gets crowded with the variable input. NCERT's farmer with 4 hectares: one worker has too much land; adding workers raises output proportionally more; from the 4th worker the land gets crowded and MP falls.

⤵ Why marginal product first rises and then falls

One input fixed4 hectares (capital) in NCERT's example

Add the variable inputthe factor proportion — labour per hectare — changes

At first, better proportionsMP rises: 10, 14, 16

Then crowdingeach worker has too little land: MP falls 10, 6, 1

Shapes followTP rises at a falling rate; MP and AP are inverse-U

Shapes: the TP curve slopes upward (Fig. 3.1). The MP curve is inverse-U. AP equals MP for the first unit; while MP is above AP, AP rises (more slowly than MP); once MP falls below AP, AP falls — so AP is also inverse-U, and MP cuts AP from above at AP's maximum (Fig. 3.2). In Table 3.2, AP peaks at 13.33 at L = 3; MP is 16 there and then 10, below the next AP of 12.5 — the discrete version of that crossing.

Reading Figures 3.1 and 3.2 (pages 41–42)Fig. 3.1: a rising TP curve, with L units of labour giving at most q₁. Fig. 3.2: inverse-U MP and AP curves, MP crossing AP at P where AP is maximum, at L. The point: average and marginal follow a general rule — the marginal pulls the average towards itself. NCERT's Fig. 3.2 caption calls the curves ‘of factor 1’ and ‘labour’ interchangeably; they are the same input.

Beyond NCERT — history and India

Diminishing returns to land were central to classical economics — Turgot (1760s), then Malthus, West and Ricardo (1815–17), who built his theory of rent on them.
Many textbooks describe three stages: increasing returns (MP rising), diminishing returns (MP falling but positive — the rational stage), and negative returns (MP below zero).
Disguised unemployment: when so many family members work a small plot that the marginal product of some is zero — they could leave without output falling (UPSC 2013; keec106).

Exam traps

Diminishing marginal product does not mean total product falls; TP still rises while MP is positive.
MP cuts AP from above at AP's maximum (contrast: MC cuts AC from below at AC's minimum).
The law needs at least one fixed factor — it is a short-run law.

4. Returns to scale

In simple wordsIf two identical bakeries side by side produce exactly twice what one does, that's constant returns. If one bakery twice the size produces more than twice — because big ovens are more efficient — that's increasing returns. If it produces less than twice — because managing it becomes chaotic — that's decreasing returns.

The law of variable proportions arises because proportions change when one factor is fixed. In the long run all factors can change; a special case is raising them in the same proportion. If output rises by the same proportion, there are constant returns to scale (CRS); by more, increasing returns (IRS); by less, decreasing returns (DRS). Doubling all inputs: output doubles (CRS), more than doubles (IRS), less than doubles (DRS). Formally, for t > 1: f(tx₁, tx₂) = t·f(x₁, x₂) is CRS; > is IRS; < is DRS.

Cobb-Douglas q = x₁^α x₂^β (NCERT's box, page 43)	Result
Scale both inputs by t	q₁ = (tx₁)^α (tx₂)^β = t^(α+β) · q₀
α + β = 1	q₁ = t·q₀ → CRS
α + β > 1	q₁ > t·q₀ → IRS
α + β < 1	q₁ < t·q₀ → DRS
Doubling inputs (t = 2), our numbers	α+β = 0.5: ×1.41 · α+β = 1: ×2 · α+β = 1.5: ×2.83

Returns to scale: Cobb-Douglas exponents, and the pattern hidden in Table 3.1.

Beyond NCERT — sources of scale economies, and a check on Table 3.1

Table 3.1 itself shows IRS then CRS: doubling (1,1) to (2,2) raises output from 1 to 10 (×10); (2,2) to (4,4) from 10 to 50 (×5); (3,3) to (6,6) from 30 to 60 (exactly ×2).
The Cobb-Douglas form is named after Charles Cobb and Paul Douglas (1928), who fitted it to US manufacturing data.
Sources of IRS often cited: specialisation and division of labour (Adam Smith's pin factory, 1776), indivisible machines, bulk buying; sources of DRS: coordination and management problems as a firm grows.

Exam traps

Returns to scale (all inputs varied, long run) ≠ law of variable proportions (one input varied, short run).
Cobb-Douglas returns depend on α + β, not on α or β alone.
A production function can show IRS at small scale and CRS or DRS at large scale — as Table 3.1 does.

5. Short-run costs

In simple wordsA coaching centre pays rent of ₹20,000 a month whether it has 10 students or 100 — that's fixed. Each extra student needs more printed notes and teacher hours — that's variable. Spread the rent over more students and the rent per student keeps falling.

A given output can usually be produced in several ways — output 50 in Table 3.1 by (L = 6, K = 3), (4, 4) or (3, 6). At given input prices the firm picks the least expensive; the cost function gives the least cost of each output, given input prices and technology. In the short run, the cost of fixed inputs is total fixed cost (TFC), the same at every output; the cost of variable inputs is total variable cost (TVC), rising with output; TC = TVC + TFC. Per unit: SAC = TC/q, AVC = TVC/q, AFC = TFC/q, and SAC = AVC + AFC. SMC = ΔTC/Δq; since TFC does not change, SMC is the change in TVC. SMC is undefined at zero output; TVC is the sum of SMCs (the area under the SMC curve), and AVC is the average of the SMCs up to that output.

q	TFC	TVC	TC	AFC	AVC	SAC	SMC
0	20	0	20	–	–	–	–
1	20	10	30	20	10	30	10
2	20	18	38	10	9	19	8
3	20	24	44	6.67	8	14.67	6
4	20	29	49	5	7.25	12.25	5
5	20	33	53	4	6.6	10.6	4
6	20	39	59	3.33	6.5	9.83	6
7	20	47	67	2.86	6.71	9.57	8
8	20	60	80	2.5	7.5	10	13
9	20	75	95	2.22	8.33	10.56	15
10	20	95	115	2	9.5	11.5	20

Our recomputation matches Table 3.3 except for rounding: NCERT prints SAC at q = 9 as 10.55 (95/9 = 10.556, so 10.56 rounded) and AVC at q = 7 as 6.7 (47/7 = 6.71). The SMCs add up: 10 + 8 + 6 + 5 + 4 + 6 + 8 + 13 + 15 + 20 = 95 = TVC at q = 10. NCERT's worked example: SMC at q = 5 = 53 − 49 = 4.

Table 3.3 to scale: TFC, TVC and TC.

AFC from Table 3.3's TFC: a rectangular hyperbola.

Shapes. TFC is a horizontal line; TVC and TC rise, TC lying TFC above TVC. AFC falls as output rises — very large near zero output, approaching zero as output grows — and is a rectangular hyperbola: q × AFC is always TFC (the area of the rectangle under it). SMC is U-shaped: by the law of variable proportions, the variable input needed per extra unit of output first falls and then rises, so with given input prices marginal cost first falls then rises. AVC starts equal to SMC, falls while SMC is below it, and rises once SMC exceeds it — so it is U-shaped and SMC cuts AVC from below at AVC's minimum. SAC = AVC + AFC: it falls while both fall, keeps falling while AFC's fall outweighs AVC's rise, then rises — U-shaped, above AVC by AFC, with its minimum to the right of AVC's, where SMC cuts it from below.

Table 3.3 to scale: AFC, AVC, SAC and SMC with their minima.

⤵ From the law of variable proportions to a U-shaped marginal cost

MP of the variable input risesfewer extra workers needed per extra unit of output

SMC fallswith the wage given, each extra unit costs less (Table 3.3: 10, 8, 6, 5, 4)

MP fallsmore extra workers needed per extra unit

SMC rises6, 8, 13, 15, 20 — the U shape

Averages followAVC and SAC U-shaped; SMC cuts both at their minima from below

Reading Table 3.3 and Figures 3.3–3.8 (pages 45–48)Table 3.3 gives TFC (₹20), TVC, TC, AFC, AVC, SAC and SMC for outputs 0–10. Fig. 3.3: TFC flat at c₁, TVC and TC rising (at q₁, TVC = c₂, TC = c₃). Fig. 3.4: AFC hyperbola with the rectangle OFCq₁ = TFC. Fig. 3.5: AFC as the slope (tan θ) of a ray from the origin to the TFC line. Fig. 3.6: AVC with rectangle OVBq₀ = TVC. Fig. 3.7: AVC as tan θ of a ray to the TVC curve. Fig. 3.8: SMC cutting AVC at its minimum P (q₁) and SAC at its minimum S (q₂), q₂ to the right of q₁. The point: averages are slopes of rays and heights of rectangles; marginals are slopes of the total curve. In the table, AVC is lowest at q = 6 and SAC at q = 7, matching Fig. 3.8's ordering. Minor typos: ‘Otput’ in Fig. 3.3; ‘continuous to fall’ for ‘continues’.

NCERT details to read carefully

SMC cuts AVC and SAC from below at their minimum points; AVC's minimum comes at a lower output than SAC's.
SMC depends only on variable cost — fixed cost does not affect it.
The AFC curve never touches the axis; TFC = AFC × q is constant.
Rounding: SAC at q = 9 is 10.56, not 10.55.

6. Long-run costs

In simple wordsOver a few years a growing bakery can move to a bigger building, buy bigger ovens and reorganise everything. Up to a point, each loaf gets cheaper; beyond it, the business gets unwieldy and costs per loaf creep up again.

In the long run all inputs vary, so there are no fixed costs: total cost and total variable cost coincide. LRAC = TC/q; LRMC = TC at q − TC at q − 1; the sum of LRMCs up to an output is the total cost. The shape of LRAC comes from returns to scale: under IRS, doubling output needs less than double the inputs, so cost less than doubles and average cost falls; under DRS average cost rises; under CRS it is constant. A typical firm is argued to have IRS at first, then CRS, then DRS — so LRAC is U-shaped, with CRS at its minimum. LRMC equals LRAC for the first unit, lies below it while LRAC falls and above it while it rises, so LRMC is U-shaped and cuts LRAC from below at its minimum.

Long-run costs, using an illustrative function to show NCERT's shapes.

⤵ From returns to scale to the shape of LRAC

Increasing returns to scaleinputs (and cost) rise less than output: LRAC falls

Constant returnsinputs and cost rise in proportion: LRAC at its minimum, flat

Decreasing returnsinputs and cost rise faster than output: LRAC rises

U-shaped LRACLRMC cuts it from below at the minimum (Fig. 3.9)

Reading Figure 3.9 (page 49)U-shaped LRAC and LRMC curves, LRMC cutting LRAC at its minimum M at output q₁. The point: in the long run the U shape comes from returns to scale, not from fixed factors.

Beyond NCERT — the envelope and the evidence

LRAC is often drawn as the envelope of many short-run average cost curves, one for each plant size (Jacob Viner, 1931).
Many empirical studies find LRAC L-shaped — falling, then flat over a wide range — rather than clearly rising; the rising part is debated. Present both: the textbook U and the empirical L.
The minimum efficient scale is the smallest output at which LRAC reaches its minimum; it matters for debates on the size of Indian manufacturing firms (keec103).

Exam traps

Long run: no fixed cost (Exercise 15).
The SAC's U shape comes from variable proportions; the LRAC's from returns to scale.
At the minimum of LRAC, CRS holds and LRMC = LRAC.

NCERT's in-text questions — short answers

Isoquant box (page 38): Can you identify the sets of inputs that lie on the isoquant q = 50?

From Table 3.1: (L = 3, K = 6), (4, 4) and (6, 3) — the same three combinations NCERT later lists in section 3.7.

Page 45: Plot the data in Table 3.3 with output on the x-axis and costs on the y-axis.

See the diagrams in section 5: TFC flat at 20; TVC 0 → 95 and TC 20 → 115; AFC falling 20 → 2; AVC minimum 6.5 at q = 6; SAC minimum 9.57 at q = 7; SMC 10, 8, 6, 5, 4, 6, 8, 13, 15, 20.

Page 46: Check that the sum of marginal costs up to an output equals TVC at that output.

At q = 5: 10 + 8 + 6 + 5 + 4 = 33 = TVC; at q = 10: the ten SMCs sum to 95 = TVC. It works at every output.

NCERT exercise — answer outlines

Questions 1–21 are conceptual; 22–30 numerical. Every numerical answer is recomputed. Try first, then open.

1–4. Production function; total product; average product; marginal product of an input.

Production function: maximum output from each input combination, given technology, q = f(L, K). TP: output as one input varies, others fixed. AP = TP/L. MP = ΔTP/ΔL (TP at L − TP at L − 1); undefined at zero input. Use Table 3.2.

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

TP at any level = sum of the MPs of all units up to it (10 + 14 + 16 + 10 + 6 + 1 = 57). TP rises while MP > 0, at an increasing rate while MP rises and a decreasing rate once MP falls; TP would be maximum where MP = 0 and fall if MP turned negative (Beyond NCERT).

6. Short run and long run.

Short run: at least one factor fixed; output varies only through variable factors. Long run: all factors variable; no fixed factor. Defined by flexibility, not calendar time, and differ across processes.

7–8. Law of diminishing marginal product; law of variable proportions.

With other inputs fixed, the MP of a factor initially rises and, beyond a level of employment, falls (NCERT treats the two names as one law). Reason: factor proportions first improve, then the fixed factor gets crowded (the 4-hectare farmer). Table 3.2: MP 10, 14, 16, then 10, 6, 1.

9–11. When does a production function show constant, increasing or decreasing returns to scale?

When all inputs rise by the same proportion t: output rises by t (CRS: f(tx₁, tx₂) = t·f), by more (IRS: >), by less (DRS: <). Cobb-Douglas: α + β = 1, > 1, < 1.

12. The cost function.

The least cost of producing each level of output, given input prices and technology; the firm picks the cheapest of the input combinations that can produce the output (e.g. three ways to make 50 in Table 3.1).

13–14. TFC, TVC, TC and AFC, AVC, SAC — how related?

TC = TFC + TVC; SAC = AFC + AVC, where each average = total ÷ q. TFC constant; TVC and TC rise with output and differ by TFC. Example from Table 3.3 at q = 4: TC 49 = 20 + 29; SAC 12.25 = 5 + 7.25.

15. Can there be fixed cost in the long run?

No: in the long run all inputs can be varied, so every cost is variable; TC = TVC.

16. What does the AFC curve look like, and why?

A downward-sloping rectangular hyperbola: AFC = TFC/q, so AFC × q = TFC is constant; large near zero output, approaching (never reaching) zero as output grows.

17. Shapes of SMC, AVC and SAC.

All U-shaped. SMC falls then rises (variable proportions); AVC and SAC fall while SMC is below them and rise once it is above; SAC lies above AVC by AFC, its minimum to the right of AVC's; SMC cuts both from below at their minima.

18–19. Why does SMC cut AVC at AVC's minimum? Where does SMC cut SAC?

If SMC < AVC the next unit pulls the average down; if SMC > AVC it pulls it up; so AVC stops falling exactly where SMC = AVC — its minimum. The same logic: SMC cuts SAC at SAC's minimum, from below. Table 3.3: SMC 6 < AVC 6.5 at q = 6, then 8 > 6.71.

20. Why is the SMC curve U-shaped?

Because of the law of variable proportions: while MP of the variable input rises, each extra unit of output needs less of it, so SMC falls; once MP falls, each extra unit needs more, so SMC rises (input price given).

21. Shapes of LRMC and LRAC.

Both U-shaped: LRAC falls under IRS, is flat at its minimum under CRS, rises under DRS; LRMC lies below LRAC while it falls and above while it rises, cutting it from below at its minimum.

22. TP of labour: L = 0, 1, 2, 3, 4, 5 → TP = 0, 15, 35, 50, 40, 48. Find AP and MP.

MP: 15, 20, 15, −10, +8. AP: 15, 17.5, 16.67, 10, 9.6. Note: this schedule is unusual — TP falls at L = 4 and rises again at L = 5, which a normal production function (with free disposal of labour) would not show; compute it as given.

23. AP of labour: L = 1…6 → AP = 2, 3, 4, 4.25, 4, 3.5 (TP = 0 at L = 0). Find TP and MP.

TP = AP × L: 2, 6, 12, 17, 20, 21. MP: 2, 4, 6, 5, 3, 1.

24. MP of labour: L = 1…6 → MP = 3, 5, 7, 5, 3, 1 (TP = 0 at L = 0). Find TP and AP.

TP (running sum): 3, 8, 15, 20, 23, 24. AP: 3, 4, 5, 5, 4.6, 4.

25. TC: q = 0…6 → 10, 30, 45, 55, 70, 90, 120. Find TFC and the TVC, AFC, AVC, SAC, SMC schedules.

TFC = TC at q = 0 = 10. TVC: 0, 20, 35, 45, 60, 80, 110. AFC: 10, 5, 3.33, 2.5, 2, 1.67. AVC: 20, 17.5, 15, 15, 16, 18.33. SAC: 30, 22.5, 18.33, 17.5, 18, 20. SMC: 20, 15, 10, 15, 20, 30.

26. TC: q = 1…6 → 50, 65, 75, 95, 130, 185; AFC at q = 4 is ₹5. Find TVC, TFC, AVC, AFC, SAC, SMC.

TFC = 5 × 4 = 20. TVC: 30, 45, 55, 75, 110, 165. AFC: 20, 10, 6.67, 5, 4, 3.33. AVC: 30, 22.5, 18.33, 18.75, 22, 27.5. SAC: 50, 32.5, 25, 23.75, 26, 30.83. SMC: 30 (= 50 − 20), 15, 10, 20, 35, 55.

27. SMC: q = 1…6 → 500, 300, 200, 300, 500, 800; TFC = ₹100. Find TVC, TC, AVC, SAC.

TVC (running sum): 500, 800, 1000, 1300, 1800, 2600. TC: 600, 900, 1100, 1400, 1900, 2700. AVC: 500, 400, 333.33, 325, 360, 433.33. SAC: 600, 450, 366.67, 350, 380, 450.

28. Q = 5 L^(1/2) K^(1/2). Maximum output with L = 100, K = 100?

5 × 10 × 10 = 500. (α + β = 1: constant returns to scale.)

29. Q = 2L²K². Maximum output with L = 5, K = 2? With L = 0, K = 10?

2 × 25 × 4 = 200. With L = 0: 0 — both inputs are essential in a multiplicative form. (α + β = 4: IRS.)

30. Q = 5L + 2K. Maximum output with L = 0, K = 10?

5 × 0 + 2 × 10 = 20 — inputs are perfect substitutes here, so output is possible with zero labour.

⤵ Answer frame for cost and product numericals

Find the fixed partTFC = TC at q = 0, or AFC × q

Build totalsTVC = TC − TFC; TP = AP × L or a running sum of MPs

Build averagesdivide totals by q (or L)

Build marginalsdifference between successive totals

Checksum of marginals = total; marginal cuts the average at its turning point

What to remember

Numbers

NCERT's farmer2 hours of labour × 1 hectare → 2 tonnes (q = K × L)

Table 3.1: output 10(L,K) = (4,1), (2,2), (1,4)

Table 3.1: output 50(6,3), (4,4), (3,6)

Table 3.2 TP (K = 4)10, 24, 40, 50, 56, 57

Table 3.2 MP / AP10, 14, 16, 10, 6, 1 / 10, 12, 13.33, 12.5, 11.2, 9.5

MP and AP peaksboth at L = 3 (16 and 13.33)

Cobb-Douglas returnsα + β = 1 CRS; > 1 IRS; < 1 DRS

Table 3.3 TFC₹20 at every output

Table 3.3 TVC0, 10, 18, 24, 29, 33, 39, 47, 60, 75, 95

Table 3.3 SMC10, 8, 6, 5, 4, 6, 8, 13, 15, 20 (sum 95)

Minimum AVC / SAC6.5 at q = 6 / 9.57 at q = 7

NCERT's SMC exampleq = 5: 53 − 49 = 4

Exercises 28 / 29 / 30500 / 200 and 0 / 20

Cobb–Douglas / Viner †1928 / 1931

Ricardo on diminishing returns †1815–17

One-liners

The production function gives the maximum output — efficiency is built in.
Short run: something is fixed. Long run: nothing is.
TP is the sum of MPs; AP is their average.
MP rises then falls because factor proportions first improve, then crowd.
MP cuts AP from above at AP's peak; MC cuts AC from below at AC's bottom.
Returns to scale scale all inputs; variable proportions vary one.
TC = TFC + TVC; SAC = AFC + AVC.
AFC is a rectangular hyperbola — fixed cost spread thinner.
SMC is U-shaped because MP is inverse-U.
AVC bottoms out before SAC.
LRAC is U-shaped because of IRS, then CRS, then DRS.

Traps to avoid

NCERT's text says MP rises by 10 then 12; its own Table 3.2 gives 14 and 16 — use the table.
Diminishing marginal product does not mean total product falls.
Short run/long run is not a calendar distinction.
Returns to scale ≠ law of variable proportions.
SMC is unaffected by fixed cost.
There is no fixed cost in the long run.
SMC cuts AVC and SAC from below at their minima; MP cuts AP from above at its maximum.
Table 3.3's SAC at q = 9 is 10.56 when rounded (NCERT 10.55).
In Exercise 22 TP falls then rises — compute as given, but it is not a normal schedule.

How to strategise

Prelims — what UPSC asks

Marginal product underlies the definition of disguised unemployment: workers whose marginal productivity is zero (2013; shared with keec106).
Expect statement questions on: MP–AP and MC–AC crossing rules; why AFC is a rectangular hyperbola; short run vs long run; returns to scale vs diminishing returns; economies of scale and LRAC.

Mains — where it appears and how to answer

Rarely asked directly. Use the tools in GS3: diminishing returns on small, fragmented farms and disguised unemployment; economies of scale in manufacturing and MSME growth; high fixed costs (and falling AFC) in infrastructure, power and telecom, which favour large networks.
Where scale or firm-size policy is discussed, present attributed views side by side (e.g. scale economies versus the employment and competition benefits of small firms) without present-day political commentary.

Self-check

Tap an option. NCERT's own exercise questions come first; the rest test the figures and common confusions.

1. From Table 3.2, the marginal product of the 3rd worker is:

2. The law of variable proportions applies when:

3. If q = x₁^0.6 x₂^0.6, doubling both inputs multiplies output by about:

4. The average fixed cost curve is:

5. The short-run marginal cost curve cuts the AVC curve:

6. In Table 3.3 (TFC = ₹20), the SMC of the 5th unit is:

7. The LRAC curve is U-shaped because:

UPSC questions from this chapter

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Prelims

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