Production and Costs Class 12 Notes

Q: Q10 A firm has total fixed cost of ₹50. Its total variable cost is ₹90 for 3 units of output and ₹120 for 4 units. Calculate, for 4 units, the AVC, SAC and SMC.

For 4 units AVC is ₹30, SAC is ₹42.50 and SMC is ₹30. Given: TFC = 50; TVC(3) = 90; TVC(4) = 120. Formula: AVC = TVC÷q; SAC = (TFC + TVC)÷q; SMC = TC(4) − TC(3). Steps: AVC = 120÷4 = 30. TC(4) = 170, so SAC = 170÷4 = 42.5. TC(3) = 140, so SMC = 170 − 140 = 30. Final answer: AVC = ₹30; SAC = ₹42.50; SMC = ₹30.

Key takeaways

The production function gives maximum output for each input combination; the short run has a fixed input, the long run does not.
TP is the sum of MPs; AP is their average. MP and AP are inverted-U shaped and MP cuts AP at its maximum.
Raising all inputs together gives constant, increasing or decreasing returns to scale.
TC = TFC + TVC, and SAC = AVC + AFC; SMC, AVC and SAC are U-shaped with SMC cutting AVC and SAC at their minima.
LRAC is U-shaped because returns to scale go from increasing to constant to decreasing.

This page is part of the Introductory Microeconomics chapter list for Class 12 Economics. It follows consumer behaviour and moves to the producer.

3.1Production Function

A production function gives the maximum output a firm can produce from each combination of inputs, using the most efficient available technology. It assumes inputs are used efficiently, so wasteful use is ignored. Better technology gives a new production function that yields more output from the same inputs. An isoquant joins input combinations giving equal output.

A firm combines inputs, also called factors of production, such as labour, machines, land and raw materials, to make output. Take a shoe-maker with two workers, two machines and 10 kg of leather. If each worker uses the machine she is good at, they might make 10 pairs; if they swap machines, perhaps only 8. The production function records only the efficient figure, 10, because it shows the maximum output for a given set of inputs.

Production function (two inputs)q = f(x₁, x₂) · q is the maximum output from x₁ units of factor 1 and x₂ units of factor 2

A production function is defined for a given state of technology. If an improvement lets the same inputs yield more output, we have a new, higher production function.

An isoquant is to production what an indifference curve is to consumption. It is the set of all input combinations that give the same maximum output. Isoquants slope downward, because if one input rises the other can fall while output stays the same, and isoquants further from the origin show higher output.

3.2The Short Run and the Long Run

In the short run at least one input cannot be changed, so it is the fixed input, and the firm varies output only through the variable input. In the long run every input can be varied and nothing is fixed. The two are separated by whether inputs can be changed, not by any fixed number of days or years.

A bakery that has signed a lease on its oven cannot change its oven size at short notice, but it can hire more helpers. In the short run the oven is a fixed input and labour is the variable input. Over a longer period it can move to a bigger shop and buy more ovens, so in the long run all inputs are variable.

The lengths of the short and long run differ between industries. A street vendor can double her stock in a day, while a power plant may take years. For this reason we define the two periods by whether all inputs can be varied, never by calendar time.

3.3Total Product, Average Product and Marginal Product

Keeping other inputs fixed, total product is the output obtainable from different amounts of one variable input. Average product is output per unit of that input, and marginal product is the addition to output from one more unit. Total product equals the sum of marginal products, and average product is their average.

Product concepts for the variable input x₁TP = f(x₁; x₂ fixed) · AP = TP ÷ x₁ · MP = ΔTP ÷ Δx₁ = TP(x₁) − TP(x₁ − 1)

Marginal products are additions to total product, so the sum of the MPs of every unit up to a given level equals TP at that level. Average product at any level is therefore the average of all marginal products up to it. AP and MP are also called the average and marginal returns to the variable input. MP is not defined at zero input.

Product schedule with a fixed second input (worked illustration)
Units of input	Total product	Marginal product	Average product
1	8	8	8
2	20	12	10
3	36	16	12
4	48	12	12
5	55	7	11
6	58	3	9.67

3.4The Law of Diminishing Marginal Product and the Law of Variable Proportions

As a firm keeps raising one input with the others fixed, the marginal product of that input eventually falls. This is the law of diminishing marginal product. The law of variable proportions adds that marginal product first rises, because factor proportions improve, and falls only after a certain point, when the process becomes crowded with the variable input.

Think of one extra helper in a small kitchen. The first few helpers let the cook specialise, so each adds more than the last. But once the kitchen is crowded, the next helper has no space or tools to work with, and adds less. The factor proportions have changed: at first they become more suitable for production, then less. In the schedule above, marginal product rises up to 3 units of the input and then falls.

3.5Shapes of Total Product, Marginal Product and Average Product Curves

The total product curve rises as the variable input increases. Because of the law of variable proportions, marginal product rises and then falls, so its curve is an inverted U. Average product is also an inverted U. Marginal product cuts average product from above at the maximum point of average product.

When MP is above AP, adding another unit pulls the average up. When MP is below AP, the average is pulled down. So AP is rising whenever MP > AP, falling whenever MP < AP, and at its peak MP = AP. This is the same reasoning you use for a cumulative average of test scores.

Figure 3.1: Average and marginal productData from the product schedule. MP climbs to 16 at the third unit and then falls. AP rises while MP is above it and falls once MP drops below it, so MP crosses AP at AP's maximum.

3.6Returns to Scale

Returns to scale describe what happens to output when all inputs are increased in the same proportion. If output rises by the same proportion, returns are constant. If it rises by more, returns are increasing, and if by less, decreasing. This is a long-run concept, since it needs every input to vary.

Types of returns to scale (inputs multiplied by t > 1)
Type	Condition	If inputs double
Constant (CRS)	f(tx₁, tx₂) = t · f(x₁, x₂)	Output exactly doubles
Increasing (IRS)	f(tx₁, tx₂) > t · f(x₁, x₂)	Output more than doubles
Decreasing (DRS)	f(tx₁, tx₂) < t · f(x₁, x₂)	Output less than doubles

For a Cobb–Douglas function q = x₁^αx₂^β, returns are constant if α + β = 1, increasing if α + β > 1, and decreasing if it is less than 1, because multiplying both inputs by t multiplies output by t^α+β.

3.7Costs

A firm minimises cost by choosing the cheapest input combination for each output level; the resulting output-cost relation is the cost function. In the short run, total cost is fixed cost plus variable cost. Average and marginal costs are derived from it. In the long run all inputs are variable, so total cost equals total variable cost.

The same output can usually be made with different input mixes, and with input prices given, the firm chooses the least costly one. For every output level, this gives the lowest possible cost: the cost function.

Short run costs

Short-run cost conceptsTC = TFC + TVC · AFC = TFC ÷ q · AVC = TVC ÷ q · SAC = TC ÷ q = AFC + AVC · SMC = ΔTC ÷ Δq = TC(q) − TC(q − 1)

Total fixed cost (TFC) is spent on the fixed inputs and is the same at every output level. Total variable cost (TVC) is spent on the variable inputs and rises with output. Since fixed cost does not change, marginal cost in the short run comes entirely from the change in variable cost, and the sum of marginal costs up to q equals TVC. AVC is the average of marginal costs up to that point.

Illustrative cost schedule (TFC = ₹100)
Output	TVC	TC	AFC	AVC	SAC	SMC
1	60	160	100	60	160	60
2	100	200	50	50	100	40
3	130	230	33.3	43.3	76.7	30
4	170	270	25	42.5	67.5	40
5	230	330	20	46	66	60
6	300	400	16.7	50	66.7	70

Shapes of the short run cost curves

TFC is a horizontal line. TVC and TC rise with output, and TC lies above TVC by exactly the fixed cost.
AFC falls steadily as the same fixed cost is spread over more units; the curve is a rectangular hyperbola (AFC × q = TFC always).
SMC is U-shaped. At first marginal product rises, so each unit needs less of the variable input and marginal cost falls. After the law of variable proportions sets in, marginal cost rises.
AVC is U-shaped too. It starts at the same value as SMC, falls while SMC is below it and rises once SMC is above it, so SMC cuts AVC from below at AVC's minimum.
SAC = AVC + AFC is U-shaped, lies above AVC by the amount of AFC, and reaches its minimum to the right of AVC's minimum. SMC cuts it from below at its minimum.

Figure 3.2: Short-run cost curvesUsing the schedule above. SMC (red) falls to 30 and then rises; it cuts AVC (teal) near its minimum between 4 and 5 units, and SAC (purple) near its minimum between 5 and 6 units. AFC (dashed) falls throughout.

Long run costs

In the long run there are no fixed costs, so total cost equals total variable cost, and LRAC = TC ÷ q. Long-run marginal cost (LRMC) is the change in total cost for one more unit of output. The shape of LRAC follows returns to scale. Under increasing returns, inputs rise by less than output, so average cost falls; under constant returns it stays level; under decreasing returns it rises. Typically a firm shows increasing, then constant, then decreasing returns, so LRAC is U-shaped, and LRMC cuts it from below at its minimum.

Figure 3.3: Long-run average and marginal costIllustrative curves: LRAC = 0.5(q − 6)² + 10, with minimum ₹10 at 6 units, and LRMC = 1.5q² − 12q + 28, which cuts LRAC at that minimum.

Worked Examples

Example 1: Marginal and average product

Given: With the other input fixed, total product for 1, 2, 3, 4 and 5 units of labour is 8, 20, 36, 48 and 55.
Formula: MP = TP(L) − TP(L − 1); AP = TP ÷ L
Steps: MP: 8, 12, 16, 12, 7. AP: 8, 10, 12, 12, 11. MP is above AP up to the third unit, where AP rises; at the fourth unit MP = AP = 12, which is AP's maximum; after that MP is below AP and AP falls.
Answer: AP peaks at 12 units of output per unit of labour, between 3 and 4 units of labour, and MP crosses AP exactly there.

Example 2: Short-run costs

Given: TFC = ₹100. TVC for 3, 4 and 5 units of output is ₹130, ₹170 and ₹230.
Formula: TC = TFC + TVC; AVC = TVC ÷ q; SAC = TC ÷ q; SMC = TC(q) − TC(q − 1)
Steps: TC at 3, 4, 5: 230, 270, 330. At q = 4: AVC = 170 ÷ 4 = 42.5; SAC = 270 ÷ 4 = 67.5; AFC = 100 ÷ 4 = 25 (42.5 + 25 = 67.5 ✓). SMC at 4 = 270 − 230 = 40; SMC at 5 = 330 − 270 = 60.
Answer: At 4 units: AVC = ₹42.5, SAC = ₹67.5, SMC = ₹40.

Example 3: Identifying returns to scale

Given: Three Cobb–Douglas functions: (a) q = x₁^0.5x₂^0.5; (b) q = x₁^0.6x₂^0.6; (c) q = x₁^0.3x₂^0.4. Both inputs double.
Formula: Output is multiplied by 2^α+β
Steps: (a) 2^1.0 = 2. (b) 2^1.2 ≈ 2.30. (c) 2^0.7 ≈ 1.62.
Answer: (a) constant, (b) increasing, (c) decreasing returns to scale.

Common Mistakes

Believing marginal product always falls. It rises first and then falls, as the law of variable proportions says.
Thinking fixed cost changes with output in the short run. TFC is the same at every level; AFC falls because it is spread over more units.
Saying SMC cuts AVC from above. It cuts from below, at AVC's minimum.
Defining the short run as less than a year. It is defined by whether at least one input is fixed.
Treating diminishing returns and diminishing returns to scale as the same. The first varies one input; the second varies all inputs together.

10 Important Questions for Class 12 Board and School Examinations

Questions are written in original words. Marks are shown beside each question.

Q1When marginal product is greater than average product, average product: (A) falls (B) rises (C) is constant (D) is zero 1 mark · MCQ

(B) Rises.

A marginal unit above the average pulls the average up.

Q2Assertion (A): SMC cuts the AVC curve from below at the minimum of AVC. Reason (R): AVC falls when SMC is below it and rises when SMC is above it. Choose: (a) both true, R explains A; (b) both true, R does not explain A; (c) A true, R false; (d) A false, R true. 1 mark · Assertion-reason

(a) Both are true and R correctly explains A.

Where SMC crosses AVC, the average changes from falling to rising, which is its minimum.

Q3Distinguish between the short run and the long run in production. 3 marks

In the short run at least one input is fixed; in the long run all inputs can be varied.

Short run: some inputs fixed, others variable.
Long run: no fixed inputs.
Neither is defined by calendar time.

Example: a bakery can hire more helpers at once but needs time to install a larger oven.

A firm’s decisions in the short run are about how many variable inputs to use, and in the long run about the scale of production.

Q4State the relationship between total product, marginal product and average product. 3 marks

Total product is the sum of marginal products, and average product is the average of marginal products.

TP up to a level = MP of each unit added up.
AP = TP ÷ units of the input.
MP cuts AP from above at AP's maximum.

Example: MPs of 8, 12 and 16 give TP = 36 and AP = 12 at 3 units.

Q5Why does the average fixed cost curve slope downward throughout? 3 marks

AFC falls because total fixed cost stays constant while output increases.

AFC = TFC ÷ q.
TFC does not change with output.
A larger q divides the same TFC among more units, so AFC falls and approaches zero.

Example: ₹100 over 4 units is ₹25; over 5 units, ₹20.

Thus the average fixed cost curve is a rectangular hyperbola, approaching the horizontal axis but never touching it.

Q6Explain the law of variable proportions. 4 marks

The law says that the marginal product of a variable input first rises and, beyond a point, falls.

Setting: one input is raised while others are fixed.
Early stage: factor proportions become more suitable, so MP rises.
Later stage: the process becomes crowded with the variable input, so MP falls.
Curve: MP is an inverted U.

Example: extra helpers first speed up a small kitchen, then get in each other's way.

The law explains the U-shape of the short-run marginal cost curve and applies only when some input is fixed.

Q7Explain constant, increasing and decreasing returns to scale with an example. 4 marks

Returns to scale compare the change in output with the proportionate change in all inputs.

Constant: output rises in the same proportion.
Increasing: output rises by a larger proportion.
Decreasing: output rises by a smaller proportion.
Cobb–Douglas: returns depend on whether α + β is equal to, greater than or less than 1.

Example: doubling both inputs raises output to 2.3 times when α + β = 1.2.

Returns to scale occur only in the long run, when all inputs change together. A firm that doubles machines and labour may find that coordination problems keep output from doubling.

Q8Explain why the short-run marginal cost, average variable cost and short-run average cost curves are U-shaped. 6 marks

All three fall at first and rise later because of the law of variable proportions and the spreading of fixed cost.

SMC falls while marginal product rises, then rises when it falls.
AVC follows SMC: it falls while SMC is below it and rises when SMC is above it.
SAC = AVC + AFC. At first both AVC and AFC fall, so SAC falls.
Later AVC rises faster than AFC falls, so SAC rises.
SMC cuts AVC and SAC from below at their minimum points.
SAC's minimum lies to the right of AVC's minimum.

Thus the cost curves are U-shaped.

In summary, the early fall in cost comes from better use of fixed inputs and spreading of fixed cost, and the later rise from diminishing marginal returns.

Q9Explain the shape of the long-run average cost curve. How is the long-run marginal cost curve related to it? 6 marks

The LRAC curve is U-shaped because of returns to scale: it falls under increasing returns, is flat at constant returns and rises under decreasing returns.

Under increasing returns, inputs rise less than output, so average cost falls.
Under constant returns, average cost does not change.
Under decreasing returns, inputs rise more than output, so average cost rises.
A typical firm shows these in turn, giving a U shape.
LRMC is also U-shaped and lies below LRAC while LRAC falls and above it while LRAC rises.
So LRMC cuts LRAC from below at its minimum.

At that minimum point, returns to scale are constant.

A firm chooses its long-run plan by choosing the most suitable short-run plant for each output, so LRAC is the envelope of the short-run average cost curves. The lowest point of LRAC marks the most efficient scale of output.

Q10A firm has total fixed cost of ₹50. Its total variable cost is ₹90 for 3 units of output and ₹120 for 4 units. Calculate, for 4 units, the AVC, SAC and SMC. 4 marks · Numerical

For 4 units AVC is ₹30, SAC is ₹42.50 and SMC is ₹30.

Given: TFC = 50; TVC(3) = 90; TVC(4) = 120.

Formula: AVC = TVC÷q; SAC = (TFC + TVC)÷q; SMC = TC(4) − TC(3).

Steps: AVC = 120÷4 = 30. TC(4) = 170, so SAC = 170÷4 = 42.5. TC(3) = 140, so SMC = 170 − 140 = 30.

Final answer: AVC = ₹30; SAC = ₹42.50; SMC = ₹30.

10 Points for State PSC and UPSC Aspirants

The Production Linked Incentive (PLI) schemes, approved from November 2020 for 14 sectors with an outlay of about ₹1.97 lakh crore, reward incremental output.Why it matters: applies production and cost ideas to industrial policy.Source: DPIIT, Government of India
MSMEs are classified by investment and turnover (composite criteria from 2020), with no separate manufacturing and services limits.Why it matters: firm size and scale are frequent prelims topics.Source: Ministry of MSME
The Annual Survey of Industries (ASI) by the NSO covers factories registered under the Factories Act, 1948 and reports output, employment and fixed capital.Why it matters: the main official source for production data.Source: MoSPI, ASI
Make in India was launched on 25 September 2014 to raise manufacturing and benefit from economies of scale.Why it matters: a link between returns to scale and industrial policy.Source: DPIIT, Government of India
The law of diminishing returns explains why extra fertiliser on a fixed plot raises output at a falling rate.Why it matters: an agricultural application of variable proportions.Source: NCERT Introductory Microeconomics
Railways, power transmission and water supply have high fixed costs and falling average cost over a wide range, which can make them natural monopolies.Why it matters: connects cost curves to regulation.Source: Economic Survey, Ministry of Finance
The Mahalanobis model of the Second Five Year Plan (1956–61) favoured capital goods and heavy industry.Why it matters: links the capital–labour choice to planning.Source: NITI Aayog
The incremental capital–output ratio (ICOR) measures extra capital needed for one extra unit of output.Why it matters: a planning concept built on the production function.Source: Economic Survey, Ministry of Finance
RBI's India KLEMS database measures productivity growth using capital, labour, energy, materials and services inputs.Why it matters: the practical form of a multi-input production function.Source: Reserve Bank of India
Goods and Services Tax input tax credit lowers the cost of inputs, which shifts firms' cost curves down.Why it matters: ties costs to tax design.Source: GST Council, Government of India

These are revision notes, not official predictions of exam content.

Quick Revision

Production function: maximum output for given inputs and technology.
Short run: some input fixed; long run: all inputs variable.
AP = TP÷x; MP = ΔTP÷Δx; MP cuts AP at AP's maximum.
MP and AP curves are inverted U-shaped.
Returns to scale: CRS, IRS, DRS (all inputs change).
TC = TFC + TVC; SAC = AVC + AFC.
SMC, AVC and SAC are U-shaped; SMC cuts them at their minima.
LRAC U-shaped: IRS, then CRS, then DRS.

Glossary:

Marginal cost Opportunity cost Perfect competition Production function Returns to scale

Related chapters: The Theory of the Firm under Perfect Competition, which uses these cost curves to find the firm's supply curve; Non-Competitive Markets, where the monopolist faces the same cost curves. From Class 11: Measures of Central Tendency.

Sources

NCERT textbooks: Introductory Microeconomics, Class 12, National Council of Educational Research and Training. Syllabus reference. Accessed 23 October 2026.
Department for Promotion of Industry and Internal Trade, Government of India. Production Linked Incentive and Make in India. Accessed 23 October 2026.
Ministry of Micro, Small and Medium Enterprises, Government of India. Accessed 23 October 2026.
Economic Survey, Ministry of Finance, Government of India. Accessed 23 October 2026.
Ministry of Statistics and Programme Implementation (Annual Survey of Industries). Official statistics.

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Syllabus year 2026-27 · Last updated 23 October 2026

Class 12 Economics Chapter 3: Production and Costs (NCERT Introductory Microeconomics)