Class | Subject | Book | Chapter | Session | Questions covered |
|---|---|---|---|---|---|
XII | Economics | Microeconomics (NCERT) | 3 – Production and Costs | 2026-27 | 30 of 30 |
Chapter at a glance
Concept | Key point |
|---|---|
Production function | – maximum output from given inputs with given technology  |
Short run / long run | Short run: at least one fixed input; long run: all inputs variable |
TP, AP, MP | ; (change in TP per extra unit of L); TP = sum of MPs   |
Law of diminishing MP / variable proportions | MP of a variable input eventually falls; TP rises at increasing rate, then decreasing rate, then falls |
Returns to scale | Constant (output rises in the same proportion as inputs), increasing (more than), decreasing (less than) |
Costs | TC = TFC + TVC; AC = AFC + AVC;  |
Shapes | AFC – rectangular hyperbola; AVC, SAC, SMC – U-shaped; SMC cuts AVC and SAC at their minima from below |
Long run | No fixed cost; LRAC and LRMC U-shaped (returns to scale); LRMC cuts LRAC at its minimum |
Exercises
Explain the concept of a production function.
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A production function is a technological relationship between physical inputs and physical output. It shows the maximum quantity of output that can be produced from different combinations of inputs, for a given state of technology:
where is labour and is capital. E.g. . A change in technology changes the production function.
A production function shows the maximum output obtainable from each combination of inputs with given technology: q = f(L, K).
What is the total product of an input?
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Total product (TP) of a variable input (say labour) is the total output produced at different levels of employment of that input, keeping other inputs constant. It is also called the total return or total physical product.
Total product is the total output obtained from different quantities of a variable input, other inputs being held constant.
What is the average product of an input?
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Average product (AP) is the output per unit of the variable input:
Average product is output per unit of the variable input: AP_L = TP_L / L.
What is the marginal product of an input?
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Marginal product (MP) is the change in total output from employing one more unit of the variable input, other inputs constant:
Marginal product is the change in total product from one more unit of the variable input: MP_L = ΔTP/ΔL.
Explain the relationship between the marginal products and the total product of an input.
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- TP is the sum of MPs: up to that level of employment.
- When MP is positive and rising, TP increases at an increasing rate.
- When MP is positive but falling, TP increases at a diminishing rate.
- When MP = 0, TP is at its maximum.
- When MP is negative, TP falls.
TP is the sum of MPs; TP rises at an increasing rate while MP rises, at a diminishing rate while MP falls but is positive, is maximum when MP = 0 and falls when MP is negative.
Explain the concepts of the short run and the long run.
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- Short run – the period in which at least one factor of production is fixed (e.g. plant, machinery). Output can be changed only by changing variable inputs (labour, raw materials).
- Long run – the period in which all factors of production can be varied, including plant size; the firm can change its scale of operation.
These are not defined in calendar time; they depend on whether inputs can be varied.
In the short run at least one input is fixed; in the long run all inputs can be varied.
What is the law of diminishing marginal product?
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The law of diminishing marginal product states that if we keep increasing the employment of one input, keeping other inputs fixed, eventually a point is reached after which the marginal product of that input starts falling. This is because the fixed input gets divided among more and more units of the variable input, so each additional unit has less of the fixed input to work with.
As more units of a variable input are used with fixed inputs, its marginal product eventually declines.
What is the law of variable proportions?
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The law of variable proportions states that as the quantity of a variable input is increased with other inputs fixed (so the proportion between inputs changes), the marginal product first increases and then decreases (and may become negative). TP first increases at an increasing rate, then at a diminishing rate, and finally falls. Initially, the variable input makes better use of the fixed input; later, the fixed input becomes scarce relative to it.
When one input is increased with others fixed, its MP first rises and then falls (TP rises at an increasing, then a diminishing rate, then falls), because the proportion of inputs changes.
When does a production function satisfy constant returns to scale?
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When all inputs are increased in the same proportion and output increases in the same proportion: for . E.g. doubling all inputs doubles output.
When a proportional increase in all inputs raises output in the same proportion: f(tL, tK) = t·f(L, K).
When does a production function satisfy increasing returns to scale?
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When a proportional increase in all inputs leads to a more than proportional increase in output: for . E.g. doubling inputs more than doubles output (due to specialisation, indivisibilities).
When a proportional increase in all inputs raises output more than proportionately: f(tL, tK) > t·f(L, K).
When does a production function satisfy decreasing returns to scale?
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When a proportional increase in all inputs leads to a less than proportional increase in output: for . E.g. doubling inputs less than doubles output (due to managerial difficulties at large scale).
When a proportional increase in all inputs raises output less than proportionately: f(tL, tK) < t·f(L, K).
Briefly explain the concept of the cost function.
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A cost function shows the minimum cost of producing each level of output, given the prices of inputs and the technology:
The firm chooses the least-cost combination of inputs for each output level. Short-run cost functions include fixed and variable costs; in the long run, all costs are variable.
A cost function gives the minimum cost of producing each level of output with given input prices and technology: C = C(q).
What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
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- Total fixed cost (TFC) – the cost of fixed inputs; it does not change with output (rent, interest on capital, salaries of permanent staff). It is incurred even at zero output.
- Total variable cost (TVC) – the cost of variable inputs; it changes with output (raw materials, wages of casual labour, power). It is zero at zero output.
- Total cost (TC) – the total expenditure on all inputs:
TC curve is parallel to TVC curve, starting from the level of TFC.
TFC does not vary with output, TVC varies with output, and TC = TFC + TVC.
What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
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- Average fixed cost (AFC)
- Average variable cost (AVC)
- Average cost (AC/SAC)
The vertical gap between SAC and AVC equals AFC; it narrows as output rises.
AFC = TFC/q, AVC = TVC/q, AC = TC/q, and AC = AFC + AVC.
Can there be some fixed cost in the long run? If not, why?
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No. In the long run all inputs are variable – the firm can change its plant size, machinery and all other factors. Since no input is fixed, there is no fixed cost; all costs are variable costs in the long run.
No – in the long run all inputs can be varied, so all costs are variable.
What does the average fixed cost curve look like? Why does it look so?
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The AFC curve is a downward-sloping curve, a rectangular hyperbola, approaching but never touching the two axes.
Reason: , and TFC is constant. As output increases, the same fixed cost is spread over more units, so AFC keeps falling. Since is constant, the area under every point of the curve is the same – the property of a rectangular hyperbola. AFC never becomes zero, because TFC is positive.
AFC is a downward-sloping rectangular hyperbola, because a constant TFC is spread over more output (AFC × q = TFC is constant).
What do the short run marginal cost, average variable cost and short run average cost curves look like?
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All three are U-shaped (see the figure in Q 16):
- SMC – first falls, reaches a minimum and then rises; this reflects first increasing and then diminishing marginal product of the variable input.
- AVC – also U-shaped, for the same reason (the law of variable proportions).
- SAC – U-shaped, since SAC = AFC + AVC: initially both fall; later the rise in AVC outweighs the fall in AFC. The minimum of SAC lies to the right of the minimum of AVC.
SMC cuts AVC and SAC from below at their minimum points.
SMC, AVC and SAC are all U-shaped; SMC cuts AVC and then SAC from below at their minimum points, and the minimum of SAC lies to the right of that of AVC.
Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
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- When SMC < AVC, the additional unit costs less than the average, so it pulls AVC down – AVC falls.
- When SMC > AVC, the additional unit costs more than the average, so it pulls AVC up – AVC rises.
- AVC stops falling and has not yet started rising only when SMC = AVC – this is the minimum point of AVC.
So the SMC curve cuts the AVC curve from below at its minimum point.
Because AVC falls while SMC is below it and rises while SMC is above it, so AVC is at its minimum exactly where SMC = AVC.
At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
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The SMC curve cuts the SAC curve at the minimum point of SAC, from below.
Reason: the same marginal–average relationship holds. When SMC < SAC, SAC falls; when SMC > SAC, SAC rises. SAC is minimum when SMC = SAC. (Since SAC lies above AVC and AFC keeps falling, this point lies to the right of the minimum of AVC.)
At the minimum point of SAC, because SAC falls while SMC is below it and rises while SMC is above it.
Why is the short run marginal cost curve ‘U’-shaped?
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Because of the law of variable proportions. In the short run:
- initially, the marginal product of the variable input increases, so each additional unit of output needs less of the input → SMC falls;
- after a point, the marginal product diminishes, so each additional unit of output needs more of the input → SMC rises.
Since (with wage constant), SMC moves inversely with MP, giving a U-shape.
Because of the law of variable proportions: MP of the variable input first rises (SMC falls) and then diminishes (SMC rises); SMC = w/MP_L.
What do the long run marginal cost and the average cost curves look like?
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Both LRAC and LRMC are U-shaped, due to returns to scale:
- at low output, increasing returns to scale – costs fall;
- then constant returns to scale – costs constant (minimum);
- then decreasing returns to scale – costs rise.
LRMC cuts LRAC from below at the minimum point of LRAC.
LRAC and LRMC are U-shaped (increasing, then constant, then decreasing returns to scale), and LRMC cuts LRAC from below at its minimum.
The following table gives the total product schedule of labour (L: 0, 1, 2, 3, 4, 5; TP: 0, 15, 35, 50, 40, 48). Find the corresponding average product and marginal product schedules of labour.
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L | TP | AP = TP/L | MP = ΔTP |
|---|---|---|---|
0 | 0 | – | – |
1 | 15 | 15 | 15 |
2 | 35 | 17.5 | 20 |
3 | 50 | 16.67 | 15 |
4 | 40 | 10 | –10 |
5 | 48 | 9.6 | 8 |
AP: 15, 17.5, 16.67, 10, 9.6; MP: 15, 20, 15, –10, 8.
The following table gives the average product schedule of labour (L: 1–6; AP: 2, 3, 4, 4.25, 4, 3.5). Find the total product and marginal product schedules. It is given that the total product is zero at zero level of labour employment.
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L | AP | TP = AP × L | MP |
|---|---|---|---|
0 | – | 0 | – |
1 | 2 | 2 | 2 |
2 | 3 | 6 | 4 |
3 | 4 | 12 | 6 |
4 | 4.25 | 17 | 5 |
5 | 4 | 20 | 3 |
6 | 3.5 | 21 | 1 |
TP: 2, 6, 12, 17, 20, 21; MP: 2, 4, 6, 5, 3, 1.
The following table gives the marginal product schedule of labour (L: 1–6; MP: 3, 5, 7, 5, 3, 1). 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.
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L | MP | TP (cumulative MP) | AP = TP/L |
|---|---|---|---|
1 | 3 | 3 | 3 |
2 | 5 | 8 | 4 |
3 | 7 | 15 | 5 |
4 | 5 | 20 | 5 |
5 | 3 | 23 | 4.6 |
6 | 1 | 24 | 4 |
TP: 3, 8, 15, 20, 23, 24; AP: 3, 4, 5, 5, 4.6, 4.
The following table shows the total cost schedule of a firm (Q: 0–6; TC: 10, 30, 45, 55, 70, 90, 120). What is the total fixed cost schedule of this firm? Calculate the TVC, AFC, AVC, SAC and SMC schedules of the firm.
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TFC = TC at zero output = ₹ 10 at every level of output.
Q | TC | TFC | TVC | AFC | AVC | SAC | SMC |
|---|---|---|---|---|---|---|---|
0 | 10 | 10 | 0 | – | – | – | – |
1 | 30 | 10 | 20 | 10 | 20 | 30 | 20 |
2 | 45 | 10 | 35 | 5 | 17.5 | 22.5 | 15 |
3 | 55 | 10 | 45 | 3.33 | 15 | 18.33 | 10 |
4 | 70 | 10 | 60 | 2.5 | 15 | 17.5 | 15 |
5 | 90 | 10 | 80 | 2 | 16 | 18 | 20 |
6 | 120 | 10 | 110 | 1.67 | 18.33 | 20 | 30 |
TFC = ₹ 10 throughout; TVC, AFC, AVC, SAC and SMC are as in the table (e.g. SMC: 20, 15, 10, 15, 20, 30).
The following table gives the total cost schedule of a firm (Q: 1–6; TC: 50, 65, 75, 95, 130, 185). It is also given that the average fixed cost at 4 units of output is ₹ 5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output.
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TFC = AFC × Q = 5 × 4 = ₹ 20 (so TC at zero output = 20).
Q | TC | TFC | TVC | AFC | AVC | SAC | SMC |
|---|---|---|---|---|---|---|---|
1 | 50 | 20 | 30 | 20 | 30 | 50 | 30 |
2 | 65 | 20 | 45 | 10 | 22.5 | 32.5 | 15 |
3 | 75 | 20 | 55 | 6.67 | 18.33 | 25 | 10 |
4 | 95 | 20 | 75 | 5 | 18.75 | 23.75 | 20 |
5 | 130 | 20 | 110 | 4 | 22 | 26 | 35 |
6 | 185 | 20 | 165 | 3.33 | 27.5 | 30.83 | 55 |
TFC = ₹ 20; the other schedules are as in the table (e.g. TVC: 30, 45, 55, 75, 110, 165; SMC: 30, 15, 10, 20, 35, 55).
A firm’s SMC schedule is shown in the following table (Q: 1–6; SMC: 500, 300, 200, 300, 500, 800). The total fixed cost of the firm is ₹ 100. Find the TVC, TC, AVC and SAC schedules of the firm.
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TVC is the cumulative sum of SMC; TC = TFC (100) + TVC.
Q | SMC | TVC | TC | AVC | SAC |
|---|---|---|---|---|---|
0 | – | 0 | 100 | – | – |
1 | 500 | 500 | 600 | 500 | 600 |
2 | 300 | 800 | 900 | 400 | 450 |
3 | 200 | 1,000 | 1,100 | 333.33 | 366.67 |
4 | 300 | 1,300 | 1,400 | 325 | 350 |
5 | 500 | 1,800 | 1,900 | 360 | 380 |
6 | 800 | 2,600 | 2,700 | 433.33 | 450 |
TVC: 500, 800, 1,000, 1,300, 1,800, 2,600; TC: 600, 900, 1,100, 1,400, 1,900, 2,700; AVC and SAC as in the table.
Let the production function of a firm be . Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.
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Maximum output = 500 units.
Let the production function of a firm be . 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?
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- With L = 5, K = 2: .
- With L = 0, K = 10: (both inputs are essential in this production function).
200 units with L = 5, K = 2; zero output with L = 0, K = 10.
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 = 5L + 2K.
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(Here the inputs are perfect substitutes, so output is possible with capital alone.)
Maximum output = 20 units.
Topic checklist
- ☒ Production function, TP, AP, MP and their relation (Q 1–5, 22–24)
- ☒ Short run and long run; law of variable proportions (Q 6–8)
- ☒ Returns to scale and production functions (Q 9–11, 28–30)
- ☒ Cost concepts and cost curves (Q 12–21, 25–27)