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Production and Costs

NCERT Class 11 · Economics Based on NCERT Class 11 Economics textbook · Free CBSE study kit

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Chapter Notes

Overview
This chapter explains the behaviour of a producer, focusing on how inputs are transformed into output and the costs incurred in the process. It introduces the production function, the concepts of total, average, and marginal products, and the laws of diminishing marginal product and variable proportions. The chapter also covers short-run and long-run costs, including fixed and variable costs, and the shapes of various cost curves. The one big idea a student must walk away with is that a firm's objective is to maximise profit, which requires understanding the relationship between inputs and output (production) and the cost of employing those inputs.
Key Concepts (24)
Production
The process by which inputs are transformed into 'output'.
e.g. A tailor uses a sewing machine, cloth, thread, and his own labour to produce shirts.
Production Function
The relationship between inputs used and output produced by a firm; for various quantities of inputs used, it gives the maximum quantity of output that can be produced.
e.g. For a farmer using land (K) and labour (L), the production function could be q = K × L, where q is wheat produced.
Short Run
A period in which at least one factor of production (labour or capital) cannot be varied and remains fixed.
e.g. If capital is fixed at 4 units, the firm can only vary labour to change output in the short run.
Long Run
A period in which all factors of production can be varied; there is no fixed factor.
e.g. A firm can increase both labour and capital simultaneously to produce more output in the long run.
Isoquant
The set of all possible combinations of two inputs that yield the same maximum possible level of output.
e.g. From Table 3.1, output of 10 units can be produced with (4L, 1K), (2L, 2K), or (1L, 4K); all these combinations lie on the same isoquant for q=10.
Total Product (TP)
The relationship between the variable input and output, keeping all other inputs constant.
e.g. With capital fixed at 4 units, as labour increases from 0 to 6, TP increases from 0 to 57 (from Table 3.2).
Average Product (AP)
Output per unit of variable input, calculated as AP_L = TP_L / L.
e.g. With 2 units of labour and TP=24, AP_L = 24/2 = 12 (from Table 3.2).
Marginal Product (MP)
The change in output per unit of change in the input when all other inputs are held constant, calculated as MP_L = ΔTP_L / ΔL.
e.g. When labour increases from 1 to 2, TP changes from 10 to 24, so MP_L = (24-10)/1 = 14 (from Table 3.2).
Law of Diminishing Marginal Product / Law of Variable Proportions
The marginal product of a factor input initially rises with its employment level, but after reaching a certain level of employment, it starts falling.
e.g. In Table 3.2, MP_L rises from 10 to 16 (up to 3 units of labour) and then falls to 10, 6, and 1 as labour increases further.
Returns to Scale
The change in output when all inputs are increased by the same proportion.
e.g. If doubling all inputs doubles output, it is constant returns to scale; if output more than doubles, it is increasing returns to scale; if less than doubles, it is decreasing returns to scale.
Constant Returns to Scale (CRS)
When a proportional increase in all inputs results in an increase in output by the same proportion.
e.g. For the Cobb-Douglas function q = x1^α x2^β, if α+β=1, then f(tx1, tx2) = t.f(x1, x2), showing CRS.
Increasing Returns to Scale (IRS)
When a proportional increase in all inputs results in an increase in output by a larger proportion.
e.g. For the Cobb-Douglas function, if α+β>1, then f(tx1, tx2) > t.f(x1, x2).
Decreasing Returns to Scale (DRS)
When a proportional increase in all inputs results in an increase in output by a smaller proportion.
e.g. For the Cobb-Douglas function, if α+β<1, then f(tx1, tx2) < t.f(x1, x2).
Cost Function
Describes the least cost of producing each level of output given prices of factors of production and technology.
e.g. From Table 3.3, to produce 5 units of output, the least cost (TC) is Rs 53.
Total Fixed Cost (TFC)
The cost that a firm incurs to employ fixed inputs; it remains constant for all levels of output.
e.g. In Table 3.3, TFC is Rs 20 for all output levels from 0 to 10.
Total Variable Cost (TVC)
The cost that a firm incurs to employ variable inputs; it increases as output increases.
e.g. In Table 3.3, TVC increases from Rs 0 at q=0 to Rs 95 at q=10.
Total Cost (TC)
The sum of total fixed cost and total variable cost: TC = TFC + TVC.
e.g. At q=5, TC = 20 + 33 = Rs 53 (from Table 3.3).
Short Run Average Cost (SAC)
Total cost per unit of output in the short run: SAC = TC / q.
e.g. At q=5, SAC = 53/5 = Rs 10.6 (from Table 3.3).
Average Variable Cost (AVC)
Total variable cost per unit of output: AVC = TVC / q.
e.g. At q=5, AVC = 33/5 = Rs 6.6 (from Table 3.3).
Average Fixed Cost (AFC)
Total fixed cost per unit of output: AFC = TFC / q.
e.g. At q=5, AFC = 20/5 = Rs 4 (from Table 3.3).
Short Run Marginal Cost (SMC)
The change in total cost per unit of change in output: SMC = ΔTC / Δq.
e.g. When output increases from 4 to 5, TC changes from 49 to 53, so SMC = 4/1 = Rs 4 (from Table 3.3).
Long Run Average Cost (LRAC)
Cost per unit of output in the long run: LRAC = TC / q.
e.g. In the long run, there are no fixed costs, so TC = TVC.
Long Run Marginal Cost (LRMC)
The change in total cost per unit of change in output in the long run: LRMC = (TC at q1 units) – (TC at q1 – 1 units).
e.g. If TC at 5 units is Rs 100 and at 4 units is Rs 80, LRMC = 20.
Cobb-Douglas Production Function
A production function of the form q = x1^α x2^β, where α and β are constants.
e.g. If q = L^0.5 K^0.5, then α+β=1, so it exhibits constant returns to scale.
Formulas & Equations (16)
q = f(L, K)
Reads as: Output is a function of labour and capital.
Variables: q = maximum output; L = labour; K = capital.
Use when: To represent the production function in a general form.
⚠ Students forget that this gives the maximum output for given inputs, not actual output.
AP_L = TP_L / L
Reads as: Average product of labour equals total product of labour divided by labour.
Variables: AP_L = average product of labour; TP_L = total product of labour; L = labour.
Use when: To calculate output per unit of labour.
⚠ Students confuse AP with MP and use the wrong formula.
MP_L = ΔTP_L / ΔL
Reads as: Marginal product of labour equals change in total product of labour divided by change in labour.
Variables: MP_L = marginal product of labour; ΔTP_L = change in total product; ΔL = change in labour.
Use when: To find the additional output from one more unit of labour.
⚠ Students forget that ΔL is usually 1, so they incorrectly use the formula for non-unit changes.
MP_L = TP at L units – TP at (L – 1) units
Reads as: Marginal product of the Lth unit of labour equals total product at L units minus total product at L minus 1 units.
Variables: MP_L = marginal product of labour; TP = total product; L = labour.
Use when: When inputs change in discrete units (e.g., 1 unit at a time).
⚠ Students forget to subtract the previous TP, leading to incorrect MP values.
f(tx1, tx2) = t.f(x1, x2) for CRS
Reads as: For constant returns to scale, if both inputs are multiplied by t, output is multiplied by t.
Variables: t = scaling factor (>1); x1, x2 = inputs; f = production function.
Use when: To check if a production function exhibits constant returns to scale.
⚠ Students confuse CRS with IRS or DRS and misapply the inequality signs.
f(tx1, tx2) > t.f(x1, x2) for IRS
Reads as: For increasing returns to scale, if both inputs are multiplied by t, output is more than t times.
Variables: t = scaling factor (>1); x1, x2 = inputs; f = production function.
Use when: To check if a production function exhibits increasing returns to scale.
⚠ Students write the inequality in the wrong direction.
f(tx1, tx2) < t.f(x1, x2) for DRS
Reads as: For decreasing returns to scale, if both inputs are multiplied by t, output is less than t times.
Variables: t = scaling factor (>1); x1, x2 = inputs; f = production function.
Use when: To check if a production function exhibits decreasing returns to scale.
⚠ Students forget that DRS implies less than proportional increase in output.
q = x1^α x2^β (Cobb-Douglas)
Reads as: Output equals x1 raised to alpha times x2 raised to beta.
Variables: q = output; x1, x2 = inputs; α, β = constants.
Use when: To represent a specific production function and analyse returns to scale.
⚠ Students forget that α+β determines returns to scale: =1 for CRS, >1 for IRS, <1 for DRS.
TC = TFC + TVC
Reads as: Total cost equals total fixed cost plus total variable cost.
Variables: TC = total cost; TFC = total fixed cost; TVC = total variable cost.
Use when: To calculate total cost from its components.
⚠ Students forget that TFC is constant and does not change with output.
SAC = TC / q
Reads as: Short run average cost equals total cost divided by quantity of output.
Variables: SAC = short run average cost; TC = total cost; q = output.
Use when: To find cost per unit in the short run.
⚠ Students use TVC instead of TC in the numerator.
AVC = TVC / q
Reads as: Average variable cost equals total variable cost divided by quantity of output.
Variables: AVC = average variable cost; TVC = total variable cost; q = output.
Use when: To find variable cost per unit.
⚠ Students forget that AVC is undefined at q=0.
AFC = TFC / q
Reads as: Average fixed cost equals total fixed cost divided by quantity of output.
Variables: AFC = average fixed cost; TFC = total fixed cost; q = output.
Use when: To find fixed cost per unit.
⚠ Students think AFC is constant, but it decreases as output increases.
SAC = AVC + AFC
Reads as: Short run average cost equals average variable cost plus average fixed cost.
Variables: SAC = short run average cost; AVC = average variable cost; AFC = average fixed cost.
Use when: To derive SAC from its components.
⚠ Students forget that this relation holds only in the short run.
SMC = ΔTC / Δq
Reads as: Short run marginal cost equals change in total cost divided by change in output.
Variables: SMC = short run marginal cost; ΔTC = change in total cost; Δq = change in output.
Use when: To find the additional cost of producing one more unit.
⚠ Students forget that in the short run, ΔTC = ΔTVC because TFC is constant.
LRAC = TC / q
Reads as: Long run average cost equals total cost divided by quantity of output.
Variables: LRAC = long run average cost; TC = total cost; q = output.
Use when: To find cost per unit in the long run.
⚠ Students forget that in the long run, TC = TVC (no fixed costs).
LRMC = (TC at q1 units) – (TC at q1 – 1 units)
Reads as: Long run marginal cost equals total cost at q1 units minus total cost at q1 minus 1 units.
Variables: LRMC = long run marginal cost; TC = total cost; q1 = output level.
Use when: When output changes in discrete units in the long run.
⚠ Students confuse LRMC with SMC and forget that LRMC is derived from long run total cost.
How It Works
Derivation of Total Product from Production Function
  1. Step 1: Fix all inputs except one (e.g., capital fixed at 4 units).
  2. Step 2: Vary the variable input (labour) from 0 to 6 units.
  3. Step 3: Record the maximum output for each level of labour from the production function table (Table 3.1).
  4. Step 4: The resulting schedule of labour and output is the Total Product of labour schedule (Table 3.2).
💡 Total product is the maximum output possible for each level of the variable input, assuming efficient use of inputs.
Calculation of Marginal Product and Average Product
  1. Step 1: From the TP schedule, calculate MP_L = TP at L units – TP at (L-1) units for each L.
  2. Step 2: Calculate AP_L = TP_L / L for each L.
  3. Step 3: Verify that the sum of all MP_L up to a given L equals TP_L.
💡 MP is the slope of the TP curve; AP is the slope of a ray from the origin to a point on the TP curve.
Law of Variable Proportions (Diminishing Marginal Product)
  1. Step 1: Increase the variable input (labour) while keeping other inputs fixed.
  2. Step 2: Initially, factor proportions become more suitable, so MP rises.
  3. Step 3: After a certain level, the production process becomes crowded, so MP starts falling.
  4. Step 4: This explains the inverse U-shape of the MP curve.
💡 The law applies only in the short run when at least one factor is fixed.
Derivation of Short Run Cost Schedules
  1. Step 1: Identify TFC (constant for all output levels).
  2. Step 2: For each output level, find TVC from the cost function.
  3. Step 3: Calculate TC = TFC + TVC.
  4. Step 4: Calculate AFC = TFC / q, AVC = TVC / q, SAC = TC / q.
  5. Step 5: Calculate SMC = ΔTC / Δq (or ΔTVC / Δq).
💡 SMC is undefined at q=0; AFC is a rectangular hyperbola.
Relationship between SMC, AVC, and SAC
  1. Step 1: When SMC < AVC, AVC is falling.
  2. Step 2: When SMC > AVC, AVC is rising.
  3. Step 3: SMC cuts AVC at its minimum point.
  4. Step 4: Similarly, SMC cuts SAC at its minimum point.
  5. Step 5: The minimum of SAC lies to the right of the minimum of AVC.
💡 The SMC curve always cuts the AVC and SAC curves from below at their respective minima.
Derivation of Long Run Cost Curves from Returns to Scale
  1. Step 1: Under IRS, as output increases, average cost falls (LRAC downward sloping).
  2. Step 2: Under CRS, average cost remains constant (LRAC flat).
  3. Step 3: Under DRS, as output increases, average cost rises (LRAC upward sloping).
  4. Step 4: The LRAC curve is U-shaped: downward part due to IRS, flat part due to CRS, upward part due to DRS.
  5. Step 5: LRMC cuts LRAC at its minimum point.
💡 In the long run, there are no fixed costs, so LRAC = LRMC at the first unit.
Exam Traps — Don't Make These Mistakes
⚠ Confusing Total Product with Marginal Product
✗ Students often write that TP is the sum of all APs.
→ TP is the sum of all marginal products, not average products.
✓ Total product is the sum of marginal products of all units of the variable input up to that level.
⚠ Misinterpreting the Law of Diminishing Marginal Product
✗ Students write that MP always falls from the beginning.
→ The law states that MP initially rises and then falls after a certain point.
✓ The law of variable proportions says that MP first increases, reaches a maximum, and then decreases.
⚠ Confusing Short Run and Long Run Costs
✗ Students write that TFC exists in the long run.
→ In the long run, all factors are variable, so there are no fixed costs.
✓ In the long run, there are no fixed costs; TC = TVC.
⚠ Incorrectly Identifying the Shape of AFC Curve
✗ Students write that AFC is a downward-sloping straight line.
→ AFC is a rectangular hyperbola, not a straight line; it falls continuously but never touches the axes.
✓ AFC curve is a rectangular hyperbola; as output increases, AFC decreases but never becomes zero.
⚠ Misapplying Returns to Scale to Short Run
✗ Students write that returns to scale apply in the short run.
→ Returns to scale require all inputs to be varied, which is only possible in the long run.
✓ Returns to scale is a long-run concept because all factors of production can be varied only in the long run.
⚠ Confusing Average Product and Marginal Product Relationship
✗ Students write that when AP is rising, MP is less than AP.
→ When AP is rising, MP is greater than AP; when AP is falling, MP is less than AP.
✓ When AP is rising, MP > AP; when AP is falling, MP < AP; MP cuts AP at its maximum.
Compare & Contrast
Variability of factors of production
Short Run
Long Run
In the short run, at least one factor is fixed; in the long run, all factors are variable.
Definition and calculation
Average Product (AP)
Marginal Product (MP)
AP is output per unit of input (TP/L), while MP is the additional output from one more unit of input (ΔTP/ΔL).
Behaviour with output
Total Fixed Cost (TFC)
Total Variable Cost (TVC)
TFC remains constant at all output levels, while TVC increases as output increases.
Shape of the curve
Average Fixed Cost (AFC)
Average Variable Cost (AVC)
AFC is a rectangular hyperbola (always falling), while AVC is U-shaped (falls then rises).
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA (3 marks), 1 LA (5 marks) — typically 10 marks total.
Most asked: Law of Diminishing Marginal Product / Law of Variable Proportions · Relationship between TP, AP, and MP · Shapes of short run cost curves (SAC, AVC, SMC) · Returns to Scale (CRS, IRS, DRS) · Difference between short run and long run · Calculation of TP, AP, MP from given schedules · Calculation of TC, TVC, TFC, AFC, AVC, SAC, SMC from given schedules
Don't skip: Explain the law of variable proportions with the help of a schedule and diagram.; Derive and explain the shapes of SAC, AVC, and SMC curves with a diagram.; Explain the relationship between TP, AP, and MP with a schedule and diagram.; Distinguish between short run and long run costs.; Numerical problems on calculating TP, AP, MP, or TC, TVC, TFC, AFC, AVC, SAC, SMC from given data.
One-Line Revision (read aloud before the exam)
  1. Production function shows the maximum output possible from given inputs.
  2. In the short run, at least one factor is fixed; in the long run, all factors are variable.
  3. Total product is the sum of marginal products of all units of the variable input.
  4. Average product is total product divided by the number of units of the variable input.
  5. Marginal product is the change in total product due to a one-unit change in the variable input.
  6. The law of variable proportions states that MP first rises, then falls.
  7. MP curve cuts AP curve from above at the maximum point of AP.
  8. Returns to scale refer to the change in output when all inputs are increased proportionally.
  9. Constant returns to scale: output increases by the same proportion as inputs.
  10. Increasing returns to scale: output increases by a larger proportion than inputs.
  11. Decreasing returns to scale: output increases by a smaller proportion than inputs.
  12. Total cost is the sum of total fixed cost and total variable cost.
  13. Average fixed cost is a rectangular hyperbola; it falls as output increases.
  14. Short run average cost, average variable cost, and marginal cost curves are all U-shaped.
  15. SMC curve cuts AVC and SAC curves at their respective minimum points from below.
  16. In the long run, there are no fixed costs; LRAC and LRMC are U-shaped.
  17. LRMC cuts LRAC at its minimum point.
  18. The Cobb-Douglas production function is q = x1^α x2^β; returns to scale depend on α+β.
  19. AFC = TFC/q, AVC = TVC/q, SAC = TC/q, and SAC = AVC + AFC.
  20. SMC = ΔTC/Δq = ΔTVC/Δq in the short run because TFC is constant.

MCQs — 10 Questions with Answers

Q1. If a firm uses 2 units of labour and 3 units of capital to produce 18 units of output, what is the Average Product of labour?

  • A. 6 units
  • B. 9 units ✓
  • C. 3 units
  • D. 12 units

Answer: B — Average Product of labour = Total Product ÷ Units of labour = 18 ÷ 2 = 9 units.

Q2. Which of the following is correct about the short-run production?

  • A. Both labour and capital can be varied freely
  • B. At least one factor of production remains fixed ✓
  • C. All factors of production must remain constant
  • D. Only labour can be used as input

Answer: B — In the short-run, at least one factor (usually capital) is fixed and cannot be changed; only the variable factor (labour) can be adjusted.

Q3. What does an isoquant represent?

  • A. Different levels of output using the same inputs
  • B. Different combinations of inputs that produce the same output ✓
  • C. The total cost of production at different output levels
  • D. The profit earned at different price levels

Answer: B — An isoquant is the locus of all input combinations (labour and capital) that yield the same maximum level of output.

Q4. Total Cost of producing 10 units is Rs 500 and Total Cost of producing 11 units is Rs 545. What is the Marginal Cost of the 11th unit?

  • A. Rs 45 ✓
  • B. Rs 50
  • C. Rs 55
  • D. Rs 495

Answer: A — Marginal Cost = ΔTC ÷ ΔQ = (545 − 500) ÷ (11 − 10) = Rs 45 per unit.

Q5. In the Law of Variable Proportions, Stage II is preferred by firms because:

  • A. Marginal Product becomes negative
  • B. Total Product is still rising and Marginal Product is positive ✓
  • C. Average Product reaches its maximum
  • D. All inputs are fully utilized with no waste

Answer: B — In Stage II, Total Product continues to rise (MP is positive), making it the economically rational zone for production, unlike Stage III where MP turns negative.

Q6. Which statement about Fixed Cost (FC) is NOT correct?

  • A. Fixed Cost remains constant regardless of output level
  • B. Fixed Cost must be paid even if the firm produces zero output
  • C. Average Fixed Cost falls as output increases
  • D. Fixed Cost increases proportionally with increase in output ✓

Answer: D — Fixed Cost by definition does not change with output level; it remains constant, so it cannot increase proportionally with output.

Q7. A firm's Total Fixed Cost is Rs 1000 and Total Variable Cost for 5 units of output is Rs 500. What is the Average Total Cost per unit?

  • A. Rs 100
  • B. Rs 200
  • C. Rs 300 ✓
  • D. Rs 500

Answer: C — Average Total Cost = Total Cost ÷ Quantity = (TFC + TVC) ÷ Q = (1000 + 500) ÷ 5 = Rs 300 per unit.

Q8. When Marginal Cost equals Average Cost, which of the following must be true?

  • A. Average Cost is at its maximum point
  • B. Average Cost is at its minimum point ✓
  • C. Total Cost is zero
  • D. Marginal Cost is zero

Answer: B — The MC curve intersects the AC curve at the minimum point of AC; this is the point where neither pulling down (MC < AC) nor pulling up (MC > AC) occurs.

Q9. Study the following data: Output (units): 0, 1, 2, 3, 4 Total Product: 0, 5, 12, 18, 22 If Marginal Product of the 3rd unit is 6, what is the Total Product of the 2nd unit?

  • A. 5 units
  • B. 6 units
  • C. 7 units
  • D. 12 units ✓

Answer: D — The table directly gives Total Product at 2 units of labour as 12. This is confirmed by the Marginal Product check: MP of the 3rd unit = TP3 − TP2 = 18 − 12 = 6, which matches the value given in the question.

Q10. Which of the following is an example of a fixed factor in the short-run?

  • A. Raw materials purchased for production
  • B. Wages paid to temporary workers
  • C. Factory building and machinery ✓
  • D. Electricity consumed during production

Answer: C — In the short-run, capital (factory building and machinery) is fixed because it cannot be quickly bought or sold; raw materials, wages, and electricity are variable costs that change with output.

Flashcards

What is a production function?

A production function is the relationship between inputs used and maximum output that can be produced for a given technology.

Define Total Product (TP).

Total Product is the total amount of output produced by a firm using a given quantity of inputs.

What is Marginal Product (MP)?

Marginal Product is the change in total output when one more unit of a variable input (like labour) is used, holding other inputs constant.

How is Average Product (AP) calculated?

Average Product = Total Product ÷ Number of units of the variable factor.

What is the difference between short-run and long-run production?

In the short-run at least one factor is fixed, but in the long-run all factors can be varied.

Define an isoquant.

An isoquant is the set of all possible combinations of two inputs that produce the same maximum level of output.

What is Total Cost (TC)?

Total Cost is the sum of Total Fixed Costs (TFC) and Total Variable Costs (TVC).

How is Marginal Cost (MC) calculated?

Marginal Cost = Change in Total Cost ÷ Change in Quantity of output, or ΔTC/ΔQ.

Why is Average Fixed Cost (AFC) always falling?

Because the same fixed cost is spread over an increasing number of units as output rises, so per-unit fixed cost decreases.

State the relationship between MC and AC curves.

MC cuts the AC curve at its minimum point; when MC is below AC, AC falls, and when MC is above AC, AC rises.

Important Board Questions

Define production function and explain with an example how it shows the relationship between inputs and output. [2 marks]

State that production function q = f(L,K) shows maximum output from given inputs for a fixed technology. Give one real example (e.g., farmer using land and labour to produce wheat, or tailor using cloth, thread, and labour to produce shirts).

A firm has the following cost data: Output: 1, 2, 3, 4, 5 Total Cost (Rs): 50, 80, 105, 140, 180 Calculate the Marginal Cost and Average Cost for the 4th unit of output. Show all working steps. [5 marks]

For MC: use formula MC = ΔTC ÷ ΔQ = (TC4 − TC3) ÷ (4 − 3). For AC: use formula AC = TC ÷ Q = TC4 ÷ 4. Calculate both values step-by-step and show each calculation clearly.

Explain the Law of Variable Proportions with reference to the three stages of production. Why is Stage II considered the economically rational zone for firms? Use a numerical or graphical illustration. [6 marks]

Define the three stages: Stage I (MP rising), Stage II (MP positive but falling, TP rising), Stage III (MP negative). Explain why Stage II is preferred: MP remains positive so TP keeps rising, and firm operates efficiently without wastage of variable input. Include or derive MP and TP values to show the transition between stages, or draw a TP-MP curve showing all three stages clearly.

Assertion-Reason Questions for Production and Costs

Q1. Assertion (A):

A production function must assume that inputs are used efficiently to produce the maximum possible output for any given combination of inputs.

Reason (R):

Efficiency in production means no wastage of resources and optimal utilization of available inputs according to existing technology.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true, and the reason correctly explains why production functions must assume efficiency—they define maximum output by definition, which requires efficient input use. This is the core principle of production function modeling.

Q2. Assertion (A):

In the short run, a textile factory cannot increase output beyond a certain limit because at least one factor of production remains fixed.

Reason (R):

The short run is a time period where capital can be easily adjusted while labour cannot be changed.

Answer: C — A is true but R is false — The assertion is correct—the short run has fixed factors that limit output flexibility. However, the reason is not necessarily true: the reason assumes capital is always variable and labour always fixed, but either factor could be fixed depending on the firm's circumstances. The reason overgeneralizes.

Q3. Assertion (A):

Two different combinations of labour and capital that produce identical output levels must lie on the same isoquant.

Reason (R):

An isoquant is defined as a curve representing all input combinations that produce the same maximum level of output.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both assertion and reason are true, and the reason directly explains why combinations with identical output lie on the same isoquant—this is the definition of an isoquant. The assertion follows logically from the reason's definition.

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Case-Based Questions (CBQ) for Production and Costs

Case Study:

Rajesh owns a small garment manufacturing unit in Tamil Nadu that produces school uniforms. The factory currently operates with 5 sewing machines (capital) and employs 20 workers (labour). His production data shows that with this combination, he produces 500 uniforms per month. Recently, the demand for uniforms increased, and Rajesh wants to increase production to 750 uniforms per month. However, due to limited factory space and existing layout, he cannot immediately install new machines. He can only hire more workers on a contract basis.

Q1. Which of the following best describes Rajesh's current production scenario?

  • A. Long-run production because he can vary all factors freely
  • B. Short-run production because capital (sewing machines) is fixed at 5 units ✓
  • C. Long-run production because he employs 20 workers
  • D. Short-run production because he wants to increase output

Answer: B

Q2. To increase output from 500 to 750 uniforms per month in the short run, which factor should Rajesh primarily adjust?

  • A. Capital (install new sewing machines immediately)
  • B. Labour (hire additional contract workers) ✓
  • C. Both capital and labour equally
  • D. Technology (upgrade the sewing machine models)

Answer: B

Q3. If Rajesh's production function for uniforms is q = 10 × L^0.5 × K^0.5, where L is labour and K is capital, what is the maximum output with 4 workers and 9 machines? (Hint: √4 = 2, √9 = 3)

  • A. 120 uniforms
  • B. 360 uniforms
  • C. 240 uniforms
  • D. 180 uniforms ✓

Answer: D

Q4. In the long run, if Rajesh wants to maintain flexibility to adjust output, which strategy would be most effective?

  • A. Increase only labour while keeping machines fixed permanently
  • B. Keep the factory layout unchanged regardless of demand
  • C. Vary both capital and labour simultaneously to optimize production ✓
  • D. Focus only on hiring permanent employees

Answer: C

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