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These are complete exercise solutions for Samacheer Kalvi 11th Economics Chapter 4 — Cost and Revenue Analysis. Solve each question yourself first, then verify your method and answer below. Pay special attention to the cost curve relationships and revenue formulas — they appear frequently in board exams.
Key Concepts (Quick Recap)
Cost Concepts
| Concept | Definition | Formula |
|---|
| Total Fixed Cost (TFC) | Cost that does not vary with output | TFC = TC – TVC |
| Total Variable Cost (TVC) | Cost that varies directly with output | TVC = TC – TFC |
| Total Cost (TC) | Sum of all costs at a given output | TC = TFC + TVC |
| Average Fixed Cost (AFC) | Fixed cost per unit of output | AFC = TFC / Q |
| Average Variable Cost (AVC) | Variable cost per unit of output | AVC = TVC / Q |
| Average Cost (AC) | Total cost per unit of output | AC = TC / Q = AFC + AVC |
| Marginal Cost (MC) | Addition to total cost from producing one more unit | MC = ΔTC / ΔQ |
| Semi-Variable Cost | Cost that is partly fixed and partly variable | e.g., electricity bill |
Revenue Concepts
| Concept | Definition | Formula |
|---|
| Total Revenue (TR) | Total earnings from sale of output | TR = P × Q |
| Average Revenue (AR) | Revenue per unit of output | AR = TR / Q = P |
| Marginal Revenue (MR) | Addition to total revenue from selling one more unit | MR = ΔTR / ΔQ |
Short-Run Cost Curve Relationships
- AFC falls continuously as output increases (rectangular hyperbola).
- AVC first falls, reaches a minimum, then rises (U-shaped).
- AC is U-shaped — it falls initially due to falling AFC and AVC, then rises as AVC dominates.
- MC is also U-shaped — it intersects both AVC and AC at their respective minimum points.
- The vertical distance between AC and AVC equals AFC, which shrinks as output rises.
Long-Run Cost Curves
- Long-Run Average Cost (LAC) is the envelope of all short-run AC curves — it is flatter and U-shaped.
- Long-Run Marginal Cost (LMC) passes through the minimum point of LAC.
- In the long run, there is no fixed cost; all costs are variable.
Revenue Under Different Market Structures
| Market Structure | AR Curve | MR Curve | AR vs MR |
|---|
| Perfect Competition | Horizontal (perfectly elastic) | Horizontal, coincides with AR | AR = MR = Price |
| Monopoly | Downward sloping | Downward sloping, below AR | AR > MR |
| Monopolistic Competition | Downward sloping (elastic) | Downward sloping, below AR | AR > MR |
I. Choose the Best Answer
Q1. In the short run, which of the following costs remains constant at all levels of output? (a) Total Cost (b) Total Variable Cost (c) Total Fixed Cost (d) Marginal Cost
Answer(c) — Total Fixed Cost (TFC) does not change with output in the short run. Whether output is zero or 100 units, fixed costs like rent, insurance, and salaries of permanent staff remain the same.
Q2. The MC curve intersects the AC curve at its: (a) Rising portion (b) Falling portion (c) Minimum point (d) Maximum point
Answer(c) — When MC is below AC, AC falls; when MC is above AC, AC rises. Therefore, MC must equal AC at AC's minimum point. This is a fundamental cost curve relationship and a frequently tested concept.
Q3. When AR is constant, MR equals: (a) Zero (b) AR (c) Less than AR (d) Greater than AR
Answer(b) — Under perfect competition, price (AR) is constant. Since each additional unit sells at the same price, the addition to revenue (MR) equals that price. Hence AR = MR = Price.
Q4. Which of the following is a semi-variable cost? (a) Rent (b) Raw materials (c) Electricity charges (d) Wages of casual labour
Answer(c) — Electricity charges have a fixed component (meter rent, minimum charge) and a variable component (charge per unit of consumption). This makes it semi-variable. Rent is fully fixed; raw materials and casual wages are fully variable.
Q5. The break-even point is reached when: (a) TR > TC (b) TR = TC (c) TR < TC (d) MR = MC
Answer(b) — The break-even point is the output level where Total Revenue equals Total Cost, meaning the firm earns zero economic profit (normal profit only). Below this point, the firm incurs a loss.
Q6. Average Fixed Cost curve is: (a) U-shaped (b) Upward sloping (c) Downward sloping throughout (d) Horizontal
Answer(c) — Since AFC = TFC / Q and TFC is constant, AFC falls continuously as output increases. The AFC curve is a rectangular hyperbola — it is downward sloping throughout and never touches the X-axis.
Q7. The vertical distance between AC and AVC curves equals: (a) MC (b) AFC (c) TC (d) TVC
Answer(b) — AC = AFC + AVC. Therefore, AC – AVC = AFC. The vertical gap between the AC and AVC curves represents Average Fixed Cost, which shrinks as output increases.
II. Fill in the Blanks
1. The cost that does not change with the level of output is called Fixed Cost. 2. Marginal Cost = ΔTC / ΔQ. 3. Average Cost = Average Fixed Cost + Average Variable Cost. 4. When MR becomes negative, Total Revenue decreases. 5. The LAC curve is also called the Envelope Curve because it envelopes all short-run AC curves. 6. Under perfect competition, the AR curve is horizontal (perfectly elastic). 7. Total Revenue = Price × Quantity. 8. The point where TR = TC is called the Break-Even Point. 9. When MC is below AC, the AC curve falls. 10. Semi-variable cost is also known as Semi-Fixed Cost. 11. In the long run, all costs are variable (there are no fixed costs). 12. The AFC curve is a rectangular hyperbola. 13. The area under the MC curve gives Total Variable Cost. 14. When AR is downward sloping, MR lies below AR.
III. True or False
1. "Fixed cost is zero when output is zero"
AnswerFalse Fixed cost remains constant at all output levels, including zero. Even when a firm produces nothing, it still pays rent, insurance, and other fixed obligations. The cost that is zero at zero output is Variable Cost.
2. "Average Fixed Cost falls continuously as output increases"
AnswerTrue Since AFC = TFC / Q, as Q increases, AFC decreases. The AFC curve is a rectangular hyperbola that approaches but never touches the X-axis.
3. "Marginal Cost depends only on variable cost"
AnswerTrue In the short run, fixed cost does not change when output changes. Therefore, the change in total cost equals the change in variable cost. MC = ΔTC / ΔQ = ΔTVC / ΔQ.
4. "Under monopoly, AR is greater than MR"
AnswerTrue A monopolist must lower price to sell additional units, which reduces revenue on all previous units. Hence, MR is always less than AR when the demand curve (AR curve) slopes downward.
5. "The long-run average cost curve is U-shaped because of diminishing returns"
AnswerFalse Diminishing returns are a short-run phenomenon (some factors are fixed). The LAC curve is U-shaped because of economies and diseconomies of scale. Initially, increasing returns to scale (economies) lower LAC; eventually, decreasing returns to scale (diseconomies) raise LAC.
6. "When MR = 0, Total Revenue is maximum"
AnswerTrue When MR is positive, each additional unit adds to TR, so TR is rising. When MR is negative, each additional unit reduces TR. Therefore, TR is at its maximum when MR = 0.
IV. Match the Following
Set 1 — Cost Concepts and Definitions
| Column I | Column II |
|---|
| (a) Total Fixed Cost | (iii) Does not vary with output |
| (b) Marginal Cost | (v) Addition to total cost from one more unit |
| (c) Average Variable Cost | (i) TVC divided by output |
| (d) Semi-Variable Cost | (vi) Partly fixed and partly variable |
| (e) Long-Run Average Cost | (ii) Envelope curve |
| (f) Average Fixed Cost | (iv) TFC divided by output; rectangular hyperbola |
Set 2 — Revenue Under Different Markets
| Column I | Column II |
|---|
| (a) Perfect Competition | (iii) AR = MR = Price |
| (b) Monopoly | (i) AR > MR; AR slopes downward |
| (c) Break-even Point | (iv) TR = TC |
| (d) Marginal Revenue | (v) Change in TR divided by change in quantity |
| (e) Average Revenue | (ii) TR divided by quantity; equals price |
| (f) When MR = 0 | (vi) TR is maximum |
V. Answer Briefly
Q1. Distinguish between Fixed Cost and Variable Cost.
Answer
| Basis | Fixed Cost | Variable Cost |
|---|
| Definition | Does not change with output | Changes directly with output |
| Examples | Rent, insurance, salaries of permanent staff | Raw materials, fuel, casual wages |
| At zero output | Remains the same (not zero) | Becomes zero |
| Curve shape | Horizontal straight line | Initially rises at decreasing rate, then at increasing rate |
| Long run | Does not exist (all costs become variable) | Exists |
| Also called | Overhead cost, supplementary cost | Prime cost, direct cost |
Q2. What is the relationship between MC and AC?
Answer
The relationship between Marginal Cost and Average Cost has three phases: 1. When MC < AC: The average cost falls because the additional unit costs less than the current average, pulling the average down. 2. When MC = AC: The average cost is at its minimum point. The MC curve intersects the AC curve at its lowest point. 3. When MC > AC: The average cost rises because the additional unit costs more than the current average, pushing the average up.
The same relationship holds between MC and AVC. This is analogous to a student's GPA — if your latest grade (MC) is below your current GPA (AC), your GPA falls; if above, it rises.
Q3. Why is the short-run Average Cost curve U-shaped?
Answer
In the short run, AC = AFC + AVC. Initially, as output increases, both AFC and AVC fall. AFC falls continuously because fixed cost is spread over more units. AVC initially falls due to better utilisation of variable factors and increasing returns to the variable factor. However, after a certain output level, the law of diminishing returns sets in — each additional unit of variable input contributes less, so AVC starts rising. Once the rise in AVC outweighs the fall in AFC, the AC curve begins to rise, creating the U-shape.
Q4. Define Marginal Revenue. How is it calculated?
Answer
Marginal Revenue is the addition to total revenue from the sale of one more unit of output. It measures the rate of change of total revenue.
FormulaMR = ΔTR / ΔQ = TR_n – TR_{n-1}
Under perfect competition (constant price): MR = AR = Price, because each unit sells at the same price.
Under monopoly/imperfect competition (declining price): MR < AR, because to sell one more unit, the firm must lower the price on all units, so the gain from the extra unit is partly offset by the loss on previous units.
Example: If TR at 5 units is ₹500 and TR at 6 units is ₹540, then MR = 540 – 500 = ₹40.
VI. Answer in Detail
Q1. Explain the various short-run cost curves with suitable diagrams and their interrelationships.
Answer
In the short run, some factors of production are fixed. This gives rise to both fixed and variable costs. The key short-run cost curves are:
Total Cost Curves:
- TFC curve: A horizontal straight line parallel to the X-axis, since fixed cost does not change with output.
- TVC curve: Starts from the origin (TVC = 0 at zero output) and rises — first at a decreasing rate (increasing returns), then at an increasing rate (diminishing returns). It is an inverse-S shaped curve.
- TC curve: Starts from the point where TFC meets the Y-axis (since TC = TFC + TVC and at zero output TC = TFC). It is parallel to the TVC curve, with the vertical distance between them equal to TFC at all output levels.
Average Cost Curves:
- AFC curve: A rectangular hyperbola. Since AFC = TFC / Q and TFC is constant, AFC falls continuously as output increases. It never touches the X-axis.
- AVC curve: U-shaped. Initially falls as variable factors are used more efficiently, then rises due to diminishing returns. The minimum of AVC occurs at a lower output than the minimum of AC.
- AC curve: U-shaped. AC = AFC + AVC, so it lies above both. The vertical gap between AC and AVC equals AFC, which shrinks as output increases. This means AC and AVC curves converge at high output levels but never touch.
- MC curve: U-shaped. It cuts both the AVC and AC curves at their respective minimum points from below. When MC is below AVC/AC, those curves fall; when MC is above, they rise. The MC curve reaches its minimum before the AVC and AC curves reach theirs.
Key Relationships: 1. MC intersects AC at its minimum point. 2. MC intersects AVC at its minimum point. 3. The gap between AC and AVC narrows as output increases (because AFC shrinks). 4. When MC < AC, AC falls; when MC > AC, AC rises. 5. TC = TFC + TVC at every output level.
Q2. Explain the concept of Long-Run Average Cost (LAC) curve. Why is it called the envelope curve?
Answer
The long run is a period in which all factors of production are variable — there are no fixed costs. The firm can choose any plant size (scale of operation).
Construction of the LAC Curve:
- The firm can operate with different plant sizes, each represented by a different short-run AC curve (SAC_1, SAC_2, SAC_3, etc.).
- For any given output, the firm selects the plant size that minimises cost. This means choosing the SAC curve with the lowest point (or relevant portion) for that output.
- The LAC curve is drawn by tracing the lower boundary of all the short-run AC curves. It is the locus of the least-cost points for every level of output.
Why Called the Envelope Curve:
- The LAC curve "envelopes" or wraps around all the short-run AC curves. Each SAC curve is tangent to the LAC curve at exactly one point, and the LAC curve never lies above any SAC curve at any output level.
- Only at the minimum point of the LAC curve does it touch the minimum point of one SAC curve (the optimal plant size). At all other output levels, the LAC is tangent to a SAC curve at a point other than that SAC's minimum.
Shape of LAC Curve:
- The LAC curve is U-shaped, but flatter (broader) than the short-run AC curves.
- Falling portion: Economies of scale — as the firm increases its scale, it benefits from specialisation, bulk purchasing, technical advantages, and managerial efficiencies.
- Rising portion: Diseconomies of scale — beyond a certain size, coordination problems, bureaucratic delays, and communication failures increase per-unit costs.
Long-Run Marginal Cost (LMC):
- The LMC curve passes through the minimum point of the LAC curve, just as SMC passes through the minimum of SAC.
- LMC = ΔLTC / ΔQ.
- LMC is below LAC when LAC is falling, above LAC when LAC is rising, and equals LAC at LAC's minimum.
Q3. Explain the relationship between Average Revenue and Marginal Revenue under different market conditions.
Answer
The relationship between AR and MR depends on the market structure in which the firm operates:
1. Perfect Competition:
- There are many buyers and sellers, and the product is homogeneous. The firm is a price taker.
- The firm can sell any quantity at the prevailing market price.
- Since price is constant, each additional unit adds the same amount to total revenue.
ResultAR = MR = Price. The AR curve is a horizontal straight line at the market price level. The MR curve coincides with it.
- Example: If market price is ₹10 per unit, then TR at 5 units = ₹50, TR at 6 units = ₹60. MR = 60 – 50 = ₹10 = AR = Price.
2. Monopoly:
- There is a single seller facing a downward-sloping demand curve. The monopolist must lower price to sell more.
ResultAR > MR at all output levels. The AR curve slopes downward, and the MR curve lies below it, also downward sloping.
- Why AR > MR: When the monopolist sells one more unit at a lower price, the revenue from that unit is partly offset by the loss of revenue on all previous units that could have been sold at the higher price. Therefore, MR is less than the price (AR).
FormulaMR = AR – (AR × 1/Q × ΔAR/ΔQ × Q), simplified as MR = AR + Q × (dAR/dQ). Since dAR/dQ is negative (AR is falling), MR < AR.
3. Monopolistic Competition:
- Many firms sell differentiated products. Each firm faces a downward-sloping demand curve that is relatively elastic (due to close substitutes).
ResultAR > MR, similar to monopoly. The AR curve slopes downward and the MR curve lies below it.
- The difference from monopoly is that the AR curve is more elastic (flatter) because consumers can switch to substitutes.
4. Relationship Summary Table:
Answer
| Market | AR Shape | MR Position | AR vs MR | TR Behaviour |
|---|
| Perfect Competition | Horizontal | Coincides with AR | AR = MR = Price | TR rises proportionally with Q |
| Monopoly | Downward sloping | Below AR | AR > MR | TR rises then falls |
| Monopolistic Competition | Downward sloping (elastic) | Below AR | AR > MR | TR rises then falls |
Numerical Illustration (Monopoly):
| Q | Price (AR) | TR | MR |
|---|
| 1 | 10 | 10 | 10 |
| 2 | 9 | 18 | 8 |
| 3 | 8 | 24 | 6 |
| 4 | 7 | 28 | 4 |
| 5 | 6 | 30 | 2 |
| 6 | 5 | 30 | 0 |
| 7 | 4 | 28 | –2 |
This table shows that AR > MR throughout, and when MR = 0, TR is maximum (₹30 at Q = 5 or 6 units).
Common Mistakes to Avoid
1. Confusing Fixed Cost with Total Cost at zero output — At zero output, TC = TFC (not zero). Variable cost is what becomes zero, not fixed cost. Students often incorrectly state that fixed cost is zero at zero output.
2. Treating AC and MC as the same — AC is cost per unit (TC/Q); MC is the cost of the last unit (ΔTC/ΔQ). They are equal only at the minimum point of the AC curve.
3. Saying "all costs are fixed in the short run" — In the short run, costs are divided into fixed and variable. Only in the long run do all costs become variable (there are no fixed costs).
4. Drawing the AFC curve as U-shaped — AFC is a rectangular hyperbola that falls continuously. It never rises and never touches the X-axis. Only AVC and AC are U-shaped.
5. Confusing break-even point with shut-down point — The break-even point is where TR = TC (normal profit). The shut-down point is where TR = TVC (the firm covers only variable costs and minimises losses by continuing production in the short run rather than shutting down).
6. Assuming MR = AR always — This is true only under perfect competition. Under monopoly and monopolistic competition, AR > MR. The difference between AR and MR widens as the demand curve becomes less elastic.
7. Forgetting that LAC is flatter than SAC — The LAC curve is an envelope of SAC curves and is U-shaped but broader/flatter. Students often draw it as steep as the SAC curves, which is incorrect.
8. Ignoring semi-variable costs — Not all costs neatly fit into fixed or variable categories. Electricity bills, telephone charges, and maintenance costs have both fixed and variable components. These are semi-variable (or semi-fixed) costs.
Exam Checklist
- [ ] Definitions of all cost concepts memorised (TFC, TVC, TC, AFC, AVC, AC, MC)
- [ ] Definitions of all revenue concepts memorised (TR, AR, MR)
- [ ] All key formulas can be written from memory (TC = TFC + TVC, AC = AFC + AVC, MC = ΔTC/ΔQ, MR = ΔTR/ΔQ, TR = P × Q)
- [ ] Shape of each short-run cost curve explained (AFC = rectangular hyperbola, AVC/AC/MC = U-shaped)
- [ ] MC intersects AC and AVC at their minimum points — both the fact and the reason understood
- [ ] LAC as envelope curve — definition, construction, and why it is U-shaped (economies and diseconomies of scale)
- [ ] AR and MR relationship under perfect competition, monopoly, and monopolistic competition
- [ ] Break-even point (TR = TC) and shut-down point (TR = TVC) clearly distinguished
- [ ] Numerical practice: calculating MC, AC, MR, TR from given schedules
- [ ] Diagram practice: able to draw short-run cost curves, LAC envelope, and revenue curves under different market structures
Internal Links
- [Chapter 4 Guide — Cost and Revenue Analysis](/school/tamil-nadu-state-board/class/11/economics/cost-and-revenue-analysis)
- [All Class 11 Economics Solutions](/school/tamil-nadu-state-board/class/11/economics/solutions)
- [Class 11 Economics Subject Guide](/school/tamil-nadu-state-board/class/11/economics)
