This MCQ module is based on: Supply Curves, Elasticity of Supply & Exercises
TOPIC 11 OF 13
Supply Curves, Elasticity of Supply & Exercises
🎓 Class 12
Economics
CBSE
Theory
Chapter 4 — The Theory of the Firm under Perfect Competition
⏱ ~28 min
🌐 Language: [gtranslate]
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Supply Curves, Market Supply, Price Elasticity & Exercises
Parts 1 and 2 finished the foundations: a price-taking firm with AR = MR = p, and the three conditions that pin down its profit-maximising output. Part 3 reaps the harvest. We now derive the firm's supply curve in the short and long run — and discover that it is simply the rising portion of MC, sitting above the relevant cost floor (AVC short run, LRAC long run). We then explore what shifts a supply curve (technology, input prices, taxes, expectations, related goods, the number of firms in the market) and add up individual supply curves horizontally to obtain the market supply. The chapter closes with the price elasticity of supply. The page ends with full model answers to every NCERT exercise — Q1 to Q27 — alongside a one-page summary and a glossary of key terms.
4.4 Supply Curve of a Firm
A firm's supply? is the quantity it chooses to sell at a given price, with technology and the prices of factors of production held fixed. A table that lists the quantity supplied at each price (other things constant) is a supply schedule; its graphical version, with output on the X-axis and price on the Y-axis, is the supply curve?. NCERT distinguishes the short-run supply curve from the long-run supply curve.
4.4.1 Short-Run Supply Curve of a Firm
Split the derivation into two cases, exactly as the textbook does.
📖 Case 1 — Price ≥ minimum AVC
Suppose the market price is p₁ and p₁ > min AVC. Equate p₁ with SMC on the rising part of the SMC curve — this gives output q₁. At q₁, AVC ≤ p₁, so all three conditions for profit maximisation hold. Hence the firm supplies q₁.
📖 Case 2 — Price < minimum AVC
Suppose the market price is p₂ and p₂ < min AVC. The third condition (p ≥ AVC) is violated at every positive output. So the firm supplies zero.
Combining the two cases yields the textbook conclusion:
⭐ Short-Run Supply Curve
The short-run supply curve of a firm is the rising part of the SMC curve from and above minimum AVC, together with zero output for all prices strictly less than minimum AVC. There is a "kink" — actually a discontinuity — at the minimum-AVC point: just above it the firm supplies a positive output; just below it, zero.
Figure 4.8 — Short-run supply curve. Bold blue: rising part of SMC above minimum AVC. Bold yellow: zero supply along the price axis when p < min AVC. The two pieces meet at the shut-down point.
4.4.2 Long-Run Supply Curve of a Firm
The same logic applies, with one key change: in the long run there are no fixed costs to keep the firm in the market when revenue can't cover cost. So the relevant comparison is now p versus LRAC, not AVC.
- If p₁ ≥ min LRAC, equate p₁ with LRMC on the rising part of LRMC; the firm supplies that output.
- If p₂ < min LRAC, the firm exits — supply is zero.
⭐ Long-Run Supply Curve
The long-run supply curve of a firm is the rising part of the LRMC curve from and above minimum LRAC, together with zero output for all prices less than minimum LRAC.
Figure 4.10 — Long-run supply curve. Bold blue: rising LRMC above min LRAC. Bold yellow: zero supply for all p < min LRAC.
4.4.3 The Shut-Down Point
Move down the supply curve from any high price. The last price–output combination at which the firm produces a positive output is the shut-down point?. In the short run this is min AVC, where SMC cuts AVC. In the long run it is min LRAC.
4.4.4 Normal Profit and the Break-Even Point
NCERT defines normal profit as the minimum profit needed to keep the firm in the existing business — equal to the entrepreneur's opportunity cost. Profit over and above this level is supernormal profit. The point on the supply curve at which the firm earns only normal profit is the break-even point; geometrically, it is the point of minimum AC at which the supply curve cuts the AC curve (LRAC long run, SAC short run).
💡 Opportunity Cost
Opportunity cost of an activity = the gain foregone from the second-best alternative. NCERT's example: with Rs 1,000 you could get 0% (home safe), 10% (Bank-1) or 5% (Bank-2). Investing in your family business means you forego the best alternative — Bank-1's Rs 100 — so the opportunity cost is Rs 100.
4.5 Determinants of a Firm's Supply Curve (What Shifts Supply?)
Because the supply curve is essentially a slice of the MC curve, anything that moves MC moves supply. NCERT highlights two main forces and a third (taxes) in a separate box.
Technological progress
An organisational or technical innovation lets the same inputs produce more output. MC falls at every q — MC curve shifts right/down. Supply curve shifts to the right: more is supplied at every price.
Input prices ↑
A rise in any input price (e.g. wage rate) raises both AC and MC at every q. MC curve shifts left/up. Supply curve shifts to the left: less is supplied at every price.
Unit tax
A unit tax of Rs t raises LRMC and LRAC at every q by exactly Rs t. LRMC and LRAC shift up by Rs t. The long-run supply curve therefore shifts left: at any given market price the firm supplies fewer units.
Expectations
If firms expect higher future prices they may withhold output today, shifting current supply left; expectations of lower future prices have the opposite effect.
Prices of related goods
If a firm can produce two goods, a rise in the price of one may make it shift resources away from the other — supply of the second good falls.
Number of firms
As the number of firms in the market increases (decreases), the market supply curve shifts to the right (left), even when individual firm supply curves are unchanged.
4.5.1 Impact of a Unit Tax — NCERT's Geometric Treatment
A unit tax? is a tax of Rs t per unit of output sold. If the firm produces and sells 10 units, the total tax is 10 × Rs t = Rs 10t. Before the tax, the firm has cost curves LRMC₀ and LRAC₀. After the imposition of a unit tax of Rs t, the firm pays an extra Rs t for each unit produced — so its LRMC and LRAC at every q rise by exactly Rs t. The new curves LRMC₁ and LRAC₁ sit Rs t above the old ones.
Because the supply curve is the rising part of LRMC above min LRAC, the supply curve shifts left/up by Rs t. At any market price, the firm now supplies fewer units. This is precisely how an excise/unit tax discourages production at the margin.
4.6 Market Supply Curve
The market supply curve? shows the total output that all firms in the market produce in aggregate at each market price. With n firms in the market, the market supply at price p is simply the sum of every firm's individual supply at that price:
Sₘ(p) = S₁(p) + S₂(p) + ... + Sₙ(p)
4.6.1 Geometric Construction (Two Firms, Different Cost Structures)
Imagine a market with just two firms, with different cost structures: firm 1 starts producing at p = p₁, firm 2 starts producing at p = p₂, with p₂ > p₁. The market supply curve is built piecewise:
- For p < p₁ — neither firm produces; market supply = 0.
- For p₁ ≤ p < p₂ — only firm 1 produces; market supply = S₁(p).
- For p ≥ p₂ — both firms produce; market supply = S₁(p) + S₂(p) (horizontal sum).
At market price p₃ > p₂, firm 1 supplies q₃ and firm 2 supplies q₄, so market supply at p₃ is q₅ = q₃ + q₄. Geometrically the market supply curve is obtained by horizontally adding the individual supply curves at each price level.
Figure 4.13 — Market supply curve constructed by horizontal addition of the individual supply curves at each price.
The market supply curve has been derived for a fixed number of firms. As the number of firms changes, the market supply curve shifts: more firms shift Sₘ to the right; fewer firms shift it to the left.
4.6.2 NCERT's Numerical Example
Two firms with supply functions:
S₁(p) = 0 if p < 10; S₁(p) = p − 10 if p ≥ 10
S₂(p) = 0 if p < 15; S₂(p) = p − 15 if p ≥ 15
S₂(p) = 0 if p < 15; S₂(p) = p − 15 if p ≥ 15
Adding piecewise:
Sₘ(p) = 0 if p < 10
Sₘ(p) = (p − 10) if 10 ≤ p < 15
Sₘ(p) = (p − 10) + (p − 15) = 2p − 25 if p ≥ 15
Sₘ(p) = (p − 10) if 10 ≤ p < 15
Sₘ(p) = (p − 10) + (p − 15) = 2p − 25 if p ≥ 15
4.7 Price Elasticity of Supply
The price elasticity of supply? measures how responsively quantity supplied reacts to a change in the price of the good. NCERT denotes it by eₛ:
eₛ = (% change in quantity supplied) ÷ (% change in price)
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (ΔQ / ΔP) × (P₁ / Q₁)
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (ΔQ / ΔP) × (P₁ / Q₁)
4.7.1 NCERT's Worked Numerical Example
Suppose the cricket-ball market is perfectly competitive. At P₁ = Rs 10, Q₁ = 200. At P₂ = Rs 30, Q₂ = 1000. Then:
% ΔQ = (1000 − 200) / 200 × 100 = 400%
% ΔP = (30 − 10) / 10 × 100 = 200%
eₛ = 400 / 200 = 2
% ΔP = (30 − 10) / 10 × 100 = 200%
eₛ = 400 / 200 = 2
An elasticity of 2 means a 1% rise in price brings forth a 2% rise in quantity supplied — supply is fairly responsive.
4.7.2 Properties
- If the supply curve is vertical, supply is completely insensitive to price ⇒ eₛ = 0.
- For a positively sloped supply curve, a price rise raises quantity supplied ⇒ eₛ > 0.
- The price elasticity of supply, like the price elasticity of demand, is independent of units.
4.7.3 The Geometric Method (Three Cases)
For a straight-line supply curve, the elasticity at a point S is the ratio Mq₀ / Oq₀, where M is the point at which the line (extended if needed) cuts the quantity axis.
- Panel (a): straight line cuts the price axis at its positive range. M lies in the negative quantity range. So Mq₀ > Oq₀, hence eₛ > 1 at every point.
- Panel (b): straight line passes through the origin. Then M coincides with the origin, Mq₀ = Oq₀, and eₛ = 1 at every point.
- Panel (c): straight line cuts the quantity axis at a positive value. Then Mq₀ < Oq₀, hence eₛ < 1 at every point.
Figure 4.14 — Three cases of price elasticity for straight-line supply curves: (a) cuts price axis ⇒ eₛ > 1; (b) through origin ⇒ eₛ = 1; (c) cuts quantity axis ⇒ eₛ < 1.
Illustrative supply curve: zero output below min AVC, then rising MC above it. The "kink" at p = 14 is the shut-down point.
Activity 4.3 — A Tax Diary
- Pick a familiar everyday product (sugar, cement, petrol).
- Find out the central + state unit tax (excise/VAT/GST cess) currently applied.
- Discuss how this unit tax shifts the LRMC, LRAC and supply curves of a typical firm in that industry.
- Predict whether the market supply will shift by the full tax or by less (think: producers vs. consumers, elasticity).
Sample observation: Petrol carries excise + VAT amounting to roughly Rs 35–45 per litre across Indian states (figures fluctuate). Each rupee of unit tax shifts the firm's LRMC and LRAC up by Rs 1, so the long-run supply curve of refineries and pumps shifts left. The full upward shift in the supply curve is by the amount of the tax. How much of this tax burden is borne by consumers depends on the relative elasticities of demand and supply (a topic chapter 5 explores under market equilibrium).
Competency-Based Questions — Supply & Elasticity
Scenario: A perfectly competitive market for ceramic tiles consists of 50 identical firms. For each firm, min AVC = Rs 12, min SAC = Rs 18, min LRAC = Rs 20. The rising portion of every firm's SMC at price p (Rs 12 ≤ p ≤ 50) is given by q = (p − 12) / 2.
Q1. Derive the short-run market supply schedule at p = 10, p = 14, p = 20, p = 30.
L3 Apply
Answer: At p = 10 (< 12 = min AVC), each firm produces 0; market supply = 0. At p = 14, q = (14−12)/2 = 1 per firm; market supply = 50 × 1 = 50. At p = 20, q = (20−12)/2 = 4; market supply = 50 × 4 = 200. At p = 30, q = (30−12)/2 = 9; market supply = 50 × 9 = 450.
Q2. Identify the short-run shut-down point and the long-run break-even point. At which point will normal profit just be earned?
L4 Analyse
Answer: Short-run shut-down point = the price–output combination at which the SMC curve cuts AVC at its minimum, i.e. p = min AVC = Rs 12. Long-run break-even (and shut-down) point = where supply cuts LRAC at its minimum, i.e. p = min LRAC = Rs 20. Normal profit (π = 0) is earned exactly at the long-run break-even point, p = Rs 20.
Q3. Government imposes a unit tax of Rs 4 per tile. Show analytically the new long-run supply schedule of one firm at p = 24 and p = 30, and evaluate whether the firm will produce.
L5 Evaluate
Answer: The unit tax raises LRMC and LRAC at every q by Rs 4. New min LRAC = 20 + 4 = Rs 24. The firm will produce only if p ≥ Rs 24. At p = 24, the firm just earns normal profit at the new break-even output. At p = 30, after-tax MC equation becomes q = (30 − 12 − 4)/2 = 7. The firm produces 7 tiles. Net effect of the tax is therefore to shift the long-run supply curve upward by Rs 4 (= leftward at every price), reducing market quantity at any given price.
Q4 (HOT). Suppose the price elasticity of supply for the tile industry is 1.5 in this market. Calculate the percentage change in market supply when price rises from Rs 20 to Rs 24, and compare with the change you would predict from the firm-level supply equation.
L6 Create
Answer: % ΔP = (24 − 20)/20 × 100 = 20%. With eₛ = 1.5, predicted % ΔQ = 1.5 × 20% = 30%. From the firm equation: at p = 20, q = 4 per firm × 50 firms = 200; at p = 24, q = (24−12)/2 = 6 per firm, market = 300. Actual % ΔQ = (300 − 200)/200 × 100 = 50%. The actual elasticity = 50/20 = 2.5, larger than the assumed 1.5. The discrepancy means our simple linear MC formula gives a more elastic supply than the assumed industry figure — possibly because real-world supply is constrained by capacity, learning effects or input bottlenecks.
Assertion–Reason Questions — Supply & Elasticity
Options for all items: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true, R is false. (D) A is false, R is true.
Assertion (A): The short-run supply curve of a firm is the rising portion of its SMC curve from and above the minimum AVC.
Reason (R): The firm produces a positive output only if all three profit-maximisation conditions hold; the short-run cost-cover condition rules out production when p < min AVC.
Reason (R): The firm produces a positive output only if all three profit-maximisation conditions hold; the short-run cost-cover condition rules out production when p < min AVC.
Correct option: (A). Both true; R explains A directly. Below min AVC, condition 3 is violated and the firm produces zero; above min AVC, conditions 1 and 2 force the firm onto the rising part of SMC.
Assertion (A): A unit tax shifts a firm's long-run supply curve to the left.
Reason (R): A unit tax raises the firm's LRMC and LRAC at every output level by exactly the amount of the tax, and the supply curve is the rising portion of LRMC above min LRAC.
Reason (R): A unit tax raises the firm's LRMC and LRAC at every output level by exactly the amount of the tax, and the supply curve is the rising portion of LRMC above min LRAC.
Correct option: (A). Both true; R explains A. Because supply tracks LRMC (above min LRAC), and LRMC has shifted up by the tax, the supply curve too shifts up by the tax — i.e. left at any given price.
Assertion (A): A straight-line supply curve passing through the origin has price elasticity equal to one at every point on the curve.
Reason (R): For such a supply curve, when extended, the line meets the quantity axis at the origin itself, so Mq₀ = Oq₀ and the geometric ratio Mq₀/Oq₀ equals 1.
Reason (R): For such a supply curve, when extended, the line meets the quantity axis at the origin itself, so Mq₀ = Oq₀ and the geometric ratio Mq₀/Oq₀ equals 1.
Correct option: (A). Both true; R is the correct geometric explanation. The "M coincides with O" geometry is exactly what makes eₛ = 1 at every point.
4.8 Complete NCERT Exercises — Model Answers
Below are full model answers to every exercise question in NCERT Chapter 4 (Q1–Q27). Toggle each to reveal.
Exercise Q1
What are the characteristics of a perfectly competitive market?
A perfectly competitive market has four defining features:
(1) Large number of buyers and sellers — each is so small that none can influence the market by their own size.
(2) Homogeneous product — every firm sells an identical good; output of any one firm cannot be told apart from another's.
(3) Free entry and exit of firms — no barriers to firms entering the market or leaving it.
(4) Perfect information — all buyers and sellers fully know the price, quality and other relevant details of the market.
The single distinguishing consequence is price-taking behaviour: no individual firm can influence price.
(1) Large number of buyers and sellers — each is so small that none can influence the market by their own size.
(2) Homogeneous product — every firm sells an identical good; output of any one firm cannot be told apart from another's.
(3) Free entry and exit of firms — no barriers to firms entering the market or leaving it.
(4) Perfect information — all buyers and sellers fully know the price, quality and other relevant details of the market.
The single distinguishing consequence is price-taking behaviour: no individual firm can influence price.
Exercise Q2
How are the total revenue of a firm, market price, and the quantity sold by the firm related to each other?
Total revenue (TR) is the product of market price (p) and quantity sold (q): TR = p × q. Under perfect competition the price is given (constant), so TR rises in direct proportion to q. The graph of TR against q is an upward-sloping straight line through the origin with slope equal to p.
Exercise Q3
What is the 'price line'?
The price line is the horizontal straight line drawn at a height equal to the market price p, plotted with output on the X-axis and price (or revenue per unit) on the Y-axis. Under perfect competition the price line plays three roles simultaneously: it is the firm's AR curve, its MR curve and the demand curve facing the firm — the latter is perfectly elastic at p.
Exercise Q4
Why is the total revenue curve of a price-taking firm an upward-sloping straight line? Why does the curve pass through the origin?
Because TR = p × q with p constant, TR is a linear function of q — its graph is a straight line. The slope (= p) is positive, so the line slopes upward. When q = 0, TR = 0, so the line begins at the origin. The line therefore passes through the origin and rises with a constant slope equal to the market price.
Exercise Q5
What is the relation between market price and average revenue of a price-taking firm?
AR = TR / q = (p × q) / q = p. So under perfect competition, the firm's average revenue equals the market price at every output level. Plotted against q, AR is a horizontal straight line at height p — it coincides with the price line.
Exercise Q6
What is the relation between market price and marginal revenue of a price-taking firm?
MR = ΔTR / Δq = [p(q₂) − p(q₁)] / (q₂ − q₁) = p(q₂ − q₁)/(q₂ − q₁) = p. So MR is constant and equal to the market price at every level of output. Hence under perfect competition AR = MR = p — and both curves coincide on the horizontal price line.
Exercise Q7
What conditions must hold if a profit-maximising firm produces positive output in a competitive market?
Three conditions, all at the optimum output q₀:
(i) Price = Marginal Cost (p = MC). This follows from the universal MR = MC rule, since MR = p for a price-taker.
(ii) MC must be non-decreasing at q₀ — i.e. MC must be on its rising stretch (this is the second-order condition that distinguishes a maximum from a minimum).
(iii) Cost-cover condition: in the short run, p ≥ minimum AVC; in the long run, p ≥ minimum LRAC. Below this floor the firm is better off producing zero.
(i) Price = Marginal Cost (p = MC). This follows from the universal MR = MC rule, since MR = p for a price-taker.
(ii) MC must be non-decreasing at q₀ — i.e. MC must be on its rising stretch (this is the second-order condition that distinguishes a maximum from a minimum).
(iii) Cost-cover condition: in the short run, p ≥ minimum AVC; in the long run, p ≥ minimum LRAC. Below this floor the firm is better off producing zero.
Exercise Q8
Can there be a positive level of output that a profit-maximising firm produces in a competitive market at which market price is not equal to marginal cost? Give an explanation.
No. As long as p > MC, producing one more unit raises TR by p and TC by MC; the firm gains (p − MC) in profit, so it should expand output. As long as p < MC, producing one less unit saves more cost (MC) than it loses revenue (p), so the firm should contract. Profit therefore rises until p = MC. Hence at any positive profit-maximising output, the market price must equal the marginal cost.
Exercise Q9
Will a profit-maximising firm in a competitive market ever produce a positive level of output in the range where the marginal cost is falling? Give an explanation.
No. Suppose the firm chose an output q₁ at which p = MC but MC was on its falling stretch. At an output slightly less than q₁, MC would be even higher (since MC is decreasing), so MC > p there. That means MR − MC = p − MC < 0 to the left of q₁ — but this implies that raising output up to q₁ reduced profit. Reversing the logic: cutting output a bit below q₁ would have increased profit. So q₁ cannot be a maximum. The firm's profit-maximising q lies on the rising part of MC — never on the falling part.
Exercise Q10
Will a profit-maximising firm in a competitive market produce a positive level of output in the short run if the market price is less than the minimum of AVC? Give an explanation.
No. If p < min AVC, then at every positive q, total revenue (p × q) is strictly less than total variable cost (AVC × q). Producing means losing (TVC − TR) plus still having to pay TFC — a total loss of TVC − TR + TFC, larger than TFC alone. Shutting down (q = 0) makes TR = TVC = 0, so the firm's loss is limited to TFC. Hence in the short run with p < min AVC, the firm produces zero — the so-called shut-down decision.
Exercise Q11
Will a profit-maximising firm in a competitive market produce a positive level of output in the long run if the market price is less than the minimum of AC? Give an explanation.
No. In the long run there are no fixed costs — the firm can vary every input. So shutting down means zero profit (zero loss). If at the best positive output the firm earns less than zero (because p < min LRAC, so TR < TC), it is strictly better off shutting down (zero) than continuing (negative). Hence the firm exits and produces zero in the long run whenever p < min LRAC.
Exercise Q12
What is the supply curve of a firm in the short run?
The short-run supply curve of a firm is the rising part of the SMC curve from and above the minimum AVC, together with zero output for all prices strictly less than the minimum AVC. Above min AVC the firm equates p with rising SMC; below min AVC the firm shuts down and supplies zero.
Exercise Q13
What is the supply curve of a firm in the long run?
The long-run supply curve of a firm is the rising part of the LRMC curve from and above the minimum LRAC, together with zero output for all prices strictly less than the minimum LRAC. Above min LRAC the firm equates p with rising LRMC; below min LRAC the firm exits and supplies zero.
Exercise Q14
How does technological progress affect the supply curve of a firm?
Technological progress lets the firm produce more output with the same inputs (or the same output with fewer inputs). At every q the firm's marginal cost falls — the MC curve shifts right/down. Because the supply curve is essentially a slice of the MC curve, the firm's supply curve also shifts right: at any given market price, the firm now supplies more output.
Exercise Q15
How does the imposition of a unit tax affect the supply curve of a firm?
A unit tax of Rs t raises the firm's LRMC and LRAC at every q by exactly Rs t — the cost curves shift up by Rs t. Since the long-run supply curve is the rising part of LRMC above min LRAC, the supply curve too shifts up by Rs t — equivalently, it shifts to the left. At any given market price the firm now supplies fewer units.
Exercise Q16
How does an increase in the price of an input affect the supply curve of a firm?
A rise in any input's price (e.g. wage rate) raises the firm's cost of production, which usually raises both AC and MC at every q. The MC curve therefore shifts left/up. As the supply curve tracks MC above the relevant cost floor, it shifts to the left: at any given market price the firm now supplies fewer units.
Exercise Q17
How does an increase in the number of firms in a market affect the market supply curve?
The market supply at any price is the horizontal sum of every firm's individual supply at that price. Adding more firms means more positive numbers being summed, so the market supply at every price rises. The market supply curve therefore shifts to the right. (A decrease in the number of firms shifts it to the left.)
Exercise Q18
What does the price elasticity of supply mean? How do we measure it?
The price elasticity of supply (eₛ) measures how responsively the quantity supplied of a good reacts to a change in its price. It is defined as the ratio of the percentage change in quantity supplied to the percentage change in price:
eₛ = (% ΔQ) ÷ (% ΔP) = (ΔQ / Q₁) ÷ (ΔP / P₁) = (ΔQ / ΔP) × (P₁ / Q₁)
For a vertical supply curve eₛ = 0; for a positively sloped supply curve eₛ > 0; eₛ is independent of units. Geometrically, on a straight-line supply curve, eₛ at a point S = Mq₀ / Oq₀ where M is the line's intersection with the quantity axis (extended if necessary).
eₛ = (% ΔQ) ÷ (% ΔP) = (ΔQ / Q₁) ÷ (ΔP / P₁) = (ΔQ / ΔP) × (P₁ / Q₁)
For a vertical supply curve eₛ = 0; for a positively sloped supply curve eₛ > 0; eₛ is independent of units. Geometrically, on a straight-line supply curve, eₛ at a point S = Mq₀ / Oq₀ where M is the line's intersection with the quantity axis (extended if necessary).
Exercise Q19
Compute the total revenue, marginal revenue and average revenue schedules in the following table. Market price of each unit of the good is Rs 10. (q = 0, 1, 2, 3, 4, 5, 6.)
With p = Rs 10, TR = 10q, AR = 10 (constant), MR = 10 (constant for q ≥ 1).
q | TR | MR | AR
0 | 0 | — | —
1 | 10 | 10 | 10
2 | 20 | 10 | 10
3 | 30 | 10 | 10
4 | 40 | 10 | 10
5 | 50 | 10 | 10
6 | 60 | 10 | 10
AR and MR coincide on the horizontal price line at Rs 10 — the trademark of perfect competition.
q | TR | MR | AR
0 | 0 | — | —
1 | 10 | 10 | 10
2 | 20 | 10 | 10
3 | 30 | 10 | 10
4 | 40 | 10 | 10
5 | 50 | 10 | 10
6 | 60 | 10 | 10
AR and MR coincide on the horizontal price line at Rs 10 — the trademark of perfect competition.
Exercise Q20
The following table shows the total revenue and total cost schedules of a competitive firm. Calculate the profit at each output level. Determine also the market price of the good. (q | TR | TC: 0|0|5; 1|5|7; 2|10|10; 3|15|12; 4|20|15; 5|25|23; 6|30|33; 7|35|40.)
Profit (π) = TR − TC.
q | TR | TC | π
0 | 0 | 5 | −5
1 | 5 | 7 | −2
2 | 10 | 10 | 0
3 | 15 | 12 | +3
4 | 20 | 15 | +5
5 | 25 | 23 | +2
6 | 30 | 33 | −3
7 | 35 | 40 | −5
Each extra unit raises TR by Rs 5, so MR = ΔTR/Δq = Rs 5. Under perfect competition, MR = AR = p. Therefore the market price is Rs 5. (Profit is maximised at q = 4 where π = +5.)
q | TR | TC | π
0 | 0 | 5 | −5
1 | 5 | 7 | −2
2 | 10 | 10 | 0
3 | 15 | 12 | +3
4 | 20 | 15 | +5
5 | 25 | 23 | +2
6 | 30 | 33 | −3
7 | 35 | 40 | −5
Each extra unit raises TR by Rs 5, so MR = ΔTR/Δq = Rs 5. Under perfect competition, MR = AR = p. Therefore the market price is Rs 5. (Profit is maximised at q = 4 where π = +5.)
Exercise Q21
The following table shows the total cost schedule of a competitive firm. The price of the good is Rs 10. Calculate the profit at each output level. Find the profit maximising level of output. (q from 0 to 10.)
With p = 10, TR = 10q. Profit = TR − TC.
q | TC | TR | π
0 | 5 | 0 | −5
1 | 15 | 10 | −5
2 | 22 | 20 | −2
3 | 27 | 30 | +3
4 | 31 | 40 | +9
5 | 38 | 50 | +12
6 | 49 | 60 | +11
7 | 63 | 70 | +7
8 | 81 | 80 | −1
9 | 101 | 90 | −11
10 | 123 | 100 | −23
The maximum profit is Rs 12 at q = 5. (Check via MR = MC: between q = 5 and q = 6, MC = ΔTC = 11 = just above price, so production is stopped at q = 5 — exactly the rising-MC profit maximum.)
q | TC | TR | π
0 | 5 | 0 | −5
1 | 15 | 10 | −5
2 | 22 | 20 | −2
3 | 27 | 30 | +3
4 | 31 | 40 | +9
5 | 38 | 50 | +12
6 | 49 | 60 | +11
7 | 63 | 70 | +7
8 | 81 | 80 | −1
9 | 101 | 90 | −11
10 | 123 | 100 | −23
The maximum profit is Rs 12 at q = 5. (Check via MR = MC: between q = 5 and q = 6, MC = ΔTC = 11 = just above price, so production is stopped at q = 5 — exactly the rising-MC profit maximum.)
Exercise Q22
Consider a market with two firms. SS₁ gives the supply schedule of firm 1 and SS₂ that of firm 2. Compute the market supply schedule.
P=0: 0,0; P=1: 0,0; P=2: 0,0; P=3: 1,1; P=4: 2,2; P=5: 3,3; P=6: 4,4.
P=0: 0,0; P=1: 0,0; P=2: 0,0; P=3: 1,1; P=4: 2,2; P=5: 3,3; P=6: 4,4.
Market supply Sₘ(p) = SS₁(p) + SS₂(p) — horizontal addition.
P | SS₁ | SS₂ | Sₘ
0 | 0 | 0 | 0
1 | 0 | 0 | 0
2 | 0 | 0 | 0
3 | 1 | 1 | 2
4 | 2 | 2 | 4
5 | 3 | 3 | 6
6 | 4 | 4 | 8
P | SS₁ | SS₂ | Sₘ
0 | 0 | 0 | 0
1 | 0 | 0 | 0
2 | 0 | 0 | 0
3 | 1 | 1 | 2
4 | 2 | 2 | 4
5 | 3 | 3 | 6
6 | 4 | 4 | 8
Exercise Q23
SS₁ and SS₂ give the supply schedules of firm 1 and firm 2. Compute the market supply schedule.
P=0: 0,0; P=1: 0,0; P=2: 0,0; P=3: 1,0; P=4: 2,0.5; P=5: 3,1; P=6: 4,1.5; P=7: 5,2; P=8: 6,2.5.
P=0: 0,0; P=1: 0,0; P=2: 0,0; P=3: 1,0; P=4: 2,0.5; P=5: 3,1; P=6: 4,1.5; P=7: 5,2; P=8: 6,2.5.
Market supply Sₘ(p) = SS₁(p) + SS₂(p).
P | SS₁ | SS₂ | Sₘ
0 | 0 | 0 | 0
1 | 0 | 0 | 0
2 | 0 | 0 | 0
3 | 1 | 0 | 1
4 | 2 | 0.5 | 2.5
5 | 3 | 1 | 4
6 | 4 | 1.5 | 5.5
7 | 5 | 2 | 7
8 | 6 | 2.5 | 8.5
Note how the slope of Sₘ kinks gently — firm 2 only starts contributing from P = 4 onwards, after which the curve becomes steeper.
P | SS₁ | SS₂ | Sₘ
0 | 0 | 0 | 0
1 | 0 | 0 | 0
2 | 0 | 0 | 0
3 | 1 | 0 | 1
4 | 2 | 0.5 | 2.5
5 | 3 | 1 | 4
6 | 4 | 1.5 | 5.5
7 | 5 | 2 | 7
8 | 6 | 2.5 | 8.5
Note how the slope of Sₘ kinks gently — firm 2 only starts contributing from P = 4 onwards, after which the curve becomes steeper.
Exercise Q24
There are three identical firms in a market. The following table shows the supply schedule of firm 1. Compute the market supply schedule.
P=0:0; 1:0; 2:2; 3:4; 4:6; 5:8; 6:10; 7:12; 8:14.
P=0:0; 1:0; 2:2; 3:4; 4:6; 5:8; 6:10; 7:12; 8:14.
With three identical firms, market supply Sₘ(p) = 3 × SS₁(p).
P | SS₁ | Sₘ
0 | 0 | 0
1 | 0 | 0
2 | 2 | 6
3 | 4 | 12
4 | 6 | 18
5 | 8 | 24
6 | 10 | 30
7 | 12 | 36
8 | 14 | 42
P | SS₁ | Sₘ
0 | 0 | 0
1 | 0 | 0
2 | 2 | 6
3 | 4 | 12
4 | 6 | 18
5 | 8 | 24
6 | 10 | 30
7 | 12 | 36
8 | 14 | 42
Exercise Q25
A firm earns a revenue of Rs 50 when the market price is Rs 10. The market price increases to Rs 15 and the firm now earns a revenue of Rs 150. What is the price elasticity of the firm's supply curve?
Q = TR / P. Initial Q₁ = 50/10 = 5; final Q₂ = 150/15 = 10. So ΔQ = 5, ΔP = 5.
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (5/5) ÷ (5/10) = 1 ÷ 0.5 = 2.
Supply is elastic — a 1% price rise produces a 2% rise in quantity supplied.
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (5/5) ÷ (5/10) = 1 ÷ 0.5 = 2.
Supply is elastic — a 1% price rise produces a 2% rise in quantity supplied.
Exercise Q26
The market price of a good changes from Rs 5 to Rs 20. As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm's supply curve is 0.5. Find the initial and final output levels of the firm.
P₁ = 5, P₂ = 20, ΔP = 15, ΔQ = 15, eₛ = 0.5.
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (15 / Q₁) ÷ (15 / 5) = (15 / Q₁) ÷ 3 = 5 / Q₁.
Setting 5 / Q₁ = 0.5 gives Q₁ = 10. Hence final output Q₂ = Q₁ + ΔQ = 25.
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (15 / Q₁) ÷ (15 / 5) = (15 / Q₁) ÷ 3 = 5 / Q₁.
Setting 5 / Q₁ = 0.5 gives Q₁ = 10. Hence final output Q₂ = Q₁ + ΔQ = 25.
Exercise Q27
At the market price of Rs 10, a firm supplies 4 units of output. The market price increases to Rs 30. The price elasticity of the firm's supply is 1.25. What quantity will the firm supply at the new price?
P₁ = 10, P₂ = 30, ΔP = 20, Q₁ = 4, eₛ = 1.25.
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (ΔQ / 4) ÷ (20 / 10) = (ΔQ / 4) ÷ 2 = ΔQ / 8.
Setting ΔQ / 8 = 1.25 gives ΔQ = 10. New supply Q₂ = 4 + 10 = 14 units.
eₛ = (ΔQ / Q₁) ÷ (ΔP / P₁) = (ΔQ / 4) ÷ (20 / 10) = (ΔQ / 4) ÷ 2 = ΔQ / 8.
Setting ΔQ / 8 = 1.25 gives ΔQ = 10. New supply Q₂ = 4 + 10 = 14 units.
4.9 Chapter 4 Summary (NCERT)
The Story in One Page
- In a perfectly competitive market, firms are price-takers.
- TR = p × q; AR = p; MR = p — so AR = MR = p (a horizontal line at the market price).
- The demand curve facing a perfectly competitive firm is perfectly elastic (horizontal at p).
- Profit (π) = TR − TC. The firm chooses q₀ to maximise π.
- Three conditions at q₀: (i) p = MC; (ii) MC is non-decreasing; (iii) p ≥ AVC (short run) / p ≥ AC (long run).
- Short-run supply curve = rising SMC above minimum AVC + zero supply when p < min AVC.
- Long-run supply curve = rising LRMC above minimum LRAC + zero supply when p < min LRAC.
- Technological progress shifts a firm's supply curve to the right; an increase in input prices or a unit tax shifts it to the left.
- Market supply curve = horizontal sum of individual firm supply curves.
- Price elasticity of supply (eₛ) = (% change in quantity supplied) ÷ (% change in price).
4.10 Key Concepts (NCERT)
Perfect Competition
Market structure with many small buyers and sellers, a homogeneous product, free entry/exit and perfect information.
Price-Taker
A firm that accepts the market price as given; cannot influence price by its own actions.
Total Revenue (TR)
Total earnings from sales: TR = p × q.
Average Revenue (AR)
Revenue per unit of output: AR = TR/q. Under perfect competition, AR = p.
Marginal Revenue (MR)
Change in TR per extra unit of output: MR = ΔTR/Δq. Under perfect competition, MR = p.
Price Line
Horizontal line at height p; under perfect competition it is the firm's AR, MR and demand curve all in one.
Profit (π)
Difference between total revenue and total cost: π = TR − TC.
Profit Maximisation
The firm's central goal — choose q₀ to maximise π. Requires MR = MC, MC non-decreasing, and the cost-cover condition.
Normal Profit
Minimum profit needed to keep the firm in business; equals the entrepreneur's opportunity cost; included in TC.
Supernormal Profit
Profit over and above the normal profit (p > AC at q₀).
Shut-Down Point
In short run: p = min AVC (where SMC cuts AVC). In long run: p = min LRAC.
Break-Even Point
Point where the firm earns only normal profit; supply curve cuts AC at its minimum.
Opportunity Cost
Gain foregone from the second-best alternative use of a resource.
Firm's Supply Curve (Short Run)
Rising part of SMC above min AVC, plus zero output when p < min AVC.
Firm's Supply Curve (Long Run)
Rising part of LRMC above min LRAC, plus zero output when p < min LRAC.
Market Supply Curve
Horizontal sum of individual firm supply curves at every price.
Unit Tax
A tax of Rs t per unit of output sold; shifts LRAC and LRMC up by Rs t.
Price Elasticity of Supply (eₛ)
Percentage change in quantity supplied per one per cent change in price; eₛ = (ΔQ/Q₁) ÷ (ΔP/P₁).
Homogeneous Product
Product whose units cannot be told apart across firms — buyers are indifferent between sellers.
Free Entry and Exit
No barriers to firms entering or leaving the market — necessary for the "large numbers" assumption.
Frequently Asked Questions — Supply Curves, Market Supply, Price Elasticity & Exercises
How is a firm's supply curve derived under perfect competition?
A perfectly competitive firm produces where MR = MC. Because MR = price, the firm chooses output where price = MC. As price rises, the firm moves up its MC curve to a higher output. The short-run supply curve is therefore the portion of the MC curve above minimum AVC — below that point the firm shuts down. The long-run supply curve is the portion of MC above minimum ATC.
What is the market supply curve and how is it constructed?
The market supply curve shows the total quantity all firms are willing to supply at each price. It is constructed by horizontal summation of individual firm supply curves: at each price, add the quantities each firm supplies. Like individual supply curves, it slopes upward because each firm's MC rises with output and because higher prices attract more firms in the long run.
What are the main determinants of a firm's supply curve?
NCERT Class 12 lists three main determinants of a firm's supply curve: (1) technology — better technology lowers MC and shifts supply rightward; (2) input prices — a fall in wages or raw-material prices lowers MC and shifts supply rightward; (3) unit taxes and subsidies — a per-unit tax shifts supply leftward, a subsidy shifts it rightward. A change in the good's own price moves the firm along its supply curve, not the curve itself.
What is price elasticity of supply?
Price elasticity of supply (es) measures the responsiveness of quantity supplied to a change in price. It is defined as the percentage change in quantity supplied divided by the percentage change in price, es = (Δq/q) ÷ (Δp/p). Supply is elastic if es > 1, unit elastic if es = 1, and inelastic if es < 1. A vertical supply curve has es = 0; a horizontal supply curve has es = ∞.
How is price elasticity of supply calculated by the percentage and geometric methods?
By the percentage method, es = (Δq/q) × (p/Δp). Substitute initial price and quantity, the absolute change in price and the absolute change in quantity supplied. By the geometric method, draw a tangent at the chosen point on the supply curve to the price axis: es is the ratio of the lower segment of the price-axis intercept to the upper segment, allowing classification (elastic, unit, inelastic) by inspection.
What is the difference between elastic, inelastic and unit-elastic supply?
Elastic supply (es > 1) means quantity supplied responds more than proportionally to a price change. Inelastic supply (es < 1) means quantity supplied responds less than proportionally — typical of agricultural goods in the short run. Unit-elastic supply (es = 1) means a given percentage rise in price causes the same percentage rise in quantity supplied. Time horizon, mobility of inputs, and storage costs determine which case prevails.
What are sample NCERT Class 12 Chapter 4 exercises?
NCERT Class 12 Chapter 4 exercises ask students to define perfect competition, derive AR and MR, derive the firm and market supply curves, state and explain the three conditions of profit maximisation, compute price elasticity of supply by both methods, and analyse how a per-unit tax shifts the firm's supply curve. This part contains complete model answers to every exercise.
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Class 12 Economics — Introductory Microeconomics
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