CH 4 · THE FIRM UNDER PERFECT COMPETITION 1 / 1
Introductory Microeconomics · Class XII

Chapter 4
The Theory of the Firm
under Perfect Competition

Chapter 3 told us what output costs. It never told us how much to produce — because that needs a price. Give the firm a price, assume it is a ruthless profit maximiser, and the supply curve falls out.

The one question this chapter answers

The firm's problem

A firm can produce any quantity it likes. How much will it actually produce and sell?

The assumption everything rests on

A firm is a ruthless profit maximiser. The amount it produces and sells is the amount that maximises its profit — nothing else.

The textbook calls this "critical, if somewhat unreasonable". Real firms also care about growth, reputation and survival. But this assumption is sharp enough to generate a testable prediction, which is what we want.

We also assume the firm sells whatever it produces, so "output" and "quantity sold" are used interchangeably throughout.

π = TR − TC
What we carry in from Chapter 3

The entire cost family: SMC, AVC, SAC, LRMC, LRAC. This chapter adds only one new ingredient — revenue — and then compares the two.

We will keep using the same firm as Chapter 3, with TFC = ₹20 and the cost schedule of Table 3.3, so you can check every number against a table you already trust.

Route map

Part A · Perfect competition

The four defining features, and the one behaviour they produce: price taking.

Part B · Revenue

TR, AR and MR — and the surprising result that AR = MR = P.

Part C · Profit maximisation

The three conditions a profit-maximising output must satisfy.

Part D · The supply curve

Short run and long run. Shut-down point and break-even point.

Part E · What shifts supply

Technology, input prices, a unit tax. Then market supply.

Part F · Elasticity of supply

Measuring responsiveness — including the geometric method.

4.1Perfect competition: the four defining features

1 · Large number of buyers and sellers

Each individual buyer and seller is very small compared to the size of the market, so no one can influence the market by their size.

2 · Homogeneous product

Every firm produces an identical product. The product of one firm cannot be differentiated from another's, so a buyer is indifferent about whom to buy from.

3 · Free entry and exit

It is easy for firms to enter the market and to leave it. This is what sustains the large number of firms — if entry were restricted, few firms would remain.

4 · Perfect information

All buyers and sellers are completely informed about price, quality and other relevant details of the product and the market.

These four exist to produce one behaviour

Together they give perfect competition its single most distinguishing characteristic: price-taking behaviour. Everything else in this chapter follows from it.

What price-taking means — and why it follows

For a firm

A price-taking firm believes that:

  • if it sets a price above the market price, it will sell nothing at all;
  • if it sets a price at or below the market price, it can sell as much as it wants.

So it never sets a price below the market price — there would be no reason to. It charges exactly the market price.

For a buyer

A price-taking buyer believes that:

  • if she offers below the market price, no firm will sell to her;
  • if she offers at or above it, she can buy as much as she wants.
Why the assumption is reasonable — the argument in four steps
  1. Start with all firms charging the same market price.
  2. One firm raises its price above the rest.
  3. Since the product is homogeneous and buyers have perfect information, that firm loses every single buyer — they have no reason to pay more for an identical good they know they can get cheaper.
  4. Because there are so many other firms, those buyers are readily absorbed elsewhere; no "adjustment problem" arises.

Being unable to sell anything above the market price is precisely what price-taking stipulates. The assumption is a consequence of the four features, not an extra one.

Challenge

Challenge — section 4.1

Consider three markets and decide, for each, which defining feature of perfect competition fails and what that implies for the firm's ability to set price:

(a) The vegetable market in a large city, with hundreds of vendors selling identical tomatoes.
(b) The market for branded soft drinks.
(c) Indian Railways' long-distance passenger services.

Then answer: if perfect competition is so rare in reality, why do we study it at all?

Are you ready for the answer? 🤔
Answer

(a) Essentially all four hold — many small sellers, a homogeneous product, easy entry, and buyers who can compare prices by walking down the row. Each vendor is close to a genuine price taker: charge more than the stall next door and you sell nothing. This is the textbook's best real-world approximation.

(b) Homogeneity fails. Products are deliberately differentiated by brand, taste and advertising. Buyers do not regard them as identical, so a firm raising its price loses some customers but not all — it has some price-setting power. This is monopolistic competition.

(c) The large-number condition and free entry both fail. There is essentially a single seller with legal and practical barriers preventing entry. It is a monopoly, and can set price subject only to what buyers will bear.

Why study it anyway — three reasons:

1. It is a benchmark. You cannot say a market is "uncompetitive" without a standard of comparison. Perfect competition is that standard — the case where no one has any power over price at all.

2. It is the simplest case that still works. Because the firm takes price as given, AR = MR = P, and the profit-maximisation problem collapses to P = MC. Every more realistic market structure is analysed by relaxing one of the four assumptions and seeing what breaks.

3. Its predictions are often approximately right for markets with many small sellers — agriculture, fish markets, foreign exchange, shares.

Note the parallel with Chapter 2. There, the consumer took prices as given. Here, the firm does too. Chapter 5 will explain who actually sets the price if everyone is taking it: nobody does — it emerges from demand meeting supply.

4.2Total revenue

Definition

Total Revenue (TR) is the market price of the good multiplied by the quantity of the good sold by the firm.

TR = p × q
Table 4.1 — Candles at a market price of ₹10 a box
Boxes soldTR (₹)
00
110
220
330
440
550
OUTPUT (boxes) REVENUE (₹) O TR 10 1 slope = Aq₁ / Oq₁ = p = ₹10 constant, because p is constant
Three properties of the TR curve

1. At zero output TR is zero, so the curve passes through the origin.
2. TR rises as output rises.
3. Since TR = p × q with p constant, this is the equation of a straight line whose slope is the market price.

Average and marginal revenue

Definition

Average Revenue (AR) is total revenue per unit of output.

AR = TRq = p × qq = p
Definition

Marginal Revenue (MR) is the increase in total revenue for a one-unit increase in the firm's output.

From Table 4.1

MR = (30 − 20) / (3 − 2) = 10

The same as the price. Coincidence?

The algebra says no

MR = (pq₂ − pq₁) / (q₂ − q₁)
     = p(q₂ − q₁) / (q₂ − q₁)
     = p

For a price-taking firm:   AR = MR = P
The intuition, without algebra

When the firm sells one more unit, that extra unit is sold at the market price — and, crucially, the firm does not have to cut the price on the units it was already selling, because it can sell any quantity at that price. So the addition to total revenue is the price.

The price line

OUTPUT PRICE / REVENUE O p Price line = AR = MR = d the firm can sell any quantity it wishes at this price… …and nothing at all above it
Definition

The price line is a horizontal straight line at a height equal to the market price. It shows the relationship between the market price and the firm's output level.

One line, three identities

The price line is simultaneously:

  • the firm's AR curve
  • the firm's MR curve
  • the demand curve facing the firm
The demand curve facing a firm is perfectly elastic

It is horizontal, so e = ∞. Any attempt to raise price drops sales to zero.

Do not confuse this with the market demand curve, which is downward sloping (Chapter 2). The market demand curve slopes down; the demand curve facing one tiny firm within that market is flat, because that firm is too small to move the price.

Challenge

Challenge — section 4.2

In Chapter 2 you proved that a market demand curve is downward sloping. In this chapter the demand curve facing a firm is horizontal.

A student objects: "These contradict each other. If every firm faces a horizontal demand curve, and the market is just all the firms added together, then adding horizontal curves must give a horizontal market demand curve. So the market demand curve should be flat too."

Resolve the apparent contradiction.

Are you ready for the answer? 🤔
Answer

There is no contradiction. The student has mixed up two different curves that happen to share the word "demand".

Market demand curve — built in Chapter 2 by adding up consumers. It shows how much all buyers together will buy at each price. It slopes downward.

Demand curve facing a firm — shows what happens to that one firm's sales as it alone changes its price, with the market price unchanged. It is horizontal.

The error is in "the market is just all the firms added together". Market demand is obtained by summing over consumers, not over firms. Firms are summed to get market supply. You cannot build a demand curve by adding up firms.

Why the firm's curve is flat even though the market's is not: the firm is infinitesimally small relative to the market. When it doubles its output, the market quantity moves by so little that the market price does not perceptibly change. The firm therefore experiences a flat segment — it is looking at a microscopic piece of the downward-sloping market curve, magnified until the slope is invisible.

A useful image: the Earth is a sphere, but the patch of ground you are standing on looks flat. Both statements are true, at different scales. The market demand curve is the sphere; the firm's demand curve is the patch under its feet.

What actually moves the market price is a change in market demand or market supply — many firms acting together, or consumers changing their behaviour. That is the subject of Chapter 5.

4.3The three conditions

If a profit-maximising firm produces a positive output q₀, then all three of these must hold at q₀.

Condition 1

The price must equal marginal cost: p = MC

Condition 2

Marginal cost must be non-decreasing at q₀ — the MC curve must not be sloping downward there.

Condition 3

In the short run, price must be at least the average variable cost: p ≥ AVC
In the long run, price must be at least the average cost: p ≥ AC

Note the logic carefully

These are necessary conditions: if the firm produces a positive output, all three must hold. Note that Conditions 1 and 2 alone would only locate the best positive output — they cannot tell you whether producing at all beats shutting down. Condition 3 supplies exactly that check.

Condition 1 — why p = MC

The argument
  1. Profit is TR − TC. Both rise as output rises.
  2. As long as the addition to revenue exceeds the addition to cost — that is, MR > MC — producing one more unit increases profit. So keep going.
  3. If MR < MC, the last unit cost more than it earned, so it reduced profit. Cut back.
  4. Profit therefore stops rising and starts falling exactly where MR = MC.
  5. For a price-taking firm MR = P. Hence P = MC.
The practical rule

Produce every unit whose marginal cost is covered by the price; stop once the next unit would cost more than the price.

What if no unit has MC exactly equal to P?

This happens constantly with real tables, and it is worth being precise about.

P = MC is a statement about smooth curves. When output is continuous, MC takes every value on its way up, so there is always some output at which it exactly equals the price. That is the condition you should quote in an exam.

Real schedules are discrete. Output comes in whole units, so MC jumps — in our worked example it goes 13 at the 8th unit and 15 at the 9th, and never touches 14. There is no output where P = MC exactly.

The operational rule for a table is therefore: produce every unit whose marginal cost is below the price, and stop at the last such unit.

The optimum is sandwiched: MC of the last unit produced ≤ P ≤ MC of the next unit.

These are the same rule. "Stop where MR = MC" and "stop when the next unit costs more than it earns" describe one decision; the equality is just what the sandwich collapses to when the steps become infinitely small.

Do not write "P = MC = 13" in an exam — that is not defensible, since P is 14. Write instead: "the firm produces 8 units, because MC of the 8th unit (₹13) is below the price while MC of the 9th (₹15) exceeds it." That is both correct and clearly reasoned. NCERT's own Exercise 21 is solved exactly this way.

Compare with Chapter 2

The consumer's rule was MRS = p₁/p₂ — adjust until the rate you are willing to trade at equals the rate the market allows. The firm's rule is the same shape: adjust until the cost of one more unit equals what one more unit earns. Both optima are found by equating a marginal benefit to a marginal cost.

Condition 2 — why MC must not be falling

OUTPUT (units) PRICE, COST (₹) 0 10 20 SMC P = MR = ₹10 q₁ — MC is FALLING here ✗ not a maximum q₄ — MC is RISING here ✓ this is the maximum q₁ q₄
Both q₁ and q₄ satisfy P = MC. Only q₄ is a profit maximum.
Why q₁ fails

Just to the left of q₁, MC is above the price — those units were losing money. So the firm's profit at an output slightly smaller than q₁ is higher than at q₁ itself. A point you can improve on by moving away from it cannot be a maximum.

At q₁, P = MC identifies a profit minimum, not a maximum. Condition 2 exists purely to throw this impostor out.

Condition 3 — when it is better to produce nothing

Short run · p must be ≥ AVC

If the firm shuts down, output, TR and TVC are all zero, so its loss is exactly −TFC (the fixed cost still has to be paid).

If it produces where p < AVC, then revenue does not even cover the variable cost. Its loss is TFC plus the uncovered variable cost — strictly worse than shutting down.

So it produces zero.

Long run · p must be ≥ AC

In the long run there are no fixed costs, so a firm that shuts down has a profit of exactly zero.

If it produces where p < AC, total cost exceeds total revenue and it makes a loss — worse than zero.

So it exits the market.

Why the two cases differ — the whole reason is fixed cost

In the short run the firm must pay TFC whether or not it produces. That cost is already sunk, so it is irrelevant to the decision. The only question is: does revenue cover the costs I can still avoid — the variable costs? If yes, produce, because any surplus over AVC helps pay off the unavoidable fixed cost.

In the long run nothing is unavoidable. Every cost can be escaped by exiting, so every cost must be covered. Hence the tougher test, p ≥ AC.

Profit maximisation — the same firm as Chapter 3

Take the firm of Table 3.3 (TFC = ₹20) and set the market price at ₹14.

OUTPUT (units) ₹ per unit 0 10 14 20 P = ₹14 SAC AVC SMC q* = 8 PROFIT = ₹32 (₹14 − ₹10) × 8
qSMCTRTCProfit
66845925
78986731
8131128032
9151269531
102014011525
Check all three conditions at q = 8

1. SMC = 13, just below P = 14; the 9th unit would cost 15 > 14. So 8 is the last unit worth producing — the discrete form of P = MC. ✓
2. SMC is rising (8 → 13 → 15). ✓
3. P = 14 > AVC = 7.5. ✓

Reading the profit off the diagram

TR = area O–P–A–q* = 14 × 8 = ₹112
TC = area O–SAC–B–q* = 10 × 8 = ₹80
Profit = the shaded rectangle = (14 − 10) × 8 = ₹32

Challenge

Challenge — section 4.3

A firm has TFC = ₹500. At its best output the market price is ₹12, its AVC is ₹10 and its SAC is ₹18.

(a) Is the firm making a profit or a loss? How much per unit?
(b) Should it shut down in the short run? Justify with the numbers.
(c) Should it stay in the industry in the long run?
(d) A manager says: "We are losing ₹6 on every unit — the more we produce, the more we lose. We must stop." Where is the flaw?

Are you ready for the answer? 🤔
Answer

(a) A loss of ₹6 per unit. Price ₹12 against SAC ₹18. The firm is not covering its full costs.

(b) No — it should keep producing in the short run. The test is P ≥ AVC: here ₹12 > ₹10. ✓

Suppose it produces 100 units:

Produce: TR = 1200 · TVC = 1000 · TFC = 500 → loss = 1200 − 1500 = −₹300

Shut down: TR = 0 · TVC = 0 · TFC = 500 → loss = −₹500

Producing loses ₹200 less than shutting down. Each unit earns ₹12 and costs ₹10 in avoidable cost, leaving ₹2 to put towards the fixed cost — a contribution the firm forfeits entirely if it stops.

(c) No — it should exit in the long run. There the test is P ≥ AC, and ₹12 < ₹18. In the long run the fixed cost is escapable, so a firm not covering full cost should leave rather than earn less than normal profit.

(d) The flaw is treating fixed cost as if it were avoidable.

The "₹6 loss per unit" is computed against SAC, which includes AFC — a cost the firm pays whether it produces or not. Shutting down does not remove that ₹500; it only removes the revenue.

The right comparison for a short-run decision is price against AVC, because AVC is the only cost the decision can actually change. Since ₹12 > ₹10, more output means less total loss, not more — the exact opposite of the manager's claim.

This is opportunity-cost thinking from Chapter 1. A sunk cost is irrelevant to a forward-looking decision, exactly as the already-bought textbook was irrelevant to how you spend tonight. The manager is being led by an accounting number instead of by the costs the decision can influence.

4.4The firm's supply curve

Definition

A firm's supply is the quantity it chooses to sell at a given price, given technology and given the prices of factors of production.

Definition

The supply curve of a firm shows the levels of output (x-axis) that a profit-maximising firm chooses to produce at different values of the market price (y-axis), holding technology and factor prices unchanged.

The idea in one sentence

We already know that for any price, the firm produces where P = MC on the rising part, provided P ≥ min AVC. So we simply feed in different prices and read off the answers — and the answers are the marginal cost curve.

Deriving the short-run supply curve

OUTPUT (units) ₹ per unit 0 SHUT-DOWN POINT = min AVC (₹6.50) BREAK-EVEN POINT = min SAC (₹9.57) supply curve SAC AVC q = 0 for all P < 6.50
Case 1 · P ≥ min AVC

Equate P with SMC on the rising part. All three conditions hold, so the firm produces that quantity.

Case 2 · P < min AVC

For every positive output, AVC exceeds the price. Condition 3 can never be satisfied, so the firm produces zero.

The conclusion

A firm's short-run supply curve is the rising part of the SMC curve from and above the minimum AVC, together with zero output for all prices strictly below minimum AVC.

Why supply slopes upward

Because it is the marginal cost curve, and MC rises because of the law of diminishing marginal product (Chapter 3). The upward slope of supply is diminishing returns, wearing a different hat.

Shut-down, normal profit and break-even

Definition

The shut-down point is the last price–output combination on the supply curve at which the firm still produces a positive output. In the short run it is the minimum point of the AVC curve; in the long run, the minimum point of the LRAC curve.

Definition

Normal profit is the minimum level of profit needed to keep a firm in its existing business. A firm that does not make normal profit will not continue. Normal profits are therefore part of the firm's total costs — think of them as the opportunity cost of entrepreneurship.

Definition

Super-normal profit is profit earned over and above normal profit. The break-even point is the point on the supply curve at which the firm earns only normal profit — the minimum point of the average cost curve.

Opportunity cost returns — from Chapter 1

You have ₹1,000. Invest it in the family business, or put it in Bank 1 at 10%, or Bank 2 at 5%, or a safe at 0%. Choosing the business forfeits the best alternative — ₹100 of interest. That forgone ₹100 is the opportunity cost.

An entrepreneur's own time and money have the same kind of alternative use. Normal profit is what covers it. A firm earning only normal profit is doing exactly as well as its next-best alternative — which is why it neither expands nor leaves.

Challenge

Challenge — section 4.4

The short-run supply curve begins at minimum AVC (the shut-down point), but the long-run supply curve begins at minimum LRAC (which is also the break-even point).

(a) Explain why the two starting points differ.
(b) A firm is producing at a price between min AVC and min SAC. Describe its situation precisely: is it profitable? Will it continue? For how long?
(c) Why is there no such "in-between" zone in the long run?

Are you ready for the answer? 🤔
Answer

(a) Because of what is escapable in each period.

In the short run, TFC must be paid regardless — it is unavoidable, so it is irrelevant to the produce-or-not decision. The firm only needs to cover the costs it can avoid: the variable ones. Hence the cut-off is min AVC.

In the long run, every cost is escapable by exiting. So every cost must be covered, and the cut-off is the higher min LRAC.

(b) The firm is making a loss, but producing is still its best available option.

P > AVC → revenue covers all variable cost and leaves a surplus.
P < SAC → but that surplus is not enough to cover the whole fixed cost.

So the firm makes a loss smaller than TFC. It cannot make a profit, but by producing it recovers part of its fixed cost, whereas shutting down would leave it losing the whole of TFC.

How long? Only as long as the short run lasts. This is a strictly temporary position — the firm is producing to minimise a loss, not to make a profit. When the fixed input finally comes up for renewal (the lease expires, the machine wears out), the decision becomes a long-run one, and at that price the firm will exit.

(c) Because the in-between zone is created entirely by fixed cost. The gap between AVC and SAC is AFC. In the long run there is no fixed cost, so AVC and AC coincide — the gap closes and the zone vanishes. Shut-down point and break-even point become the same point, min LRAC.

Compact summary. Short run: P ≥ min AVC → produce; min AVC ≤ P < min SAC → produce at a loss; P ≥ min SAC → profit. Long run: only two regions, because there is only one cut-off.

4.5What shifts a firm's supply curve

The supply curve is part of the marginal cost curve. So anything that shifts MC shifts supply — and nothing else does.

Technological progress

The same inputs now produce more output — equivalently, a given output needs fewer inputs. This lowers marginal cost at every output.

MC shifts right/downward, so the supply curve shifts right. At any given price the firm now supplies more.

A rise in input prices

If the wage rate rises, the cost of production rises. Average cost and marginal cost rise at every output.

MC shifts left/upward, so the supply curve shifts left. At any given price the firm now supplies fewer units.

Definition

A unit tax is a tax the government imposes per unit of output sold. If the unit tax is ₹2 and the firm sells 10 units, it pays 10 × ₹2 = ₹20.

The effect of a unit tax

OUTPUT COSTS (a) the tax lifts both cost curves by ₹t LRAC₀ LRAC₁ LRMC₀ LRMC₁ t every unit now costs ₹t more, so AC and MC both rise by ₹t OUTPUT PRICE (b) so the supply curve shifts left S₀ S₁ p less more at the same price, the firm now supplies fewer units
How to read it — a unit tax is a cost per unit, so it lifts LRAC and LRMC vertically by exactly the tax — measure the gap upward, not sideways. Because the supply curve is the rising part of LRMC, it moves up and to the left: read across at the same price p and the firm now supplies fewer units.
The logic in two steps

1. The firm must pay ₹t extra for each unit produced, so LRAC and LRMC both rise by exactly ₹t at every output.
2. The supply curve is the rising part of LRMC above min LRAC — so it moves up with them. A unit tax shifts the firm's supply curve to the left.

4.6Market supply — horizontal summation again

Definition

The market supply curve shows the output levels that all firms in the market together produce at each value of the market price.

Two firms with different cost structures: firm 1 supplies nothing below ₹10, firm 2 nothing below ₹15.

Firm 1 PRICE 10 15 25 S₁ Firm 2 15 S₂ Market (S₁ + S₂) 10 15 kink at ₹15 — firm 2 enters Sm
Below ₹10 nobody supplies. Between ₹10 and ₹15 only firm 1 does, so market supply coincides with S₁. At ₹15 firm 2 enters and the curve kinks, becoming flatter because two firms now respond to each price rise.
How to read it — fix a price, read across the panels at that same height, and add the quantities sideways — never add prices upward. A firm contributes nothing at prices below its own minimum AVC, which is why the market curve starts flat and then kinks at each price where a new firm joins in.

Market supply — the algebra

The two firms

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

Market supply, in three pieces

Sm(p) = 0   for p < 10
Sm(p) = p − 10   for 10 ≤ p < 15
Sm(p) = 2p − 25   for p ≥ 15

Since (p−10) + (p−15) = 2p − 25.

Check the join

At p = 15: from the middle piece, 15 − 10 = 5. From the last piece, 2(15) − 25 = 5. ✓ The two pieces meet — the curve is continuous, but its slope changes. That is the kink.

Exactly the Chapter 2 technique

Market demand was the horizontal summation of individual demand curves, and it kinked where a consumer dropped out. Market supply is the horizontal summation of individual supply curves, and it kinks where a firm enters. Same method, mirror image.

Also: if the number of firms in the market increases, the market supply curve shifts right; if it decreases, left.

Challenge

Challenge — sections 4.5–4.6

The government imposes a unit tax of ₹5 on every unit of a good sold.

(a) Show what happens to a single firm's AC and MC curves.
(b) A student says: "A tax is just a cost, so it will also shift the firm's supply curve left. Therefore a lump-sum tax of ₹5,000 per year on the firm would do the same thing." Is that right?
(c) What does your answer imply about which kind of tax changes what a firm produces?

Are you ready for the answer? 🤔
Answer

(a) A unit tax of ₹5 adds ₹5 to the cost of every unit. So both AC and MC rise by exactly ₹5 at every output, and since the supply curve is the rising part of MC, supply shifts left.

(b) No — the student is wrong, and the reason is important.

A unit tax is a variable cost: total tax = ₹5 × q. It depends on output.

A lump-sum tax is a fixed cost: ₹5,000 whatever the output — even at q = 0.

A lump-sum tax raises TFC, and therefore raises AFC and AC. But it adds nothing to the cost of producing one more unit — so MC is completely unchanged.

(c) Only taxes that change marginal cost change output.

Since the supply curve is the MC curve above min AVC, and a lump-sum tax leaves MC untouched, the lump-sum tax leaves the short-run supply curve unchanged. At any given price the firm produces exactly the same quantity as before — it simply earns ₹5,000 less profit.

The general principle: a profit-maximising firm decides output by comparing marginal revenue with marginal cost. Anything that does not enter that comparison cannot change the decision. A fixed cost is irrelevant to output — exactly as it was in the shut-down analysis.

The one qualification: in the long run the lump-sum tax raises AC, so if it pushes AC above the price the firm will exit altogether. So it does not change how much a surviving firm produces, but it can change how many firms survive — and that shifts market supply, though not any individual firm's supply curve.

4.7Price elasticity of supply

Definition

Price elasticity of supply measures the responsiveness of quantity supplied to a change in the price of the good.

eS = percentage change in quantity suppliedpercentage change in price  =  ΔQQ × PΔP
Worked example — cricket balls

At ₹10 the market produces 200 balls. At ₹30 it produces 1,000.

%ΔQ = (1000 − 200)/200 × 100 = 400%
%ΔP = (30 − 10)/10 × 100 = 200%

eS = 400200 = 2
The sign

Unlike demand, eS is positive — price and quantity supplied move in the same direction. A vertical supply curve gives eS = 0.

Units

Like elasticity of demand, eS is a ratio of percentages and so is independent of units — a pure number.

The geometric method

(a) eS > 1 PRICE S M O q₀ cuts the PRICE axis Mq₀ > Oq₀ (b) eS = 1 S O = M q₀ passes through the ORIGIN Mq₀ = Oq₀ (c) eS < 1 S O M q₀ cuts the QUANTITY axis Mq₀ < Oq₀
How to read it — extend the supply line back until it hits an axis, then compare that intercept M with the origin O. Cuts the price axis → es > 1; passes through the origin → es = 1; cuts the quantity axis → es < 1. The steepness of the line tells you nothing on its own — only where it points does.
The rule

Extend the straight-line supply curve until it meets an axis at M. Then at any point S on it:

eS = Mq₀Oq₀

Cuts the price axis → M is negative → Mq₀ > Oq₀ → eS > 1
Passes through the origin → M coincides with O → eS = 1, at every point
Cuts the quantity axis → M is positive → Mq₀ < Oq₀ → eS < 1

The same trick as Chapter 2

There, elasticity of demand at a point was lower segment ÷ upper segment. Here it is Mq₀ ÷ Oq₀. Both replace a calculation with a ratio of two lengths you can read off the diagram.

Check your understanding

Question — NCERT Ex. 25, 26 and 27

(a) A firm earns revenue of ₹50 when the price is ₹10. The price rises to ₹15 and revenue becomes ₹150. Find the price elasticity of supply.

(b) Price changes from ₹5 to ₹20 and quantity supplied rises by 15 units. eS = 0.5. Find the initial and final output.

(c) At ₹10 a firm supplies 4 units. Price rises to ₹30 and eS = 1.25. What quantity will it supply?

Are you ready for the answer? 🤔
Answer

(a) First convert revenue into quantity: q = TR / p.
q₁ = 50/10 = 5  ·  q₂ = 150/15 = 10

%ΔQ = (10−5)/5 × 100 = 100%  ·  %ΔP = (15−10)/10 × 100 = 50%
eS = 100/50 = 2

(b) %ΔP = (20−5)/5 × 100 = 300%
%ΔQ = eS × %ΔP = 0.5 × 300 = 150%

So ΔQ/Q₁ = 1.5, and ΔQ = 15, giving 15/Q₁ = 1.5Q₁ = 10, and Q₂ = 10 + 15 = 25.

(c) %ΔP = (30−10)/10 × 100 = 200%
%ΔQ = 1.25 × 200 = 250%
ΔQ = 2.5 × 4 = 10, so the new quantity is 4 + 10 = 14 units.

Challenge

Challenge — section 4.7

A straight-line supply curve passing through the origin has eS = 1 at every point — no matter how steep or flat it is.

(a) Prove this using the formula eS = (ΔQ/ΔP) × (P/Q), not the geometric rule.
(b) Explain why this does not contradict the Chapter 2 result that elasticity varies along a straight-line demand curve.

Are you ready for the answer? 🤔
Answer

(a) The proof. A straight line through the origin has the equation Q = kP for some constant k > 0 (no intercept term, because it passes through the origin).

Its slope is ΔQ/ΔP = k. Substituting:

eS = k × PQ = k × PkP = 1

The k cancels. That is why the steepness is irrelevant — every line through the origin, however tilted, has unit elasticity everywhere.

(b) No contradiction — the difference is the intercept.

Elasticity = slope × (P/Q). For a straight line the slope is constant, so elasticity varies only if the ratio P/Q varies as you move along the line.

Line through the origin (Q = kP): as you move along it, P and Q rise in exact proportion, so P/Q is constant. Constant slope × constant ratio = constant elasticity.

Line with an intercept (Q = a − bP, as in Chapter 2): the intercept a breaks the proportionality. Near the price axis Q is tiny and P/Q is enormous (e → ∞); near the quantity axis P is tiny and P/Q → 0 (e → 0). Constant slope × varying ratio = varying elasticity.

So the real rule is neither "straight lines have constant elasticity" nor "straight lines have varying elasticity". It is: a straight line has constant elasticity if and only if it passes through the origin. Chapter 2's demand curve did not; this supply curve does. Both results follow from one formula.

Chapter 4 in one page

PERFECT COMPETITION → price taking REVENUE AR = MR = P PROFIT MAX P = MC, rising P ≥ AVC (SR) SUPPLY CURVE rising MC above min AVC Chapter 3's cost curves + a price = the supply curve Add up the firms horizontally → market supply → meets market demand in Chapter 5.

Key concepts — recap

Perfect competitionPrice taking Homogeneous productFree entry and exit Total revenueAverage revenue Marginal revenuePrice line Profit maximisationP = MC Firm's supply curveShut-down point Break-even pointNormal profit Super-normal profitUnit tax Market supply curve Price elasticity of supply
The results to never forget
  1. AR = MR = P for a price taker; the price line is horizontal
  2. Profit max: P = MC, MC non-decreasing, and P ≥ AVC (SR) or P ≥ AC (LR)
  3. Supply curve = rising MC from and above min AVC, zero below
  4. Shut-down = min AVC · Break-even = min AC
  5. Market supply = horizontal summation of firms' supply curves
The traps
  1. The demand curve facing a firm is horizontal; the market demand curve is not.
  2. P = MC on a falling MC is a profit minimum.
  3. Short-run shut-down compares P with AVC, not AC — fixed cost is sunk.
  4. A lump-sum tax does not shift the supply curve; a unit tax does.

NCERT Exercises 19 and 21

Exercises 19 & 21

19. Market price is ₹10. Compute TR, MR and AR for quantities 0 to 6.

21. Price is ₹10 and the total cost schedule is below. Find the profit at each output and the profit-maximising output.

Q012345678910
TC51522273138496381101123
Are you ready for the answer? 🤔
Answer

19. TR = 10q; and since the firm is a price taker, AR = MR = ₹10 at every positive output.

Q0123456
TR0102030405060
MR101010101010
AR101010101010

21. Profit = TR − TC, with TR = 10q:

Q012345678910
TR0102030405060708090100
TC51522273138496381101123
Profit−5−5−23912117−1−11−23

Profit is maximised at q = 5, with a profit of ₹12.

Verify with the marginal rule. MC of the 5th unit = 38 − 31 = ₹7, which is below the ₹10 price — worth producing. MC of the 6th = 49 − 38 = ₹11, which is above ₹10 — not worth producing. So stop at 5. ✓ Exactly what P = MC predicts.

NCERT Exercises 22–24

Exercises 22, 23 & 24

22. Two firms with identical supply schedules (0, 0, 0, 1, 2, 3, 4 at prices 0–6). Find market supply.

23. Two firms: SS₁ = 0,0,0,1,2,3,4,5,6 and SS₂ = 0,0,0,0,0.5,1,1.5,2,2.5 at prices 0–8. Find market supply.

24. Three identical firms, each with the schedule 0,0,2,4,6,8,10,12,14 at prices 0–8. Find market supply.

Are you ready for the answer? 🤔
Answer

22. Two identical firms, so market supply = 2 × SS₁:

Price0123456
Market0002468

23. Add the two columns at each price:

Price012345678
Market00012.545.578.5

Note the kink at price 3, where firm 2 has not yet entered but firm 1 has.

24. Three identical firms, so market supply = 3 × SS₁:

Price012345678
Market006121824303642
End of Chapter 4

Next: the two blades meet

We now hold both halves of the market. Chapter 2 gave the market demand curve; Chapter 4 has just given the market supply curve. Chapter 5 puts them on one diagram and finds the single price at which the plans of every consumer and every firm finally match.

And there, at last, Chapter 1's three central problems get their answers: equilibrium quantity settles what is produced, least-cost technique settles how, and price and the wage rate settle for whom.

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