Elasticity in Economics
Learning Objectives
By the end of this page you will be able to:
- Define elasticity and explain why economists need it beyond the direction of a price-quantity relationship.
- Calculate and interpret Price Elasticity of Demand (PED) using both the basic and the midpoint (arc) formula.
- Classify demand as elastic, inelastic, unit elastic, perfectly elastic, or perfectly inelastic.
- List the determinants of PED and Price Elasticity of Supply (PES) and predict their effect.
- Connect PED to a firm's total revenue and pricing strategy.
- Calculate and interpret Cross-Price Elasticity (XED) and Income Elasticity (YED), and read their signs.
- Use elasticity to explain who really bears the burden of a tax (tax incidence).
Quick Answer
Elasticity measures how sensitive (responsive) the quantity demanded or supplied of a good is to a change in price, income, or the price of another good. Where the Law of Demand only tells us the direction of a change (price up, quantity down), elasticity tells us the size of that change — and that size is what businesses, governments, and policymakers actually need. It answers practical questions: Will raising the ticket price increase a cinema's revenue or shrink it? If the government taxes petrol, will buyers or sellers really pay for it? Is this good a luxury or a necessity? Elasticity turns the qualitative rules of demand and supply into precise, usable numbers.
Overview
Two goods can both obey the Law of Demand yet behave completely differently when price changes. Raise the price of salt by 20% and households barely cut back — they still need salt. Raise the price of a particular restaurant's meals by 20% and many diners simply go elsewhere. Both follow "price up, quantity down," but the degree of response is worlds apart. Elasticity is the tool that captures this difference.
The core idea is a ratio of percentage changes: how big is the percentage change in quantity compared with the percentage change in the thing that caused it. Because it uses percentages, elasticity is a pure number with no units — you can compare the elasticity of onions and the elasticity of air travel directly. This page covers the four elasticities every microeconomics student must know: PED (response of quantity demanded to the good's own price), PES (response of quantity supplied to price), XED (response to the price of another good), and YED (response to income). It then applies them to the two most exam-relevant uses: pricing for total revenue, and working out who bears a tax.
Core Concepts
Price Elasticity of Demand (PED)
Definition: PED measures the responsiveness of quantity demanded to a change in the good's own price. Formally, PED = (% change in Quantity Demanded) ÷ (% change in Price).
Explanation: Because demand curves slope downward, a price rise causes a quantity fall, so PED is mathematically negative. By convention economists drop the minus sign and use the absolute value, then classify the result. The larger the number, the more responsive (elastic) demand is.
| PED value (absolute) | Category | Interpretation | Typical goods |
|---|---|---|---|
| PED = 0 | Perfectly inelastic | Quantity doesn't respond to price at all | Life-saving insulin for diabetics |
| 0 < PED < 1 | Inelastic | Quantity changes less than price | Petrol, electricity, salt, cigarettes |
| PED = 1 | Unit elastic | Quantity changes exactly as much as price | Point on a curve, not a whole good |
| PED > 1 | Elastic | Quantity changes more than price | Restaurant meals, foreign holidays |
| PED = ∞ | Perfectly elastic | Any price rise drops quantity to zero | Perfect substitutes in a competitive market |
Example: If a 10% price rise causes a 20% drop in quantity demanded, PED = 20 ÷ 10 = 2, so demand is elastic.
Real-World Example: When a state raises the tax on cigarettes, sales fall only modestly — smoking is habit-forming and has few close substitutes, so demand is inelastic (PED between 0 and 1). This is exactly why "sin taxes" raise a lot of revenue: buyers keep buying.
Why It Matters: PED is the single most practically applied elasticity. It drives pricing decisions, tells governments how much revenue a tax will raise, and predicts how much a price change will actually move sales.
Common Misunderstanding: Students treat PED as a fixed property of a whole good. In fact PED changes along a straight-line demand curve — it is elastic at high prices/low quantities and inelastic at low prices/high quantities, passing through unit elastic at the midpoint.
Measuring PED: the Midpoint (Arc) Formula
Definition: The midpoint or arc formula calculates percentage changes using the average of the starting and ending values as the base: % change = (change in value) ÷ (average of the two values).
Explanation: If you compute a percentage change the ordinary way, you get a different answer depending on whether price rose or fell, because the base (the denominator) differs. Using the average of the old and new values as the base gives the same elasticity in both directions, which is why textbooks and exams favour it for calculations over a range.
Example: Price rises from ₹40 to ₹60 and quantity falls from 100 to 80 units.
- % change in quantity = (100 − 80) ÷ ((100 + 80) ÷ 2) = 20 ÷ 90 ≈ 22.2%
- % change in price = (60 − 40) ÷ ((60 + 40) ÷ 2) = 20 ÷ 50 = 40%
- PED = 22.2 ÷ 40 ≈ 0.56 (inelastic)
Why It Matters: It gives a single, consistent elasticity value for a movement between two points, so your answer doesn't change just because you swapped the "before" and "after".
Common Misunderstanding: The midpoint formula measures arc elasticity (over a range). Elasticity at a single exact point (point elasticity) is a slightly different calculation; for introductory exams the arc/midpoint method is usually what's expected.
Determinants of PED
Definition: The determinants of PED are the factors that make a good's demand more or less responsive to price.
Explanation: The main determinants are:
- Availability of substitutes — more (and closer) substitutes make demand more elastic. Branded medicine with a generic equivalent is more elastic than one with no substitute.
- Necessity vs. luxury — necessities (food staples, medicine) tend to be inelastic; luxuries (holidays, jewellery) tend to be elastic.
- Proportion of income spent — goods that take a large share of income (a car, a foreign holiday) tend to be more elastic; cheap items (a box of matches) are inelastic.
- Time horizon — demand is usually more elastic in the long run, as consumers find alternatives (after a petrol price rise, over years people buy more fuel-efficient vehicles).
- Habit and addiction — addictive goods (cigarettes, alcohol) are inelastic.
- Breadth of definition — "food" is very inelastic; "Amul butter" is elastic because narrowly-defined goods have close substitutes.
Real-World Example: Table salt is the textbook inelastic good — it has no real substitute, is a necessity, and costs a tiny fraction of income, so even a large price rise barely dents the quantity bought.
Why It Matters: These determinants let you predict elasticity without data — useful in exam questions that give a scenario rather than numbers.
Common Misunderstanding: Students assume "expensive = elastic". What matters is the share of income and the availability of substitutes, not the absolute price tag.
PED and Total Revenue
Definition: Total Revenue (TR) is price multiplied by quantity sold (TR = P × Q). PED tells us which way TR moves when a firm changes its price.
Explanation: When price changes, P and Q move in opposite directions, so TR depends on which effect is larger — and that's exactly what elasticity measures.
| Demand type | Price rise → TR | Price fall → TR |
|---|---|---|
| Inelastic (PED < 1) | TR rises | TR falls |
| Unit elastic (PED = 1) | TR unchanged | TR unchanged |
| Elastic (PED > 1) | TR falls | TR rises |
Example: A toll bridge with inelastic demand (few alternative routes) can raise tolls and collect more revenue, because traffic falls proportionally less than the price rise.
Real-World Example: Streaming services and airlines run frequent price experiments. Where demand is elastic (leisure travel, discretionary subscriptions), cutting prices to fill seats or gain subscribers raises total revenue; where it is inelastic (peak business routes), they raise fares.
Why It Matters: This is the direct commercial payoff of elasticity — it tells a firm whether raising or lowering price will grow revenue.
Common Misunderstanding: "Raising price always raises revenue." Only true for inelastic demand. For elastic demand a price rise reduces total revenue because quantity falls more than proportionally.
Price Elasticity of Supply (PES)
Definition: PES measures the responsiveness of quantity supplied to a change in price: PES = (% change in Quantity Supplied) ÷ (% change in Price).
Explanation: Because supply slopes upward, PES is positive. It is classified similarly to PED.
| PES value | Category | Meaning |
|---|---|---|
| PES = 0 | Perfectly inelastic | Fixed supply whatever the price (a specific Picasso painting, land at a fixed location) |
| 0 < PES < 1 | Inelastic supply | Producers cannot quickly expand output |
| PES = 1 | Unit elastic | Quantity supplied changes in proportion to price |
| PES > 1 | Elastic supply | Producers can easily expand or cut output |
Determinants of PES:
- Production/time period — agricultural goods are inelastic in the short run (a crop cannot be grown overnight) but far more elastic in the long run.
- Spare capacity — a factory with idle machines can raise output quickly, so supply is more elastic.
- Stock and storability — goods that can be stockpiled (grain, coal) have more elastic supply.
- Factor mobility — if labour and materials can be shifted into production easily, supply is more elastic.
- Number of producers — more producers means a faster overall supply response.
Real-World Example: After a good monsoon, farmers still cannot instantly increase this season's already-planted crop, so short-run supply of that crop is inelastic; only in later seasons can they plant more, making long-run supply more elastic.
Why It Matters: PES explains why prices of some goods (fresh produce, oil) spike sharply after a shock — inelastic supply cannot cushion a sudden demand change.
Common Misunderstanding: Students forget the crucial role of time. The same good can have inelastic short-run supply and elastic long-run supply.
Cross-Price Elasticity of Demand (XED)
Definition: XED measures how the quantity demanded of good A responds to a change in the price of good B: XED = (% change in Qd of A) ÷ (% change in Price of B).
Explanation: Here the sign is the whole point — it reveals the relationship between the two goods.
| XED value | Relationship | Example |
|---|---|---|
| XED > 0 (positive) | Substitutes | Coke and Pepsi — a Coke price rise raises demand for Pepsi |
| XED < 0 (negative) | Complements | Cars and petrol — a petrol price rise lowers demand for cars |
| XED = 0 (or near) | Unrelated goods | Bread and computers |
The larger the absolute value, the stronger the relationship (very close substitutes have a large positive XED).
Real-World Example: When onion prices spike, demand for close substitutes such as spring onions or other flavour bases rises — a positive XED — while demand for complements used alongside onions may soften.
Why It Matters: Firms use XED to watch competitors and price complementary product lines (e.g., printers and ink cartridges).
Common Misunderstanding: Students confuse the sign convention — remember: positive = substitutes, negative = complements.
Income Elasticity of Demand (YED)
Definition: YED measures how quantity demanded responds to a change in consumer income: YED = (% change in Quantity Demanded) ÷ (% change in Income).
Explanation: The sign and size classify the good.
| YED value | Good type | Example |
|---|---|---|
| YED > 1 | Luxury (income-elastic normal good) | Foreign holidays, premium smartphones |
| 0 < YED < 1 | Necessity (income-inelastic normal good) | Basic food, staple clothing |
| YED < 0 | Inferior good | Very cheap staples, long-distance bus travel (falls as income rises) |
Real-World Example: As household incomes rise in India, demand for packaged and branded foods, dining out, and two-wheelers grows faster than income (high positive YED), while demand for some inferior staples can fall — a pattern businesses track to plan for a growing middle class.
Why It Matters: YED helps firms and economists forecast how demand will change as an economy grows — luxury-goods sellers thrive in a boom but are hit hardest in a downturn.
Common Misunderstanding: A negative YED does not mean the good is "bad" — it means it is inferior in the technical sense, i.e., people switch away from it as they get richer.
Tax Incidence and Elasticity
Definition: Tax incidence is the question of who actually bears the economic burden of a tax — the buyer or the seller — regardless of who legally pays it to the government.
Explanation: The side of the market that is less elastic (less able to change its behaviour) bears more of the burden.
- Inelastic demand, elastic supply → consumers bear most of the tax (they can't easily stop buying).
- Elastic demand, inelastic supply → producers bear most of the tax (they can't easily stop supplying, and buyers walk away if prices rise).
Example: A tax on petrol falls mostly on consumers, because demand is inelastic — drivers keep buying and absorb most of the higher price.
Real-World Example: High taxes on cigarettes are borne largely by smokers because demand is highly inelastic, which is why such taxes reliably raise revenue even as they aim to discourage smoking.
Why It Matters: Governments use this logic when choosing what to tax — taxing inelastic goods raises steady revenue; taxing elastic goods raises less and mostly hurts producers.
Common Misunderstanding: The legal payer of a tax is not necessarily the one who bears it. A shop may hand the tax to the government, but if demand is inelastic, it passes almost all of it on to customers through a higher price.
Visual Learning
Key Terms
| Term | Definition | Context/Related Concept |
|---|---|---|
| Elasticity | Responsiveness of quantity to a change in price, income, or another price | Umbrella concept for PED, PES, XED, YED |
| Price Elasticity of Demand (PED) | % change in Qd ÷ % change in price | Negative; absolute value used |
| Elastic demand | PED > 1; quantity responds more than proportionally | Price fall raises total revenue |
| Inelastic demand | PED < 1; quantity responds less than proportionally | Price rise raises total revenue |
| Unit elastic | PED = 1; quantity changes in exact proportion to price | Total revenue unchanged |
| Perfectly inelastic | PED = 0; quantity fixed whatever the price | Vertical demand curve |
| Perfectly elastic | PED = ∞; any price rise ends all demand | Horizontal demand curve |
| Midpoint (arc) formula | Uses the average of two values as the base for % change | Gives the same elasticity in both directions |
| Price Elasticity of Supply (PES) | % change in Qs ÷ % change in price | Positive; depends heavily on time |
| Cross-Price Elasticity (XED) | % change in Qd of A ÷ % change in price of B | Sign shows substitute (+) or complement (−) |
| Income Elasticity (YED) | % change in Qd ÷ % change in income | Sign/size shows normal, luxury, or inferior |
| Total Revenue (TR) | Price × quantity sold | Its response to a price change reveals elasticity |
| Tax incidence | Who actually bears the burden of a tax | The more inelastic side bears more |
Common Mistakes
-
Misconception: "PED is a single fixed number for a good." Why it's wrong: Along a straight-line demand curve, elasticity changes at every point. Correct explanation: Demand is elastic at the top (high price, low quantity) and inelastic at the bottom (low price, high quantity), passing through unit elastic at the midpoint.
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Misconception: "Raising price always increases total revenue." Why it's wrong: It only does so when demand is inelastic. Correct explanation: If demand is elastic, raising price cuts quantity by a larger percentage, so total revenue falls; to raise revenue in that case you should lower the price.
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Misconception: "A negative income elasticity means the good is low quality or undesirable." Why it's wrong: The sign is a technical classification, not a value judgment. Correct explanation: A negative YED simply defines an inferior good — one people buy less of as their income rises because they switch to preferred alternatives.
-
Misconception: "The person who pays a tax to the government bears its burden." Why it's wrong: Burden depends on elasticity, not on who legally remits the tax. Correct explanation: If demand is inelastic, sellers pass most of a tax to buyers through higher prices, so buyers bear it even though the seller writes the cheque.
Comparison and Connections
| Concept A | Concept B | Key Difference |
|---|---|---|
| PED | PES | Response of quantity demanded vs quantity supplied; PED is negative, PES positive |
| XED | YED | Response to another good's price vs response to income |
| Elastic | Inelastic | Quantity responds more than / less than proportionally to price |
| Point elasticity | Arc (midpoint) elasticity | Elasticity at one exact point vs over a range between two points |
| Elasticity (this page) | Demand | Measures the size of the response vs establishes the direction of it |
Practice Questions
Recall
- Write the formula for Price Elasticity of Demand. Answer: PED = (% change in quantity demanded) ÷ (% change in price).
- What does a positive Cross-Price Elasticity tell you about two goods? Answer: That they are substitutes — a rise in the price of one increases the quantity demanded of the other.
Understanding
- Explain why PED is usually negative but expressed as a positive number. Answer: Because demand slopes downward, a price rise causes a quantity fall, giving a negative ratio; economists take the absolute value by convention so they can compare magnitudes easily.
- Why is the supply of fresh vegetables more elastic in the long run than in the short run? Answer: In the short run the crop is already planted and cannot be increased; over the long run farmers can plant more, add land or labour, and respond fully to price, making supply more elastic.
Application
- A cinema raises ticket prices by 10% and finds total revenue rises. What does this reveal about PED, and should it keep raising prices toward the revenue-maximising point? Answer: Demand is inelastic (PED < 1), since revenue rose despite the price increase. It can keep raising price toward the point where demand becomes unit elastic, where total revenue is maximised.
- Using the midpoint formula, calculate PED when price falls from ₹50 to ₹30 and quantity rises from 80 to 120 units. Answer: % change in quantity = 40 ÷ 100 = 40%; % change in price = 20 ÷ 40 = 50%; PED = 40 ÷ 50 = 0.8, so demand is inelastic over this range.
Analysis
- The government wants to raise reliable tax revenue and is deciding between taxing cigarettes or taxing restaurant meals. Using elasticity, advise it. Answer: Cigarettes have inelastic demand (habit-forming, few substitutes), so quantity barely falls when taxed and revenue is high and stable; restaurant meals have elastic demand (discretionary, many substitutes), so a tax would sharply cut sales and raise less. For reliable revenue, tax cigarettes.
- Explain how the relative elasticities of demand and supply determine who bears a new sales tax on petrol. Answer: Petrol demand is inelastic (few substitutes, a necessity for drivers) while supply is relatively more elastic, so the less-responsive side — consumers — bears most of the tax, absorbing it through a higher pump price even though sellers remit it to the government.
FAQ
Q1: What is the difference between elasticity and the slope of a curve? Slope is measured in units (rupees per kg), so it changes if you change units; elasticity uses percentages, so it is unit-free and comparable across different goods. A straight-line demand curve has a constant slope but a changing elasticity.
Q2: When should I use the midpoint formula instead of the ordinary percentage-change method? Use the midpoint (arc) formula when measuring elasticity over a range between two points, so your answer is the same whether price rose or fell. For elasticity at a single point, point elasticity is used instead.
Q3: Can a good be a luxury for one person and a necessity for another? Yes. Income elasticity depends on the consumer's circumstances. A car may be income-elastic (a luxury) for a low-income household but income-inelastic (a routine necessity) for a wealthy one.
Q4: Why do necessities tend to have inelastic demand? Because people need them regardless of price and there are few close substitutes — you cannot easily cut back on salt, basic medicine, or electricity when their prices rise, so quantity demanded changes little.
Q5: Where on a straight-line demand curve is total revenue highest? At the point where demand is unit elastic (PED = 1), which is the midpoint of a straight-line demand curve. Above it demand is elastic, below it inelastic.
Quick Revision
- Elasticity = % change in quantity ÷ % change in the cause; it is a unit-free number.
- PED = %ΔQd ÷ %ΔP; negative but stated as an absolute value. Elastic (>1), inelastic (<1), unit elastic (=1).
- Use the midpoint formula (average as base) to get a consistent PED over a range.
- Determinants of PED: substitutes, necessity vs luxury, share of income, time, habit, breadth of definition.
- PED and revenue: inelastic → raise price to raise TR; elastic → lower price to raise TR; unit elastic → TR unchanged.
- PES = %ΔQs ÷ %ΔP; positive. Depends on time, spare capacity, storability, factor mobility. More elastic in the long run.
- XED = %ΔQd(A) ÷ %ΔP(B): positive → substitutes, negative → complements.
- YED = %ΔQd ÷ %ΔY: >1 luxury, 0–1 necessity, <0 inferior good.
- Tax incidence: the more inelastic side of the market bears more of the tax burden, whoever legally pays it.
Related Topics
Prerequisites
- Demand — establishes the Law of Demand and PED, which this page develops in full.
- Supply — needed to understand PES and tax incidence.
Related Topics
- Equilibrium — elasticity determines how sharply price and quantity adjust to shocks around equilibrium.
Next Topics
- Equilibrium — where demand and supply meet, and where elasticity shapes the size of price and quantity changes.