Jupiter2U School
Chapter 08

Elasticity

Middle School

Knowing that a higher price lowers quantity demanded is only half the story. The decisive question is: by how much? Elasticity puts a number on responsiveness — and that number decides whether a tax raises revenue, whether a farmer welcomes a bumper harvest, and who really pays a sales tax.

At a glance
Core ideaElasticity puts a number on how much quantity responds to a change.
Key termPED = %ΔQd ÷ %ΔP; above 1 is elastic, below 1 inelastic.
You can…Predict whether a price rise raises or cuts total revenue.
Watch outSlope ≠ elasticity — PED changes at every point on a straight line.
Theory

The elasticity family

An elasticity is a ratio of percentage changes, which makes it unit-free (comparable across dollars, litres, tonnes). The central one is the price elasticity of demand (PED):

PED = %ΔQd ÷ %ΔP

Because demand slopes down, PED is negative; economists usually quote its absolute value. Classification:

  • |PED| > 1 → elastic (quantity is very responsive; luxuries, goods with close substitutes).
  • |PED| < 1 → inelastic (quantity barely responds; necessities, addictive goods, no substitutes).
  • |PED| = 1 → unit elastic.
  • |PED| = 0 → perfectly inelastic (vertical); |PED| = ∞ → perfectly elastic (horizontal).

Determinants of PED: availability of substitutes, whether it's a necessity or luxury, the proportion of income spent, and the time horizon (demand is more elastic in the long run). Related measures:

YED = %ΔQd ÷ %ΔIncome XED = %ΔQd of A ÷ %ΔP of B PES = %ΔQs ÷ %ΔP

YED (income elasticity): positive for normal goods, >1 for luxuries, negative for inferior goods. XED (cross elasticity): positive for substitutes, negative for complements. PES (price elasticity of supply): higher when firms have spare capacity, storable stock, and time to adjust.

|PED| > 1
Elastic · luxuries, many substitutes
|PED| < 1
Inelastic · necessities, no substitutes
|PED| = 1
Unit elastic · revenue at its peak
YED < 0
Inferior good
XED > 0
Substitutes
XED < 0
Complements
Explanation

Elasticity and total revenue — the key link

Total revenue (TR = P × Q) moves in opposite directions for the two forces: raising price lifts the "P" part but cuts the "Q" part. Which wins depends on elasticity:

  • Demand elastic → cut price to raise revenue (the big quantity gain outweighs the lower price).
  • Demand inelastic → raise price to raise revenue (quantity falls only slightly).
  • Demand unit elastic → revenue is at its maximum; small price changes leave it unchanged.

This explains why governments tax inelastic goods (petrol, tobacco, alcohol) to raise reliable revenue, and why a farmer's bumper harvest can lower total farm income: food demand is inelastic, so the price crash outweighs the extra volume — the "paradox of plenty."

Key insight — tax incidence

When a per-unit tax is imposed, the side of the market that is more inelastic bears more of the burden, regardless of who legally pays it. Cigarette taxes fall mostly on smokers (inelastic demand); a tax on a good with many substitutes falls mostly on producers.

Practical

Worked example: computing and using elasticity

Step 1 — the dataA cinema raises ticket prices from $8 to $10. Weekly attendance falls from 5,000 to 4,000.
Step 2 — percentage changes (midpoint method)Using the average as the base avoids the "which end?" ambiguity.
%ΔQ = (4000 − 5000) ÷ 4500 = −22.2%. %ΔP = (10 − 8) ÷ 9 = +22.2%.
Step 3 — PEDPED = −22.2% ÷ 22.2% = −1.0. Demand is (locally) unit elastic.
Step 4 — revenue checkOld TR = 8 × 5000 = $40,000. New TR = 10 × 4000 = $40,000. Revenue is unchanged — exactly what unit elasticity predicts.
Step 5 — income elasticityWhen average incomes rose 10%, streaming-subscription demand rose 25%. YED = 25 ÷ 10 = +2.5 → a strongly normal luxury good. In a boom its sales soar; in a recession they fall hardest.
Step 6 — decisionBecause the cinema is at unit elasticity, further price rises would push it into the elastic region and cut revenue. To grow revenue it should instead compete on income-elastic add-ons (premium seats), not headline ticket price.
Q&A
Q1Why is PED different at every point on a straight-line demand curve?

A straight demand line has constant slope (ΔQ/ΔP), but elasticity uses percentage changes, and the base values P and Q change as you move along it. At the top (high P, low Q) the same absolute change is a large % of a small Q and a small % of a large P → elastic. At the bottom it reverses → inelastic. The midpoint is exactly unit elastic. Slope and elasticity are not the same thing.

Q2Salt has PED near zero. What does that imply for a salt tax?

Consumers will buy almost the same quantity however much the price rises, so a tax barely changes behaviour: it raises stable revenue and falls almost entirely on consumers (they can't substitute away). The flip side — such a tax does little to discourage consumption, so it is a good revenue tool but a poor behavioural one.

Q3Cross elasticity of demand between two goods is −1.8. What are they?

A negative XED means they are complements — a rise in one's price cuts demand for the other (e.g. game consoles and games, cars and petrol). The large magnitude (1.8) says they are strong complements. A positive XED would signal substitutes; a value near zero, unrelated goods.

Q4Why is supply usually more elastic in the long run?

In the short run at least one factor is fixed — a firm can't build a new plant overnight, so even a big price rise brings only a modest output increase (inelastic PES). Given enough time (the long run), all factors become variable: firms expand capacity and new firms enter, so quantity responds much more fully. Time is the key determinant of elasticity on both sides of the market.

Q5An inferior good has YED = −0.4. What happens to its sales in a recession?

Negative YED means demand moves opposite to income. In a recession incomes fall, so demand for the inferior good rises (think supermarket own-brand food, bus travel, instant noodles). This is why some businesses are counter-cyclical — a useful hedge in a downturn.

← Prev: Supply & Demand ↑ Top Next: Markets & the Price Mechanism →
Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Price elasticityPEDElastic vsinelasticTotal revenue ruleIncome elasticityCross elasticityTax incidenceDeterminantsElasticity
Infographic

The key facts, visualised

PED
percent change in Qd divided by percent change in P
Elastic
|PED| > 1: quantity is very responsive to price
Inelastic
|PED| < 1: quantity barely responds to price
YED
income elasticity; positive for normal goods
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1Price rises from $10 to $12 and quantity falls from 100 to 80. Find PED.

  1. %change Q = (80-100)/100 = -20%.
  2. %change P = (12-10)/10 = +20%.
  3. PED = -20% / +20% = -1.0.

Example 2A good has PED = -0.5. Price rises 10%. What happens to quantity and to total revenue?

  1. %change Q = PED x %change P = -0.5 x 10% = -5%.
  2. Demand is inelastic, so quantity falls proportionally less than price rises.
  3. Revenue rises because the price gain outweighs the small quantity loss.
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1Why do necessities tend to be price inelastic?
They have few substitutes and must be bought regardless of price, so quantity barely changes.
2If demand is elastic, should a firm raise or cut price to increase revenue?
Cut price -- with elastic demand the quantity gain outweighs the lower price, raising revenue.
3Cross elasticity of tea vs coffee is +1.5. What does the sign mean?
Positive means they are substitutes -- a rise in coffee price raises demand for tea.
4Income elasticity of a good is -0.8. What kind of good is it?
An inferior good -- demand falls as income rises.
5When a tax is placed on a good with inelastic demand, who bears most of it?
Consumers -- because they keep buying despite the higher price, they pay most of the tax.
6List two things that make demand more elastic.
More close substitutes and a longer time to adjust both make demand more elastic.