AP® Microeconomics review sheet from Aim for Five (aimforfive.com/micro/units/2/2-3)
Unit 2 · Topic 2.3
2.3 Price Elasticity of Demand
Price elasticity of demand measures how strongly quantity demanded responds to a change in price. It tells you whether raising the price will raise or lower total revenue, and it changes along a straight-line demand curve. Expect calculation, graph and reasoning questions on it.
Key terms
- price elasticity of demand
- elastic
- inelastic
- unit elastic
- total revenue test
- availability of substitutes
The formula
Price elasticity of demand (Ed) = % change in quantity demanded ÷ % change in price.
Because price and quantity demanded move in opposite directions, the result is negative. Economists drop the minus sign and use the absolute value.
A percentage change is (new − old) ÷ old × 100. If the question gives you percentage changes, use them directly. Some questions and teachers use the midpoint method, which divides by the average of the old and new values instead of the old value; it gives a slightly different number. Use whichever method the question asks for. If it doesn't name one, write out your formula with the numbers so the reader can follow your method.
| Value of Ed | Name | What it means |
|---|---|---|
| Greater than 1 | Elastic | Quantity changes by a larger percentage than price |
| Less than 1 | Inelastic | Quantity changes by a smaller percentage than price |
| Exactly 1 | Unit elastic | Same percentage change in both |
| Infinite | Perfectly elastic | Horizontal demand curve: any price rise drops quantity to zero |
| Zero | Perfectly inelastic | Vertical demand curve: quantity doesn't change at all |
What makes demand elastic
- More close substitutes: if gas at one station rises in price, drivers go across the street.
- A larger share of your budget: you notice a 10% rise in rent more than a 10% rise in salt.
- Luxuries rather than necessities: people cut back on concert tickets more easily than on insulin.
- More time to adjust: over years, people can buy fuel-efficient cars, so gas demand becomes more elastic.
The total revenue test
Total revenue (TR) = price × quantity. Elasticity tells you which way TR moves when price changes:
| Demand is | Price rises | Price falls |
|---|---|---|
| Elastic | TR falls | TR rises |
| Inelastic | TR rises | TR falls |
| Unit elastic | TR unchanged | TR unchanged |
Elasticity along a straight-line demand curve
Slope and elasticity are different. A straight-line demand curve has the same slope everywhere, but its elasticity changes. Take demand with price on the vertical axis running from $10 at zero quantity down to zero price at 10 units. At a price of $8 (2 units) demand is elastic; at $5 (5 units, the midpoint) it's unit elastic; at $2 (8 units) it's inelastic.
So the upper-left half is elastic, the midpoint is unit elastic and the lower-right half is inelastic. Total revenue is largest at the unit-elastic midpoint: 5 × $5 = $25, compared with $16 at either $8 or $2. A profit-maximizing monopoly never chooses a price in the inelastic range, which matters in Unit 4.
When comparing two demand curves through the same point, the flatter one is more elastic at that point.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Calculating Ed and predicting revenue
A theater raises its ticket price from $20 to $22, and weekly tickets sold fall from 100 to 75. Calculate the price elasticity of demand (from the starting values). Is demand elastic or inelastic? What happens to total revenue?
Show the solutionHide the solution
- Step 1: % change in price = (22 − 20) ÷ 20 = 0.10, or 10%.
- Step 2: % change in quantity = (75 − 100) ÷ 100 = −0.25, or −25%.
- Step 3: Ed = 25% ÷ 10% = 2.5 (dropping the minus sign). Since 2.5 > 1, demand is elastic.
- Step 4: Total revenue test: with elastic demand, a price rise lowers TR. Check: before, $20 × 100 = $2,000; after, $22 × 75 = $1,650.
Answer: Ed = 2.5, elastic; total revenue falls from $2,000 to $1,650.
- Example 2Calculator allowed
Using revenue to find elasticity
A bakery cuts the price of a loaf from $8 to $6, and sales rise from 50 to 60 loaves. Use the total revenue test to decide whether demand is elastic or inelastic over this range, then confirm with the formula.
Show the solutionHide the solution
- Step 1: TR before = $8 × 50 = $400. TR after = $6 × 60 = $360.
- Step 2: Price fell and TR fell, so demand is inelastic over this range.
- Step 3: Check: % change in quantity = (60 − 50) ÷ 50 = 20%. % change in price = (6 − 8) ÷ 8 = −25%. Ed = 20% ÷ 25% = 0.8, which is less than 1.
Answer: Inelastic (Ed = 0.8); the price cut lowered total revenue from $400 to $360.
- Example 3
Slope isn't elasticity (classic trap)
A student says: 'The demand curve for a good is a straight line, so its elasticity is the same at every price.' Using demand that runs from $10 at zero quantity to 10 units at a price of zero, explain why the student is wrong.
Show the solutionHide the solution
- Step 1: The slope is the same everywhere: price drops $1 for each extra unit.
- Step 2: But elasticity compares percentage changes. At a high price and low quantity, a $1 price change is a small percentage of the price and a 1-unit quantity change is a big percentage of the quantity, so demand is elastic.
- Step 3: At a low price and high quantity, the opposite holds, so demand is inelastic.
- Step 4: Revenue confirms it: TR is $16 at $8, $25 at $5 and $16 at $2. TR rises as price falls toward $5 (elastic range) and falls as price drops below $5 (inelastic range).
Answer: Elasticity varies along a straight line: elastic above the midpoint ($5), unit elastic at $5, inelastic below it.
Common mistakes
- Calling a steep curve 'inelastic everywhere' and a flat one 'elastic everywhere'. Elasticity changes along a straight-line demand curve.
- Flipping the formula. Quantity goes on top: % change in quantity ÷ % change in price.
- Saying a price rise always increases revenue. It does only when demand is inelastic.
- Mixing up perfectly elastic (horizontal) and perfectly inelastic (vertical) curves.
On the exam
- Expect questions that give a price change and a revenue change and ask you to infer elasticity, or that ask how a firm should change price to raise revenue.
- In free responses, when you describe a perfectly inelastic demand curve, say it's vertical; for perfectly elastic, horizontal. This matters for tax incidence in topic 2.8.
Connected topics
Videos
Check yourself
4 questions on 2.3 Price Elasticity of Demand. Pick an answer to see if you got it, and why.
When the price of movie tickets rises by 10 percent, the quantity of tickets demanded falls by 25 percent. Which of the following is true?
A store cuts the price of a backpack from $40 to $30, and the number sold each week rises from 50 to 80. Based on the total revenue test, demand in this price range is
Which of the following goods most likely has the least price-elastic demand?
A city bus system's riders have inelastic demand for bus rides. If the city wants to raise more fare revenue, it should
0 of 4 answered