2.3 Price Elasticity of Demand

Price elasticity of demand (PED) measures how much the quantity demanded responds to a change in price. You calculate it as the percentage change in quantity demanded divided by the percentage change in price, then use the magnitude to label demand as elastic, inelastic, or unit elastic.

Why This Matters for the AP Microeconomics Exam

Elasticity shows up constantly in AP Microeconomics because it explains how strongly buyers react to price. Multiple-choice questions often ask you to calculate a coefficient from a table or graph, classify demand as elastic or inelastic, or predict what happens to total revenue after a price change. Free-response prompts may ask you to calculate elasticity, interpret the result, and connect it to revenue or consumer behavior.

This topic also sets up later units. Elasticity determines how tax burdens are split between buyers and sellers, how government price controls play out, and how firms set prices to manage revenue. Getting comfortable with the formula and the total revenue test now pays off across the rest of the course.

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Key Takeaways

• PED = percentage change in quantity demanded divided by percentage change in price.
• Use the magnitude (absolute value): greater than 1 is elastic, less than 1 is inelastic, equal to 1 is unit elastic.
• Elasticity is not slope. It varies along a single linear demand curve.
• The availability of substitutes is a major factor: more substitutes make demand more elastic.
• The total revenue test links elasticity to revenue: when demand is elastic, price and total revenue move in opposite directions; when inelastic, they move together.
• Show your work on calculations and use percentage changes, not just raw changes in quantity and price.

What is Price Elasticity of Demand?

Earlier topics covered how the demand curve is built, why it slopes downward, and how it shifts when market conditions change. Price elasticity of demand answers a different question: how strongly do buyers react when the price itself changes?

Price elasticity of demand (PED) measures a consumer's sensitivity to price changes. Picture two buyers, Harry and Sally, in the market for turkey sandwiches. At $10, both want 5 sandwiches. The deli raises the price to $15. Harry drops from 5 sandwiches to 1, while Sally only drops from 5 to 4. Sally is much less price sensitive, so her demand is less elastic (more inelastic) than Harry's. This example is just an application of the concept, not required AP content, but it shows what elasticity captures: the size of the buyer's response.

Calculating Price Elasticity of Demand

The formula is the percentage change in quantity demanded divided by the percentage change in price:

Ed = %ΔQd / %ΔP

Here Ed is the price elasticity of demand coefficient, and %Δ means "percent change in." Because a price increase causes quantity demanded to fall (law of demand), Ed comes out negative or zero. Economists usually take the absolute value so they can focus on the magnitude as a measure of sensitivity.

Work through Harry's numbers:

Q1 = 5, Q2 = 1, so %ΔQd = (1 - 5) / 5 * 100 = -80%

P1 = 10, P2 = 15, so %ΔP = (15 - 10) / 10 * 100 = 50%

Ed = -80 / 50 = -1.6

A 50% increase in price led to an 80% decrease in quantity demanded. The magnitude is greater than 1, so this is elastic demand: quantity changed by a larger percentage than price.

Types of Elasticity

The value of Ed sorts demand into categories that describe how sensitive buyers are to price. The benchmark that separates elastic from inelastic is a magnitude of 1, where price and quantity change proportionally.

Perfectly Inelastic Demand

The coefficient is zero, so quantity demanded does not change at all when price changes. The demand curve is vertical. People often use necessities like insulin as an illustration: buyers need the same amount regardless of price. This is an illustrative example, not required AP content.

Relatively Inelastic Demand

The magnitude is between 0 and 1, so quantity demanded responds only slightly to price changes. Gasoline is a common illustration: drivers may cut back a little, but they still need fuel for daily life, so a price increase causes a smaller percentage drop in quantity. This is an example, not required content.

Unit Elastic Demand

The magnitude is exactly 1, so the percentage change in quantity demanded equals the percentage change in price. Price and quantity move in exactly proportional amounts.

Relatively Elastic Demand

The magnitude is greater than 1, so quantity demanded is very responsive to price. Concert tickets or other leisure spending are often used as an illustration, since buyers cut back sharply when prices rise. This is an example, not required content.

Perfectly Elastic Demand

The demand curve is horizontal and the coefficient is treated as infinite: at the going price buyers will take any quantity, but any price increase drops quantity demanded to zero. A product with many close substitutes is the usual illustration. This is an example, not required content.

Keep in mind that perfectly inelastic and perfectly elastic demand are conceptual endpoints. Real goods fall somewhere along the range between them.

The Total Revenue Test

The total revenue test is another way to identify the type of elasticity. Total revenue is the money a seller brings in:

TR = P * Q

The test connects total revenue to elasticity by giving rules for how revenue responds to price changes:

• Under elastic demand, an increase in price decreases total revenue, and a decrease in price increases it. The quantity response outweighs the price change.
• Under inelastic demand, an increase in price increases total revenue, and a decrease in price decreases it. The quantity response is too small to offset the price change.
• Under unit elastic demand, a change in price leaves total revenue unchanged, because price and quantity change proportionally.

How buyers respond:

• Elastic demand: consumers are very responsive to price changes (a price increase causes a large drop in quantity demanded).
• Inelastic demand: consumers are not very responsive (a price increase causes a small drop in quantity demanded).
• Unit elastic demand: consumers respond proportionally (a 30% price increase leads to a 30% drop in quantity demanded).
• Perfectly elastic: buyers respond only at one price level.
• Perfectly inelastic: quantity demanded does not change when price changes.

The total revenue test is useful when you only need to know whether demand is elastic, inelastic, or unit elastic and do not need the exact coefficient. It also explains pricing decisions: the more elastic demand is, the more carefully a seller has to think before raising price, because revenue can fall.

How to Use This on the AP Microeconomics Exam

Problem Solving

• Always use percentage changes, not raw changes. A common scoring mistake is dividing the change in quantity by the change in price instead of dividing the percentage changes.
• Show each step: find %ΔQd, find %ΔP, then divide. This makes partial credit easier to earn and helps you catch errors.
• After you get a number, interpret it. State whether demand is elastic, inelastic, or unit elastic based on the magnitude.

Free Response

• If asked to explain the result, connect the coefficient to buyer behavior or to total revenue. For example, "Because the magnitude is greater than 1, demand is elastic, so a price increase reduces total revenue."
• Read carefully for direction. The sign tells you the relationship (negative for demand by the law of demand), but the magnitude tells you elastic versus inelastic.

Common Trap

• Treating slope as elasticity. They are not the same. On one straight demand curve, elasticity changes from elastic at the top to inelastic at the bottom.
• Forgetting the absolute value. Comparisons of "more" or "less" elastic use the magnitude.

Common Misconceptions

• "Elasticity equals slope." False. A linear demand curve has constant slope but changing elasticity along its length.
• "Elasticity is just the change in quantity divided by the change in price." That gives slope-like numbers, not elasticity. You must use percentage changes.
• "A negative elasticity means demand is weird." No. PED is normally negative because price and quantity move in opposite directions. The magnitude, not the sign, tells you elastic or inelastic.
• "Necessities are always perfectly inelastic." Real necessities are usually relatively inelastic, not perfectly inelastic. Perfect inelasticity is a conceptual extreme.
• "If price rises, total revenue always rises." Only when demand is inelastic. With elastic demand, raising price lowers total revenue.
• "More expensive goods are more elastic." Price level alone does not determine elasticity. Factors like the availability of substitutes matter more.

Related AP Microeconomics Guides

• 2.1 Demand
• 2.6 Market Equilibrium and Consumer and Producer Surplus
• 2.8 The Effects of Government Intervention in Markets
• 2.2 Supply
• 2.5 Other Elasticities
• 2.7 Market Disequilibrium and Changes in Equilibrium