When streaming services raise prices $2, almost nobody cancels. When one airline raises fares $20 on a competitive route, passengers scatter to rivals. Same direction of change, wildly different responses. Elasticity measures the sensitivity of quantity to a change in price (or income, or another good's price) — turning Lesson 3's "quantity falls" into "quantity falls by how much." Expect 4–6 MC questions and a frequent FRQ part on this.
PED = %ΔQd / %ΔP
Because demand slopes downward, PED is technically negative; AP convention uses the absolute value.
| |PED| | Category | Meaning | |---|---|---| | > 1 | Elastic | Quantity responds more than proportionally | | < 1 | Inelastic | Quantity responds less than proportionally | | = 1 | Unit elastic | Exactly proportional | | = 0 | Perfectly inelastic | Vertical demand — same quantity at any price (insulin-like) | | = ∞ | Perfectly elastic | Horizontal demand — any price rise loses all buyers |
[GRAPH: Two demand curves through the same point. Steep curve labeled "relatively inelastic"; flat curve labeled "relatively elastic". Plus two limit cases: vertical line labeled "perfectly inelastic (PED = 0)"; horizontal line labeled "perfectly elastic (PED = ∞)".]
To make elasticity independent of direction, the AP exam uses the midpoint (arc) formula:
PED = [(Q2 − Q1) / ((Q1 + Q2)/2)] ÷ [(P2 − P1) / ((P1 + P2)/2)]
Example: price rises $4 → $6, quantity falls 100 → 80.
- %ΔQ = −20 / 90 ≈ −22.2%
- %ΔP = 2 / 5 = 40%
- PED = 22.2 / 40 ≈ 0.56 → inelastic
(The simple method gives −20%/+50% = 0.4 — direction-dependent, which is why midpoint exists. Use midpoint when asked "between two points"; use simple %s when the problem hands them to you.)
Demand is more elastic when the good has: 1. Many close substitutes (one airline vs. all air travel) 2. A large share of the buyer's budget (cars vs. gum) 3. Luxury status rather than necessity 4. More time for buyers to adjust (gasoline is inelastic this week, more elastic over years) 5. Narrow definition ("Cheerios" is more elastic than "breakfast food")
Total revenue (TR) = P × Q
| Demand is… | Price ↑ | Price ↓ |
|---|---|---|
| Elastic | TR ↓ | TR ↑ |
| Inelastic | TR ↑ | TR ↓ |
| Unit elastic | TR unchanged (max) | TR unchanged (max) |
Logic: with elastic demand, the quantity effect dominates the price effect; with inelastic demand, the price effect dominates. So: "the toll rose and toll revenue rose" → demand for the bridge is inelastic. No calculation needed.
Bonus fact (frequent MC): along a straight-line demand curve, elasticity varies — elastic on the upper-left half, unit elastic at the midpoint (where TR is maximized), inelastic on the lower-right half. A straight line does not have one elasticity.
PES = %ΔQs / %ΔP (positive, since supply slopes up)
Same vocabulary (elastic > 1, inelastic < 1). The dominant determinant is time: in the market period supply is nearly fixed (perfectly inelastic — think concert seats tonight); in the short run firms vary some inputs; in the long run firms enter/exit and PES is highest. Also more elastic when inputs are easily obtained and production can ramp quickly.
YED = %ΔQd / %Δincome
XED = %ΔQd of good A / %ΔP of good B
Sign is the answer for YED and XED — don't take absolute values here; the sign carries the meaning.
A 10% tuition increase reduces enrollment by 4%. Elasticity? Effect on tuition revenue?
Solution: PED = 4% / 10% = 0.4 → inelastic. Inelastic + price ↑ → TR rises.
Interpretation: Schools with captive applicants raise price and gain revenue; the % numbers do all the work.
Price falls from $12 to $8; quantity rises from 40 to 60. Compute PED via midpoint and classify.
Solution:
- %ΔQ = 20 / 50 = 40%
- %ΔP = −4 / 10 = −40%
- |PED| = 40 / 40 = 1.0 → unit elastic. TR check: before 12 × 40 = $480; after 8 × 60 = $480 — unchanged, confirming unit elasticity.
Interpretation: The TR cross-check catches arithmetic slips instantly. Use it.
When consumer incomes rise 5%, quantity demanded of Good X falls 2%. When the price of Good Y rises 10%, quantity demanded of Good X rises 6%. Characterize Good X and its relationship to Y.
Solution:
- YED = −2/5 = −0.4 < 0 → X is an inferior good.
- XED = 6/10 = +0.6 > 0 → X and Y are substitutes.
Interpretation: Story: X could be store-brand cereal; Y the name brand. Signs first, magnitudes second.
A transit authority needs more revenue. An economist reports bus-ride PED = 0.5 at current fares. Should fares rise or fall? What if PED were 1.8?
Solution: PED 0.5 (inelastic): raise fares → TR ↑. PED 1.8 (elastic): raising fares would cut TR; lower fares to raise revenue.
Interpretation: Policy questions like this are the FRQ's favorite application — always justify with which effect (price or quantity) dominates.
1. (E) |PED| = 30/20 = 1.5 > 1 → elastic; elastic + price ↑ → TR falls (quantity effect dominates).
2. (C) Few substitutes + necessity = inelastic. (A), (B), (D), (E) all raise elasticity.
3. (C) Midpoint: %ΔQ = (45 − 55)/50 = −20%; %ΔP = (11 − 9)/10 = +20%; |PED| = 20/20 = 1.0 → unit elastic. (A) comes from halving one percentage; (B) from inverting the ratio.
4. (D) Price ↑ and TR ↑ → price effect dominated → inelastic.
5. (B) Linear demand: elastic upper half, unit elastic at midpoint (TR max), inelastic lower half. Slope constant, elasticity not.
6. (C) Negative XED → complements. Sign carries the classification.
7. (D) YED > 1 → income-sensitive normal good = luxury.
8. (C) Time is the key PES determinant — long run lets builders add supply. (A), (B), (D), (E) all reduce responsiveness.
9. (B) Perfectly inelastic = vertical = quantity fixed regardless of price.
10. (B) Inelastic demand + supply ↑ → price falls proportionally more than quantity rises → TR falls. The classic "good harvest, bad year for farmers" paradox.
11. (FRQ rubric, 7 points) - (a) 3 pts: %ΔQ = (90,000 − 100,000)/95,000 = −10.53% (1); %ΔP = 0.50/2.25 = +22.2% (1); |PED| = 10.53/22.2 ≈ 0.47 (1). - (b) 1 pt: Inelastic — |PED| < 1; quantity fell proportionally less than price rose. - (c) 2 pts: Before: 2.00 × 100,000 = $200,000; after: 2.50 × 90,000 = $225,000 (1). Yes — with inelastic demand, the fare increase raised revenue by $25,000/day (1). - (d) 1 pt: Demand becomes more elastic over time as riders find substitutes (bikes, carpools, moving); long-run responses are larger than short-run.
11. (FRQ-style) The Metro Transit Authority currently charges $2.00 per ride and sells 100,000 rides per day. It raises the fare to $2.50, and ridership falls to 90,000 per day. (a) Using the midpoint method, calculate the price elasticity of demand. Show your work. (b) Is demand elastic, inelastic, or unit elastic? Explain using your answer to (a). (c) Calculate total revenue before and after the fare increase. Was the fare increase a good revenue decision? (d) Over several years, riders can buy bikes, move, or carpool. What happens to the elasticity of demand for rides over time, and why?
1. (E) |PED| = 30/20 = 1.5 > 1 → elastic; elastic + price ↑ → TR falls (quantity effect dominates).
2. (C) Few substitutes + necessity = inelastic. (A), (B), (D), (E) all raise elasticity.
3. (C) Midpoint: %ΔQ = (45 − 55)/50 = −20%; %ΔP = (11 − 9)/10 = +20%; |PED| = 20/20 = 1.0 → unit elastic. (A) comes from halving one percentage; (B) from inverting the ratio.
4. (D) Price ↑ and TR ↑ → price effect dominated → inelastic.
5. (B) Linear demand: elastic upper half, unit elastic at midpoint (TR max), inelastic lower half. Slope constant, elasticity not.
6. (C) Negative XED → complements. Sign carries the classification.
7. (D) YED > 1 → income-sensitive normal good = luxury.
8. (C) Time is the key PES determinant — long run lets builders add supply. (A), (B), (D), (E) all reduce responsiveness.
9. (B) Perfectly inelastic = vertical = quantity fixed regardless of price.
10. (B) Inelastic demand + supply ↑ → price falls proportionally more than quantity rises → TR falls. The classic "good harvest, bad year for farmers" paradox.
11. (FRQ rubric, 7 points) - (a) 3 pts: %ΔQ = (90,000 − 100,000)/95,000 = −10.53% (1); %ΔP = 0.50/2.25 = +22.2% (1); |PED| = 10.53/22.2 ≈ 0.47 (1). - (b) 1 pt: Inelastic — |PED| < 1; quantity fell proportionally less than price rose. - (c) 2 pts: Before: 2.00 × 100,000 = $200,000; after: 2.50 × 90,000 = $225,000 (1). Yes — with inelastic demand, the fare increase raised revenue by $25,000/day (1). - (d) 1 pt: Demand becomes more elastic over time as riders find substitutes (bikes, carpools, moving); long-run responses are larger than short-run.
Exam tip: The two highest-frequency elasticity questions are (1) midpoint calculations and (2) the total revenue test. If a question mentions a price change and a revenue direction, you can classify elasticity with zero math. And remember the linear-demand fact — "elasticity varies along a straight line" eliminates two distractors instantly.