When a streaming service raises its subscription $2, almost nobody cancels. When one gas station raises prices 20 cents while the station across the street doesn't, drivers switch. 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) — it turns "quantity falls" into "quantity falls by how much." Elasticity questions are among the most common calculation items on the CLEP exam.
PED = %ΔQd / %ΔP
Because demand slopes downward, PED is technically negative; by convention we use 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 (a fixed-dose medication) |
| = ∞ | 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 the answer independent of direction, use the midpoint (arc) formula whenever a question gives you two price–quantity points:
PED = [(Q2 − Q1) / ((Q1 + Q2)/2)] ÷ [(P2 − P1) / ((P1 + P2)/2)]
Example: a food truck raises its lunch plate from $8 to $10, and daily sales fall from 110 to 90. - %ΔQ = −20 / 100 = −20% - %ΔP = 2 / 9 ≈ 22.2% - |PED| = 20 / 22.2 ≈ 0.9 → inelastic
Use the midpoint method when asked for elasticity "between two points"; use simple percentages when the problem hands them to you directly ("a 10% price increase reduces quantity 4%").
Demand is more elastic when the good has: 1. Many close substitutes (one brand of bottled water vs. water in general) 2. A large share of the buyer's budget (a car vs. a pack of gum) 3. Luxury status rather than necessity 4. More time for buyers to adjust (a commuter's gasoline demand is inelastic this week; over years, she can carpool, buy a hybrid, or move) 5. A narrow definition ("one grocery chain's store-brand cereal" 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 if a toll authority raises the toll and toll revenue rises, demand for the bridge is inelastic — no calculation needed. This is the single fastest elimination tool on the exam.
High-frequency fact: 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, because slope and elasticity are different things.
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 — hotel rooms in town tonight); in the short run, firms vary some inputs; in the long run, firms enter or exit and PES is highest. Supply is also more elastic when inputs are easy to obtain and production ramps quickly.
YED = %ΔQd / %Δincome
XED = %ΔQd of good A / %ΔP of good B
The sign IS the answer for YED and XED — never take absolute values here; the sign carries the classification. Absolute value is only the convention for PED.
1. A — Midpoint: %ΔQ = −2,000/4,000 = −50%; %ΔP = 4/12 ≈ +33.3%; |PED| = 50/33.3 = 1.5 > 1 → elastic. - B (0.67): inverts the ratio, dividing %ΔP by %ΔQ. - C (1.0): uses simple percentages from the starting points (−40%/+40%) instead of midpoints. - D (2.5): divides the raw quantity change by the raw price change with no percentages at all. - E (0.4): treats the price change percentage as the quantity change and halves it. - Fix: Between two points, always average the bases (midpoint method), and put %ΔQ on top.
2. E — A single brand at a single store has many close substitutes and is narrowly defined — both push elasticity up. - A: insulin is a medical necessity with no substitutes — nearly perfectly inelastic, the opposite case. - B: a one-week horizon leaves commuters no time to adjust; short time frames make demand inelastic. - C: household electricity is a broad necessity with few short-run substitutes. - D: table salt is a tiny budget share with no real substitute — classically inelastic. - Fix: Scan for substitutes, budget share, luxury status, time, and narrowness — the more boxes checked, the more elastic.
3. D — Price fell AND total revenue fell → the price effect dominated the quantity effect → inelastic demand. - A: elastic demand would make revenue rise when price falls (quantity effect dominates). - B: unit elastic demand would leave revenue unchanged. - C: perfectly elastic demand means buyers respond infinitely to price — revenue could not fall from a price cut. - E: the total revenue test is precisely the tool that classifies elasticity without quantity data. - Fix: P and TR move the same direction → inelastic; opposite directions → elastic; TR flat → unit elastic.
4. B — On a linear demand curve, elasticity falls as you slide down: elastic above the midpoint, unit elastic at the midpoint (TR max), inelastic below. - A: constant slope does not mean constant elasticity — elasticity uses percentages, which change along the line. - C: reverses the halves. - D: TR is maximized at the unit elastic midpoint, not where demand is most elastic. - E: slope and elasticity are different measures; they are equal nowhere in general. - Fix: Linear demand = one slope, many elasticities: elastic up top, unit elastic in the middle, inelastic down low.
5. B — With elastic demand, a price cut raises quantity more than proportionally, so total revenue rises. - A: raising price on elastic demand loses so many customers that revenue falls. - C: revenue is maximized only at unit elasticity, not where demand is elastic. - D: correct direction for inelastic demand, and the label is wrong — a price rise losing revenue is the quantity effect dominating, which argues against raising price. - E: right action, wrong reason — with elastic demand the quantity effect dominates, not the price effect. - Fix: Elastic → cut price to raise revenue; inelastic → raise price to raise revenue.
6. E — Negative cross-price elasticity means the goods are consumed together: a pricier coffee maker reduces pod purchases. - A: substitutes have positive XED. - B: unrelated goods have XED near zero, not −1.4. - C: inferior/normal classification comes from income elasticity, not cross-price. - D: same confusion — normal goods are identified by YED > 0, not by XED. - Fix: XED sign: positive = substitutes, negative = complements; the sign is the answer.
7. C — Income rose and quantity fell → YED = −4%/8% = −0.5 < 0 → inferior good. - A: a luxury requires YED > +1; this YED is negative. - B: a necessity requires YED between 0 and +1. - D: complements are identified by negative cross-price elasticity, not income elasticity. - E: substitutes are identified by positive cross-price elasticity. - Fix: Income up, quantity down → inferior; income up, quantity up → normal (over +1 = luxury).
8. B — Time is the dominant determinant of supply elasticity: over years, builders can add units, so quantity supplied responds strongly to rent changes. - A: demand-side elasticity does not determine supply elasticity. - C: prices returning to equilibrium is a different claim; it says nothing about the size of quantity response. - D: depreciation shrinks the stock; it does not explain greater responsiveness to price. - E: there is no rule pinning long-run PES at 1; it simply rises with the time horizon. - Fix: For PES, ask "how much time do producers have to adjust?" — more time, more elastic.
9. D — Fixed quantity at any price = vertical demand curve = perfectly inelastic, PED = 0. - A: horizontal with PED = ∞ is perfectly elastic — the opposite limit case. - B: mismatched pair — horizontal curves have infinite, not zero, elasticity. - C: mismatched pair — vertical curves have zero, not infinite, elasticity. - E: PED = 1 describes unit elasticity, where quantity does respond to price. - Fix: Vertical = 0 response = PED 0; horizontal = infinite response = PED ∞ (match the shape to the number).
10. C — Supply shifts right → price falls, quantity rises. With inelastic demand, %ΔP > %ΔQ, so TR = P × Q falls: the "great harvest, hard year" paradox. - A: quantity does rise, but with inelastic demand the price collapse outweighs it. - B: opposite movements don't cancel unless demand is exactly unit elastic. - D: a rightward supply shift lowers price; it cannot raise it. - E: quantity rises (movement down the demand curve), it doesn't fall. - Fix: Inelastic demand + supply increase → price falls harder than quantity rises → revenue falls.
11. C — PED 0.6 < 1 → inelastic → a price increase raises total revenue because members quit proportionally less than dues rise. - A: some members do quit, but with inelastic demand the losses are too small to offset the higher price. - B: exact offset happens only at unit elasticity (PED = 1), not 0.6. - D: the law of demand still holds — quantity falls when price rises; inelastic just means "falls a little." - E: revenue rises despite falling membership, not because of rising membership. - Fix: Inelastic (PED < 1): price and revenue move together; quantity still moves opposite to price.
12. A — Midpoint: %ΔQ = 4/12 ≈ +33.3%; %Δincome = 20,000/50,000 = +40%; YED ≈ 33.3/40 = +0.8. Positive → normal good (0 < YED < 1: a necessity-type normal good). - B (+1.2): inverts the ratio (income change over quantity change). - C (−0.8): flips the sign even though income and quantity moved in the same direction. - D: contradicts itself — a positive YED can never indicate an inferior good. - E (+2.0): divides raw changes (4 meals / 2 ten-thousands) without converting to percentages. - Fix: YED = %ΔQ over %Δincome, midpoint bases, and read the sign before the size.
1. A — Midpoint: %ΔQ = −2,000/4,000 = −50%; %ΔP = 4/12 ≈ +33.3%; |PED| = 50/33.3 = 1.5 > 1 → elastic. - B (0.67): inverts the ratio, dividing %ΔP by %ΔQ. - C (1.0): uses simple percentages from the starting points (−40%/+40%) instead of midpoints. - D (2.5): divides the raw quantity change by the raw price change with no percentages at all. - E (0.4): treats the price change percentage as the quantity change and halves it. - Fix: Between two points, always average the bases (midpoint method), and put %ΔQ on top.
2. E — A single brand at a single store has many close substitutes and is narrowly defined — both push elasticity up. - A: insulin is a medical necessity with no substitutes — nearly perfectly inelastic, the opposite case. - B: a one-week horizon leaves commuters no time to adjust; short time frames make demand inelastic. - C: household electricity is a broad necessity with few short-run substitutes. - D: table salt is a tiny budget share with no real substitute — classically inelastic. - Fix: Scan for substitutes, budget share, luxury status, time, and narrowness — the more boxes checked, the more elastic.
3. D — Price fell AND total revenue fell → the price effect dominated the quantity effect → inelastic demand. - A: elastic demand would make revenue rise when price falls (quantity effect dominates). - B: unit elastic demand would leave revenue unchanged. - C: perfectly elastic demand means buyers respond infinitely to price — revenue could not fall from a price cut. - E: the total revenue test is precisely the tool that classifies elasticity without quantity data. - Fix: P and TR move the same direction → inelastic; opposite directions → elastic; TR flat → unit elastic.
4. B — On a linear demand curve, elasticity falls as you slide down: elastic above the midpoint, unit elastic at the midpoint (TR max), inelastic below. - A: constant slope does not mean constant elasticity — elasticity uses percentages, which change along the line. - C: reverses the halves. - D: TR is maximized at the unit elastic midpoint, not where demand is most elastic. - E: slope and elasticity are different measures; they are equal nowhere in general. - Fix: Linear demand = one slope, many elasticities: elastic up top, unit elastic in the middle, inelastic down low.
5. B — With elastic demand, a price cut raises quantity more than proportionally, so total revenue rises. - A: raising price on elastic demand loses so many customers that revenue falls. - C: revenue is maximized only at unit elasticity, not where demand is elastic. - D: correct direction for inelastic demand, and the label is wrong — a price rise losing revenue is the quantity effect dominating, which argues against raising price. - E: right action, wrong reason — with elastic demand the quantity effect dominates, not the price effect. - Fix: Elastic → cut price to raise revenue; inelastic → raise price to raise revenue.
6. E — Negative cross-price elasticity means the goods are consumed together: a pricier coffee maker reduces pod purchases. - A: substitutes have positive XED. - B: unrelated goods have XED near zero, not −1.4. - C: inferior/normal classification comes from income elasticity, not cross-price. - D: same confusion — normal goods are identified by YED > 0, not by XED. - Fix: XED sign: positive = substitutes, negative = complements; the sign is the answer.
7. C — Income rose and quantity fell → YED = −4%/8% = −0.5 < 0 → inferior good. - A: a luxury requires YED > +1; this YED is negative. - B: a necessity requires YED between 0 and +1. - D: complements are identified by negative cross-price elasticity, not income elasticity. - E: substitutes are identified by positive cross-price elasticity. - Fix: Income up, quantity down → inferior; income up, quantity up → normal (over +1 = luxury).
8. B — Time is the dominant determinant of supply elasticity: over years, builders can add units, so quantity supplied responds strongly to rent changes. - A: demand-side elasticity does not determine supply elasticity. - C: prices returning to equilibrium is a different claim; it says nothing about the size of quantity response. - D: depreciation shrinks the stock; it does not explain greater responsiveness to price. - E: there is no rule pinning long-run PES at 1; it simply rises with the time horizon. - Fix: For PES, ask "how much time do producers have to adjust?" — more time, more elastic.
9. D — Fixed quantity at any price = vertical demand curve = perfectly inelastic, PED = 0. - A: horizontal with PED = ∞ is perfectly elastic — the opposite limit case. - B: mismatched pair — horizontal curves have infinite, not zero, elasticity. - C: mismatched pair — vertical curves have zero, not infinite, elasticity. - E: PED = 1 describes unit elasticity, where quantity does respond to price. - Fix: Vertical = 0 response = PED 0; horizontal = infinite response = PED ∞ (match the shape to the number).
10. C — Supply shifts right → price falls, quantity rises. With inelastic demand, %ΔP > %ΔQ, so TR = P × Q falls: the "great harvest, hard year" paradox. - A: quantity does rise, but with inelastic demand the price collapse outweighs it. - B: opposite movements don't cancel unless demand is exactly unit elastic. - D: a rightward supply shift lowers price; it cannot raise it. - E: quantity rises (movement down the demand curve), it doesn't fall. - Fix: Inelastic demand + supply increase → price falls harder than quantity rises → revenue falls.
11. C — PED 0.6 < 1 → inelastic → a price increase raises total revenue because members quit proportionally less than dues rise. - A: some members do quit, but with inelastic demand the losses are too small to offset the higher price. - B: exact offset happens only at unit elasticity (PED = 1), not 0.6. - D: the law of demand still holds — quantity falls when price rises; inelastic just means "falls a little." - E: revenue rises despite falling membership, not because of rising membership. - Fix: Inelastic (PED < 1): price and revenue move together; quantity still moves opposite to price.
12. A — Midpoint: %ΔQ = 4/12 ≈ +33.3%; %Δincome = 20,000/50,000 = +40%; YED ≈ 33.3/40 = +0.8. Positive → normal good (0 < YED < 1: a necessity-type normal good). - B (+1.2): inverts the ratio (income change over quantity change). - C (−0.8): flips the sign even though income and quantity moved in the same direction. - D: contradicts itself — a positive YED can never indicate an inferior good. - E (+2.0): divides raw changes (4 meals / 2 ten-thousands) without converting to percentages. - Fix: YED = %ΔQ over %Δincome, midpoint bases, and read the sign before the size.