Elasticity worksheet

Elasticity: answer key

1. 1. (C) |Ed| = |(-20%) / (10%)| = 2.0. Demand is elastic, meaning quantity responded more than proportionally to the price change. Option A flips the fraction, dividing price change by quantity change instead of the other way around. Option B would require the percentage changes to be equal. Option D has no connection to the given numbers.

2. 2. (B) With inelastic demand, quantity barely falls when price rises. The higher per-unit price more than compensates for the small quantity loss, so TR goes up. Option A describes what happens when demand is elastic and customers leave in large numbers. Option C requires unit elasticity, |Ed| = 1 exactly. Option D is irrelevant because the total revenue test depends entirely on elasticity, not on marginal cost or any cost measure.

3. 3. (C) Dozens of close alternatives exist for any particular brand of bottled water: other brands, tap water, filtered water, etc. All those substitutes make demand highly elastic. Raise the price and buyers just grab something else. Insulin has essentially no substitute for a diabetic patient, making demand extremely inelastic. Salt takes a tiny share of anyone's budget and has few practical alternatives. Electricity from a local utility faces no real competition either.

4. 4. (C) The slope stays constant on a linear demand curve, but elasticity does not, because it depends on the P/Q ratio, which shifts at every point. At the midpoint, that ratio yields |Ed| = 1. The top of the curve has high P and low Q, giving |Ed| > 1 (elastic). The bottom has low P and high Q, giving |Ed| < 1 (inelastic). Option D is a common mistake that confuses constant slope with constant elasticity, and those are two different things.

5. 5. (B) Negative cross-price elasticity means that when B's price rises, demand for A falls. They move together, like printers and ink. That's the signature of complements. Substitutes require a positive coefficient, because a price hike on one sends buyers toward the other. Options C and D involve income elasticity, which is a completely different measure. Normal and inferior classify goods by how they respond to income changes, not to another good's price.

6. 6. (B) Midpoint %ΔQ = (60 − 40) / 50 = 40%. Midpoint %ΔP = (8 − 12) / 10 = −40%. |Ed| = |40% / −40%| = 1.0, so demand is unit elastic. Option A likely comes from using simple percentage changes with the starting value as the base instead of the midpoint average. Option C probably results from a denominator error in one of the calculations. Option D would require quantity to change by double the percentage of price.

7. 7. (C) Negative income elasticity means people buy less of this good as their income rises. That is the definition of an inferior good. Generic store-brand cereal that gets replaced by name-brand once paychecks grow is a classic example. A normal necessity has positive Ei between 0 and 1, and a normal luxury has Ei above 1; both are positive. Option D describes a cross-price relationship, not an income-elasticity classification.

8. 8. (B) Quantity never changes regardless of what happens to price. That's a vertical line on the graph, with price moving along the y-axis while quantity stays fixed on the x-axis. |Ed| = 0. A horizontal curve is perfectly elastic, which is the exact opposite case. A slope of -1 just describes one particular downward-sloping line that still has varying elasticity along it. An upward-sloping curve describes supply.

9. 9. (C) Midpoint %ΔQ = (200 − 300) / 250 = −40%. Midpoint %ΔP = (7 − 5) / 6 = 33.3%. |Ed| = 40% / 33.3% = 1.2, so demand is elastic over this range. Option A divides the price change by the quantity change instead of the correct way around. Option B would need equal percentage changes. Option D overstates the ratio, likely from computing simple percentage changes off the initial values rather than using midpoint averages.

10. 10. (B) Price went up and total revenue went up, so the total revenue test tells us demand is inelastic. Quantity fell, but not by enough proportionally to offset the higher price. Option A gets the logic backwards: elastic demand would cause revenue to *fall* when price rises. Option C is wrong because unit elasticity means revenue stays exactly the same, and $20,900 is not $20,000. Option D is incorrect because the total revenue test exists specifically to determine elasticity from revenue data.

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