Price elasticity: -1.2 is more elastic than -0.4
Two goods have own-price elasticities of demand of -0.4 and -1.2. Asked which demand is more elastic, a candidate who compares the coefficients as written picks -0.4, because -0.4 really is the greater number. The answer is -1.2. Own-price elasticity is compared by absolute value, and 1.2 clears the threshold of 1 while 0.4 does not.
The sign is fixed, so it carries no information
Own-price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.
Own-price elasticity of demand = %ΔQd ÷ %ΔP
Along a downward-sloping demand curve those two percentages always have opposite signs, so the ratio is always negative. Always. A number that comes out negative for every good in every question cannot tell one good from another, which is why the classification thresholds are stated on the absolute value: elastic above 1, inelastic below 1, unit elastic at exactly 1.
This is also why the exam says “more elastic” instead of “larger elasticity”. Moving from -0.4 to -1.2 lowers the coefficient and raises the elasticity at the same time. Both statements are true. Only one of them is being asked about, and the answer choices are usually built so that the other one is available.
Working a full example
A producer raises price from 20 to 22, and unit sales fall from 500 to 440.
%ΔP = (22 - 20) ÷ 20 = +10%
%ΔQd = (440 - 500) ÷ 500 = -12%
Own-price elasticity = -12% ÷ 10% = -1.2
The absolute value is 1.2, above 1, so demand is elastic over this range. Revenue agrees. Total revenue was 20 × 500 = 10,000 and is now 22 × 440 = 9,680. A price increase that shrinks revenue is the signature of elastic demand, and it is the fastest way to sanity-check a coefficient under time pressure.
The same two points produce a different number under the midpoint method, which divides each change by the average of the starting and ending values rather than by the starting value alone.
Midpoint elasticity = (-60 ÷ 470) ÷ (2 ÷ 21) = -12.77% ÷ 9.52% = -1.34
Both -1.2 and -1.34 are defensible, and the wording of the item decides which one it wants. Neither of them is positive, and neither changes the classification.
Where the sign is the entire answer
Cross-price and income elasticity are built from the same ratio, but their signs are not fixed in advance. That makes the sign the thing being tested.
Cross-price elasticity divides the percentage change in quantity demanded of one good by the percentage change in the price of another. A 10% rise in the price of good B that lifts quantity demanded of good A by 4% gives +0.40, and the two goods are substitutes. A negative coefficient would make them complements.
Income elasticity divides the percentage change in quantity demanded by the percentage change in income. Income up 5%, quantity down 2%, and income elasticity is -0.40: an inferior good. Positive would mean a normal good.
Notice that +0.40 and -0.40 sit the same distance from zero and describe opposite economics. Stripping the sign here, the habit that is correct for own-price elasticity, deletes the answer. The three measures share one formula and follow three different reading rules, which is exactly why they get mixed up.
Quick reference
| Question wording | What it establishes | Risk if missed |
|---|---|---|
| “Which demand is more elastic” | Compare absolute values | Picking the coefficient nearer zero because it is the larger number |
| “Own-price elasticity is -0.8” | Inelastic, because 0.8 is below 1 | Reading the minus sign itself as a classification |
| “Cross-price elasticity is positive” | The goods are substitutes | Discarding the sign and comparing magnitudes only |
| “Income elasticity is negative” | An inferior good | Treating it as a weakly normal good |
| “Use the midpoint method” | Divide by the average of start and end values | Dividing by the starting value and reporting -1.2 for -1.34 |
The habit worth building is to ask what a sign is doing before removing it. It is the same discipline the cash conversion cycle asks for, where the minus in front of DPO is not an inconvenience to be tidied away but the whole economic point of the measure.
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