Chapter 4 told you the direction. Elasticity puts a number on the size, and that number decides whether a price rise makes you richer or poorer — which is why this chapter owns the revenue test and, later, who really pays a tax.
Price elasticity of demand is how much quantity responds to price — expressed as a ratio of percentage changes, so the units cancel and the number is comparable across any two goods.
Ed = %Δ quantity demanded ÷ %Δ price. Because demand slopes down, this is always
negative — so by convention we discuss the absolute value. Write |Ed| and the sign
stops causing trouble.
| |Ed| | Called | Means |
|---|---|---|
| > 1 | Elastic | Quantity responds more than proportionally. Buyers are sensitive. |
| < 1 | Inelastic | Quantity barely moves. Buyers are stuck. |
| = 1 | Unit elastic | Proportional. The knife edge where revenue peaks. |
| 0 | Perfectly inelastic | Vertical curve. Quantity never changes. |
| ∞ | Perfectly elastic | Horizontal curve. Any price rise kills all sales. |
Ordinary percentage changes give you a different answer depending on which end you start from. The midpoint formula removes that, and it is the one the exam wants.
Divide each change by the average of the two values rather than by the starting value:
%ΔQ = (Q₂−Q₁) ÷ ((Q₁+Q₂)/2), and the same for price. Then divide. Because both ends
use the same denominator, going up and coming back down give the identical elasticity — which the
naïve method does not.
Set two points below. The panel shows the naïve answer alongside the midpoint one so you can see how far apart they get.
The most misunderstood fact in the chapter: a straight demand curve has a constant slope but a changing elasticity. Those are different things.
High up a linear demand curve the price is large and the quantity small, so a given dollar change is a small percentage of price and a large percentage of quantity — demand is elastic. Low down the reverse holds and it is inelastic. Exactly halfway it is unit elastic.
| If demand is… | Raise the price | Cut the price |
|---|---|---|
| Elastic (|Ed| > 1) | Revenue falls | Revenue rises |
| Inelastic (|Ed| < 1) | Revenue rises | Revenue falls |
| Unit elastic | No change | No change |
One sentence to remember it by: revenue moves with whichever is less responsive. If quantity barely budges, price wins. Drag along the curve below and watch total revenue peak exactly where elasticity equals one.
Same ratio, different numerator or denominator. Here the sign carries the meaning, so do not discard it as you did for price elasticity of demand.
| Elasticity | Formula | What the sign tells you |
|---|---|---|
| Income | %ΔQ ÷ %Δ income | Positive → normal good. Negative → inferior good. Above +1 → luxury. |
| Cross-price | %ΔQ of A ÷ %ΔP of B | Positive → substitutes. Negative → complements. Near zero → unrelated. |
| Price elasticity of supply | %ΔQ supplied ÷ %ΔP | Positive throughout. Larger with more time and spare capacity. |
Tax incidence is this chapter with a wedge: whichever side is less elastic ends up paying more of a tax, for exactly the reason the revenue test works — the side that cannot easily walk away absorbs the change.
Shuffled. Several items turn on a sign, and several on which formula was asked for.
| Model | Genuinely computed | Simplified |
|---|---|---|
| Two-point elasticity | Both percentage changes by the midpoint formula, the elasticity, its classification, the naïve from-the-start figure for contrast, and the revenue change between the two points. | Two points only — no curve is fitted between them. |
| Along the curve | Price from the linear demand curve, point elasticity as (1/slope)(P/Q), total revenue at every quantity, and the revenue-maximising point found from the curve itself. | Linear demand. A constant-elasticity curve would look different, and real demand curves are neither. |