Elasticity

You’ll be able to

Calculate and interpret the price elasticity of demand
Relate elasticity to total revenue
Distinguish price elasticity of supply, income elasticity, and cross-price elasticity

Price elasticity of demand

Price elasticity of demand (Ed) measures how responsive quantity demanded is to a price change — the percentage change in quantity divided by the percentage change in price. Demand is elastic (|Ed| > 1) when quantity responds a lot (luxuries, goods with close substitutes, long time horizons); inelastic (|Ed| < 1) when it barely responds (necessities, few substitutes, short run); and unit elastic (|Ed| = 1) when the percentages match. Because price and quantity move in opposite directions, Ed is technically negative; economists usually cite its absolute value.

Elasticity and total revenue

Elasticity predicts what happens to total revenue (price × quantity) when price changes. If demand is elastic, quantity responds more than price, so a price cut raises total revenue (and a price hike lowers it). If demand is inelastic, quantity responds less than price, so a price increase raises total revenue. If unit elastic, total revenue is unchanged at the maximum. This total-revenue test lets you infer elasticity from how revenue moves — a favorite AP application, especially for pricing decisions.

Other elasticities

Beyond price elasticity of demand, three more matter. Price elasticity of supply measures how responsive quantity supplied is to price (higher when firms can adjust output easily and over longer time). Income elasticity of demand is positive for normal goods and negative for inferior goods (demand falls as income rises). Cross-price elasticity is positive for substitutes (a rise in one’s price raises demand for the other) and negative for complements (a rise in one’s price lowers demand for the other). The sign carries the economic meaning.

Price elasticity of demand

Ed = (% change in quantity demanded) / (% change in price)

Elastic if |Ed| > 1, inelastic if |Ed| < 1, unit elastic if |Ed| = 1. Total-revenue test: cut price to raise revenue when elastic; raise price to raise revenue when inelastic.

Worked example

When a coffee shop raises its price from $4 to $5, quantity sold falls from 100 to 80 cups per day. Calculate the price elasticity of demand and state whether the shop’s total revenue rose or fell.

1.% change in quantity = (80 − 100) / 100 = −20%.
2.% change in price = (5 − 4) / 4 = +25%.
3.Ed = −20% / 25% = −0.8, so |Ed| = 0.8 < 1 → demand is inelastic.
4.Total revenue: before = $4 × 100 = $400; after = $5 × 80 = $400. Revenue is unchanged here, consistent with fairly inelastic demand where a price rise nearly offsets the quantity drop.

Answer: Ed ≈ −0.8 (|Ed| = 0.8), so demand is inelastic. Total revenue held at $400. With inelastic demand, raising price does not reduce revenue — and here the modest quantity drop just offset the price increase.

Checkpoint

A firm finds that when it raises the price of its product, its total revenue increases. This tells you that the demand for the product is:

Watch out

Elasticity is about percentage changes, not absolute ones, and the price elasticity of demand is negative because price and quantity move oppositely. Compare its absolute value to 1: greater than 1 is elastic, less than 1 is inelastic.

Checkpoint

The cross-price elasticity of demand between good X and good Y is measured to be −1.5. This indicates that X and Y are:

On the exam

For cross-price and income elasticities, read the sign first: cross-price positive = substitutes, negative = complements; income positive = normal, negative = inferior. Magnitude tells you how strong, but the sign tells you what kind.

Answer the 2 checkpoints as you read.