01 / 22

Price Elasticity
of Demand

Understand how sensitive consumers are to price changes and learn to calculate, interpret, and apply the elasticity coefficient across real-world markets.

AP Microeconomics

What Is Elasticity?

In economics, elasticity measures how much one variable responds to a change in another. Price elasticity of demand (PED) specifically measures how the quantity demanded of a good responds when its price changes.

The Elasticity Formula

Price elasticity of demand is calculated as:

\(\%\;\Delta\;Q_d\)
Percentage change in quantity demanded
\(\%\;\Delta\;P\)
Percentage change in price

Why Does PED Matter?

Firms
Decide whether raising prices will increase or decrease total revenue
Governments
Predict tax revenue and the burden of excise taxes on consumers vs. producers
Consumers
Understand which goods take a larger share of their budget when prices rise

The Midpoint Method

To avoid different answers depending on the direction of the price change, economists use the midpoint (arc) method:

Classifying Elasticity

1
\(|E_d| \gt 1\): Elastic. Quantity responds more than proportionally to price. A 10% price increase causes >10% drop in \(Q_d\).
2
\(|E_d| \lt 1\): Inelastic. Quantity responds less than proportionally. A 10% price increase causes <10% drop in \(Q_d\).
3
\(|E_d| = 1\): Unit elastic. Quantity and price change by the same proportion.
4
\(|E_d| = \infty\): Perfectly elastic. Any price increase causes \(Q_d\) to drop to zero. Horizontal demand curve.
5
\(|E_d| = 0\): Perfectly inelastic. \(Q_d\) does not change at all. Vertical demand curve.

Demand Curve Shapes

Perfectly Inelastic Q P \(E_d = 0\) Inelastic Q P \(|E_d| \lt 1\) Elastic Q P \(|E_d| \gt 1\) Perfectly Elastic Q P \(|E_d| = \infty\)

Elastic vs. Inelastic: Key Distinction

Elastic (\(|E_d| \gt 1\)) Inelastic (\(|E_d| \lt 1\))
Consumer response Large change in \(Q_d\) Small change in \(Q_d\)
Substitutes Many available Few or none
Necessity vs. Luxury Tends to be a luxury Tends to be a necessity
Time horizon Long run (more options) Short run (stuck)
Price increase effect on TR TR decreases TR increases

Determinants of Elasticity

Substitutes
More substitutes means more elastic: consumers can easily switch
Necessity
Necessities (insulin, water) are inelastic: you need them regardless of price
Budget Share
Goods that take a large share of income tend to be more elastic
Time
Demand is more elastic in the long run as consumers find alternatives

Elasticity & Total Revenue

The total revenue test links elasticity to revenue outcomes. Total revenue: \( TR = P \times Q \).

1
Elastic demand: Price increase causes \(Q_d\) to fall by a larger percentage, so TR falls.
2
Inelastic demand: Price increase causes \(Q_d\) to fall by a smaller percentage, so TR rises.
3
Unit elastic: Price change has no effect on TR: the two percentage changes cancel out.

How to Calculate PED

1
Identify the two price-quantity pairs: \((P_1, Q_1)\) and \((P_2, Q_2)\).
2
Calculate \(\%\;\Delta Q_d\): \(\dfrac{Q_2 - Q_1}{(Q_2 + Q_1)/2} \times 100\).
3
Calculate \(\%\;\Delta P\): \(\dfrac{P_2 - P_1}{(P_2 + P_1)/2} \times 100\).
4
Divide: \(E_d = \dfrac{\%\;\Delta Q_d}{\%\;\Delta P}\).
5
Take the absolute value and classify: elastic, inelastic, or unit elastic.

Example 1: Movie Tickets

A cinema raises ticket prices from \($10\) to \($12\). Weekly ticket sales drop from 500 to 400.

Quantity Price ($) A (500, $10) B (400, $12) 500 $10 400 $12

Example 2: Insulin

The price of insulin rises from \($200\) to \($250\) per month. A patient's monthly doses drop from 30 to 28.

Example 3: Total Revenue Test

A streaming service considers two pricing strategies. Current price: \($15\), subscribers: 1,000.

Strategy A: \($18\) Strategy B: \($12\)
New subscribers 700 1,400
Old TR \($15 \times 1000 = $15{,}000\) \($15 \times 1000 = $15{,}000\)
New TR \($18 \times 700 = \)\($12{,}600\) \($12 \times 1400 = \)\($16{,}800\)
TR change Decreased by $2,400 Increased by $1,800

Elasticity Along a Linear Curve

Quantity Price Elastic \(|E_d| \gt 1\) Unit elastic \(|E_d| = 1\) Inelastic \(|E_d| \lt 1\)

Common Mistakes

✕ Confusing Slope with Elasticity
A steep demand curve does not always mean inelastic. Elasticity depends on percentage changes, not absolute changes. The same linear curve has different elasticities at different points.
✕ Forgetting the Midpoint Method
Using simple percentage change gives different answers depending on which point you start from. The AP exam expects the midpoint method unless told otherwise.
✕ Ignoring the Absolute Value
PED is almost always negative (law of demand), but classification uses \(|E_d|\). Saying "\(-2\) is less than \(-0.5\) so it's more inelastic" is backward.

Summary Reference Table

Classification \(|E_d|\) Price ↑ Effect on TR Example
Perfectly Inelastic 0 TR rises Life-saving drugs
Inelastic \(0 \lt |E_d| \lt 1\) TR rises Gasoline, salt
Unit Elastic 1 TR unchanged Midpoint of linear curve
Elastic \(|E_d| \gt 1\) TR falls Luxury goods, restaurants
Perfectly Elastic \(\infty\) TR falls to 0 Perfectly competitive firms

Question 1 of 5

The price of a good rises by 15% and quantity demanded falls by 10%. This good has:

Question 2 of 5

A firm faces elastic demand for its product. If it raises the price, what happens to total revenue?

Question 3 of 5

Using the midpoint method: price goes from \($4\) to \($6\), and \(Q_d\) goes from 100 to 60. What is \(|E_d|\)?

Question 4 of 5

Which of the following goods is most likely to have inelastic demand?

Question 5 of 5

On a linear demand curve, at which point is demand unit elastic?