Topic 2.3 Notes – Price Elasticity of Demand

1. What Price Elasticity of Demand Is

Price Elasticity of Demand (PED) measures how responsive quantity demanded is to a change in a good’s own price.

Economists use elasticity to measure percentage changes in quantity caused by changes in:

• Own price (this topic)
• Income
• Prices of related goods (substitutes and complements)

For this unit, we focus on own-price elasticity.

The Formula

$$E_d = \frac{\% \Delta Q_d}{\% \Delta P}$$

• It’s a percentage over percentage comparison.
• Because of the Law of Demand, $E_d$ is usually negative.
• On the AP exam, we almost always use the absolute value.

Midpoint Formula

When calculating between two points, use the midpoint method so your answer doesn’t change depending on direction:

$$\% \Delta = \frac{\text{New} - \text{Old}}{\frac{\text{New} + \text{Old}}{2}}$$

Quick example:
Price rises from 20 to 24. Quantity falls from 50 to 40.

$$\% \Delta Q = \frac{40-50}{45} = -\frac{10}{45} \approx -22.2\%$$
$$\% \Delta P = \frac{24-20}{22} = \frac{4}{22} \approx 18.2\%$$

$$E_d = \frac{-22.2\%}{18.2\%} \approx -1.22$$

Absolute value 1.22 → elastic.

Slope Is Not Elasticity

• Slope = change in Q over change in P.
• Elasticity = % change in Q over % change in P.

On a linear demand curve, slope is constant. Elasticity is not. That difference shows up constantly on MCQs.

2. The Five Types of Elasticity

The benchmark number is 1.

Perfectly Inelastic (Ed = 0)

• Quantity does not change at all.
• Vertical demand curve.
• Example: life-saving insulin in extreme cases.

Perfectly inelastic demand (vertical curve, Ed = 0)

Relatively Inelastic (0 < Ed < 1)

• %ΔQ < %ΔP.
• Steep demand curve.
• Examples: gasoline in the short run, cigarettes.

Unit Elastic (Ed = 1)

• %ΔQ = %ΔP.
• Total revenue stays constant when price changes.
• Occurs at the midpoint of a linear demand curve.

Relatively Elastic (Ed > 1)

• %ΔQ > %ΔP.
• Flatter demand curve.
• Examples: restaurant meals, vacations, luxury goods.

Perfectly Elastic (Ed = ∞)

• Consumers buy only at one price.
• Horizontal demand curve.
• Seen in the perfectly competitive firm model where the firm is a price taker.

Perfectly elastic (horizontal) and perfectly inelastic (vertical) demand

Perfectly elastic and perfectly inelastic are theoretical extremes. They help you think clearly about responsiveness.

3. Elasticity Along a Demand Curve

On a straight-line demand curve, elasticity changes as you move from top to bottom:

• Top (high P, low Q) → Elastic
• Middle → Unit elastic
• Bottom (low P, high Q) → Inelastic

Elasticity along a straight-line demand curve

Why this happens:

At high prices and low quantities, a given dollar change is a small percentage of price but causes a large percentage change in quantity. At low prices and high quantities, that same dollar change is a large percentage of price but small relative to quantity.

Always think in percentages.

4. The Total Revenue Test

Total Revenue is:

$$TR = P \times Q$$

The effect of a price change depends on elasticity.

Real-world anchors:

• Cigarette taxes raise government revenue because demand is relatively inelastic.
• Gasoline price spikes increase revenue in the short run for the same reason.
• Airlines lower prices during off-peak times because leisure travel is more elastic.

Firms use this logic constantly when deciding pricing strategies.

5. What Determines Price Elasticity of Demand

Availability of Substitutes

More substitutes → more elastic.
Few substitutes → more inelastic.

Coke has many substitutes. Insulin does not.

Necessities vs. Luxuries

Necessities → inelastic.
Luxuries → elastic.

Proportion of Income

Small share of income → inelastic (salt).
Large share → elastic (cars, tuition).

Time Horizon

More time → more elastic.

Gasoline demand is inelastic in the short run. Over time, people buy fuel-efficient cars or move closer to work, making demand more elastic.