Price Elasticity of Demand

AP Microeconomics· AP Microeconomics CED — Supply and Demand· 14 min read

1. What is Price Elasticity of Demand?★★☆☆☆⏱ 3 min

Price elasticity of demand (abbreviated PED or $E_{d}$ ) measures how responsive quantity demanded of a good is to a change in its price, holding all other determinants of demand constant. Unlike the slope of the demand curve (which measures absolute change), elasticity measures proportional change, making it unit-independent, so you can compare elasticity across goods measured in different units.

Per the AP CED, this topic makes up 6-8% of your total AP exam score, appearing regularly in multiple-choice and as a foundation for free-response questions. Because demand curves slope downward, $E_{d}$ is almost always negative; by convention, we use the absolute value of $E_{d}$ for simplicity.

📘 Definition

Price Elasticity of Demand (PED)

$E_{d}$

A measure of the responsiveness of quantity demanded of a good to a change in its own price, holding all other demand determinants constant, calculated as the ratio of percentage change in quantity demanded to percentage change in price.

Example:

PED allows meaningful comparison of demand responsiveness for cars vs. coffee, despite their different units of measurement.

2. Calculating PED: Midpoint (Arc) Method★★☆☆☆⏱ 4 min

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The general formula for PED is:

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

Simple percentage change has a "base problem": moving from point A to B gives a different elasticity than B to A, because the initial base value changes. The midpoint (arc) method solves this by using the average of the two values as the base, giving the same elasticity regardless of direction. The simplified midpoint formula (after canceling the 1/2 term) is:

E_d = \frac{(Q_2 - Q_1)(P_1 + P_2)}{(P_2 - P_1)(Q_1 + Q_2)}

📐 Worked Example

When the price of artisanal ice cream pints rises from $5 to $7, quantity demanded falls from 120 pints per week to 80 pints per week. Calculate PED using the midpoint method.

1
Label all given values clearly:
2
$Q_1 = 120,\ Q_2 = 80,\ P_1 = 5,\ P_2 = 7$
3
Calculate percentage change in quantity, using average quantity as the base:
4
$\% \Delta Q = \frac{80 - 120}{(120 + 80)/2} = \frac{-40}{100} = -0.4$
5
Calculate percentage change in price, using average price as the base:
6
$\% \Delta P = \frac{7 - 5}{(5 + 7)/2} = \frac{2}{6} \approx 0.333$
7
Divide to get $E_{d}$ , then take absolute value for standard reporting:
8
$E_d = \frac{-0.4}{0.333} \approx -1.2 \implies |E_d| = 1.2$

Exam tip:

If the prompt explicitly asks for the midpoint method, you must use the average base, not simple initial-value percentage change. This is one of the most common point deductions on PED calculation questions.

3. Elasticity Categories and the Total Revenue Test★★★☆☆⏱ 4 min

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Once you calculate $∣ E_{d} ∣$ , you can categorize demand by responsiveness, and this classification directly tells you how a price change affects total revenue ( $T R = P \times Q$ ). The five standard categories are:

Perfectly inelastic: $∣ E_{d} ∣ = 0$ , vertical demand curve, quantity does not change with price
Inelastic: $0 < ∣ E_{d} ∣ < 1$ , quantity changes less than proportionally to price
Unit elastic: $∣ E_{d} ∣ = 1$ , quantity changes proportionally to price
Elastic: $1 < ∣ E_{d} ∣ < \infty$ , quantity changes more than proportionally to price
Perfectly elastic: $∣ E_{d} ∣ = \infty$ , horizontal demand curve

The total revenue test is a shortcut to determine elasticity without calculation: it uses the direction of TR change when price changes to infer elasticity. The rule: if price and TR move in opposite directions, demand is elastic; if they move in the same direction, demand is inelastic; if TR does not change, demand is unit elastic.

📘 Definition

Total Revenue Test

A method to classify PED by observing the relationship between an own-price change and the resulting change in total revenue, holding all other demand factors constant.

Example:

If price rises and total revenue falls, demand is elastic.

📐 Worked Example

A local coffee shop observes that when it raises the price of its signature latte from $4 to $4.50, total revenue from lattes falls from $1800 per week to $1710 per week. Use the total revenue test to classify elasticity, then verify with midpoint calculation.

1
Identify direction of changes: Price increased, total revenue decreased.
2
Apply the total revenue test rule: Price and TR move in opposite directions, so demand is elastic.
3
Calculate original and new quantity from $T R = P \times Q$ :
4
$Q_1 = \frac{1800}{4} = 450,\ Q_2 = \frac{1710}{4.50} = 380$
5
Apply the midpoint formula to get $∣ E_{d} ∣$ :
6
$|E_d| = \left|\frac{(380-450)(4+4.50)}{(4.50-4)(380+450)}\right| \approx 1.43$
7
Confirm classification: $1.43 > 1$ , so demand is elastic, matching the total revenue test result.

4. Determinants of Price Elasticity of Demand★★☆☆☆⏱ 3 min

The AP exam regularly tests your ability to predict whether demand for a good will be elastic or inelastic based on its core characteristics. There are four key determinants consistently tested:

Availability of close substitutes: More close substitutes = more elastic demand. Narrow, specific goods have more substitutes than broad categories.
Necessity vs. Luxury: Necessities have inelastic demand; luxuries have elastic demand.
Time horizon: Demand is more elastic in the long run than the short run, as consumers have more time to adjust behavior and find substitutes.
Share of consumer budget: Goods that make up a smaller share of total consumer budget have more inelastic demand.

📐 Worked Example

For each pair of goods, state which has more elastic demand and identify the key determinant that explains the difference: (i) Insulin for type 1 diabetes vs. brand-name toothpaste; (ii) Airline tickets bought 3 months in advance vs. airline tickets bought 1 hour before departure.

1
For (i): Brand-name toothpaste has more elastic demand. Key determinants: Insulin is a life-saving necessity with no close substitutes, so demand is extremely inelastic. Brand-name toothpaste has many close substitutes (other brands, generics), so consumers will switch if price rises, leading to more elastic demand.
2
For (ii): Airline tickets bought 3 months in advance have more elastic demand. Key determinant: Time horizon and consumer flexibility. Travelers buying tickets 1 hour before departure have an urgent, fixed need to travel, so demand is inelastic. Travelers booking in advance can adjust dates, destination, or transport mode to get a lower price, so they are far more responsive to price changes, leading to more elastic demand.

Exam tip:

When answering AP MCQ about elasticity differences, always match your reasoning to one of the four core determinants above, aligned with the CED framework.

5. Point Elasticity and Elasticity Along Linear Demand Curves★★★☆☆⏱ 4 min

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Point elasticity measures elasticity at a single point on the demand curve, rather than over an arc between two points. It is most commonly used to analyze how elasticity changes along a linear (straight-line) demand curve. The point elasticity formula is:

E_d = \frac{dQ}{dP} \times \frac{P}{Q}

A key commonly tested relationship: even though the slope of a linear demand curve is constant, elasticity is not. As you move down the demand curve to lower price and higher quantity, $∣ E_{d} ∣$ decreases. At the midpoint of the linear demand curve, $∣ E_{d} ∣ = 1$ (unit elastic). Above the midpoint (higher price, lower quantity), $∣ E_{d} ∣ > 1$ (elastic). Below the midpoint (lower price, higher quantity), $∣ E_{d} ∣ < 1$ (inelastic).

📐 Worked Example

Suppose demand for graphic t-shirts is given by the linear function $Q_{d} = 100 - 10 P$ , where $Q$ is quantity of t-shirts and $P$ is price per t-shirt. Calculate point elasticity when $P = $4$ , and classify the result.

1
Find the slope $\frac{d Q}{d P}$ for the demand function:
2
$\frac{dQ}{dP} = -10$
3
Calculate $Q$ when $P = 4$ :
4
$Q = 100 - 10(4) = 60$
5
Plug into the point elasticity formula:
6
$E_d = (-10) \times \frac{4}{60} \approx -0.67$
7
Take absolute value and classify: $∣ E_{d} ∣ = 0.67 < 1$ , so demand is inelastic at $P = $4$ .
8
Confirm with the linear demand rule: The maximum price for this demand curve is $10, so the midpoint is at $P = 5$ . Since $P = 4$ is below the midpoint, it is expected to be inelastic, which matches our result.

6. Common Pitfalls

Wrong move:

Using initial-value percentage change instead of the midpoint method when explicitly asked for midpoint.

Why:

Students remember the basic $%Δ Q /%Δ P$ formula and forget midpoint requires an average base.

Correct move:

Whenever midpoint is required, use the average of the two quantities and two prices as the denominators for percentage change before starting calculations.

Wrong move:

Classifying $E_{d} = - 1.2$ as inelastic because $- 1.2 < 1$ .

Why:

Students forget the negative sign only reflects the downward-sloping demand curve, and classification uses absolute value.

Correct move:

Always take the absolute value of calculated $E_{d}$ immediately after solving, and use that value for classification.

Wrong move:

Assuming a steeper demand curve is always more inelastic than a flatter demand curve.

Why:

Students confuse slope (absolute change) with elasticity (proportional change).

Correct move:

Only compare elasticity via slope if both curves pass through the same point; otherwise use determinants or calculate elasticity directly.

Wrong move:

Claiming demand for the broad category 'clothing' is more elastic than demand for a specific brand of running shoes.

Why:

Students misapply the substitute availability determinant: broad categories have fewer substitutes than specific, narrow goods.

Correct move:

Remember narrower, more specific goods always have more elastic demand than broader categories of the same type.

Wrong move:

Applying the total revenue test when total revenue changes due to a demand curve shift from a change in consumer income.

Why:

Students forget the TR-elasticity relationship only applies to own-price changes that cause movement along the demand curve.

Correct move:

Confirm the only change is the own price of the good before using the total revenue test; do not use it if another factor shifted demand.

Wrong move:

Confusing unit elastic demand with perfectly inelastic demand, claiming unit elastic means quantity does not change when price changes.

Why:

Similar names lead to mixing up definitions.

Correct move:

Memorize: perfectly inelastic = $∣ E_{d} ∣ = 0$ , no quantity change; unit elastic = $∣ E_{d} ∣ = 1$ , percentage change in Q equals percentage change in P.

7. Quick Reference Cheatsheet

Concept	Formula / Rule	Notes
Basic PED definition	$E_{d} = \frac{%Δ Q _{d}}{%Δ P}$	Proportional change in quantity over proportional change in price
Midpoint (arc) PED	$E_{d} = \frac{( Q _{2} - Q _{1} ) ( P _{1} + P _{2} )}{( P _{2} - P _{1} ) ( Q _{1} + Q _{2} )}$	Required when prompt specifies midpoint method
Point elasticity (linear demand)	$E_{d} = \frac{d Q}{d P} \times \frac{P}{Q}$	Elasticity at a single point on the curve
Perfectly inelastic	$∣ E_{d} ∣ = 0$	Vertical demand curve, Q does not change with P
Inelastic	$0 < ∣ E_{d} ∣ < 1$	P and TR move in the same direction
Unit elastic	$∣ E_{d} ∣ = 1$	TR does not change when P changes
Elastic	$1 < ∣ E_{d} ∣ < \infty$	P and TR move in opposite directions
Perfectly elastic	$∣ E_{d} ∣ = \infty$	Horizontal demand curve

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · MCQ
Calculate midpoint price elasticity
2022 · FRQ
Relate PED to total revenue change
2021 · MCQ
Identify elasticity determinants

Going deeper

unit overviewAP Microeconomics Unit 2 OverviewFoundational context for supply and demand topics

What's Next

Price elasticity of demand is a foundational concept that underpins almost all subsequent topics in AP Microeconomics, from consumer surplus to tax incidence and market efficiency. Understanding how to calculate and interpret PED is critical for analyzing how price changes affect producers, consumers, and government policy outcomes. Next, you will build on this concept to study other types of elasticity, including cross-price elasticity of demand (which measures responsiveness to changes in other goods' prices) and income elasticity of demand, both regularly tested on the AP exam. You will also apply PED to analyze the impact of price controls, taxes, and producer pricing strategies.