AP · Price Elasticity of Demand · 14 min read · Updated 2026-05-10

Price Elasticity of Demand — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: Definition of price elasticity of demand, the midpoint (arc) elasticity formula, point elasticity, elasticity categories, the total revenue test, key determinants of elasticity, and the relationship between elasticity and total revenue.

You should already know: The law of demand and how to calculate percentage changes. How to calculate total revenue from price and quantity. How to interpret the slope of a demand curve.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Microeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Price Elasticity of Demand?

Price elasticity of demand (often abbreviated PED or just $E_{d}$ ) 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 in quantity per absolute change in price, elasticity measures proportional change, which makes it unit-independent: you can compare elasticity of demand for cars vs. coffee even though they are measured in different units. Per the AP Microeconomics Course and Exam Description (CED), this topic accounts for approximately 6-8% of the total AP exam score, and it appears regularly in both multiple-choice questions (MCQ) and as a foundational concept in free-response questions (FRQ). PED is often paired with total revenue analysis, consumer surplus, or tax incidence on FRQ sections. A common synonym for price elasticity of demand is own-price elasticity of demand, used to distinguish it from cross-price elasticity of demand (which measures response to changes in price of another good). Because the demand curve is downward sloping, the calculated value of $E_{d}$ will almost always be negative; by convention, economists usually report the absolute value of $E_{d}$ to simplify comparisons of elasticity size.

2. Calculating Price Elasticity: The Midpoint (Arc) Method

Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price, written generally as: $E_{d} = \frac{%Δ Q _{d}}{%Δ P}$ The midpoint (or arc) method is the most commonly tested calculation method on the AP exam, because it solves the "base problem" of simple percentage change: if you move from Point A to Point B on a demand curve, simple percentage change gives a different elasticity value than moving from B to A, because the base (initial value) changes. The midpoint method uses the average of the two values as the base, giving the same elasticity regardless of direction. The full midpoint formula, after simplifying to cancel the 1/2 term from the average, is: $E_{d} = \frac{( Q _{2} - Q _{1} ) ( P _{1} + P _{2} )}{( P _{2} - P _{1} ) ( Q _{1} + Q _{2} )}$ As a convention, we almost always work with the absolute value of $E_{d}$ , since the negative sign only confirms the downward sloping demand curve, which we already assume.

Worked Example

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

Label all values clearly: $Q_{1} = 120$ , $Q_{2} = 80$ , $P_{1} = 5$ , $P_{2} = 7$ .
Calculate percentage change in quantity: $%Δ Q = \frac{80 - 120}{( 120 + 80 ) /2} = \frac{- 40}{100} = - 0.4$ .
Calculate percentage change in price: $%Δ P = \frac{7 - 5}{( 5 + 7 ) /2} = \frac{2}{6} \approx 0.333$ .
Divide to get $E_{d}$ : $E_{d} = \frac{- 0.4}{0.333} \approx - 1.2$ .
Take absolute value for standard reporting: $∣ E_{d} ∣ = 1.2$ .

Exam tip: If the prompt explicitly says "calculate using 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

Once you calculate $∣ E_{d} ∣$ , you can categorize demand by how responsive quantity is to price changes, and this classification directly tells you how a price change will affect total revenue ( $T R = P \times Q$ ). The five standard categories are: perfectly inelastic ( $∣ E_{d} ∣ = 0$ , vertical demand curve), inelastic ( $0 < ∣ E_{d} ∣ < 1$ ), unit elastic ( $∣ E_{d} ∣ = 1$ ), elastic ( $1 < ∣ E_{d} ∣ < \infty$ ), and 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 change in TR when price changes to infer elasticity. The rule is simple: if price and total revenue 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. This relationship holds because elasticity describes the relative size of the percentage change in Q vs. P: for elastic demand, the percentage change in Q is larger than the percentage change in P, so the change in Q dominates TR.

Worked Example

Problem: A local coffee shop observes that when it raises the price of its signature latte from $4 t o$ 4.50, total revenue from lattes falls from $1800 p er w ee k t o$ 1710 per week. Use the total revenue test to classify the elasticity of demand for lattes, and verify with midpoint calculation.

Identify direction of changes: Price increased from $4 t o$ 4.50, total revenue decreased from $1800 t o$ 1710.
Apply the total revenue test: Price and TR move in opposite directions, so demand is elastic.
Verify with midpoint calculation: Original quantity = $1800/$ 4 = 450, new quantity = $1710/$ 4.50 = 380. Calculate $∣ E_{d} ∣ = \frac{( 380 - 450 ) ( 4 + 4.50 )}{( 4.50 - 4 ) ( 380 + 450 )} = \frac{( - 70 ) ( 8.5 )}{( 0.5 ) ( 830 )} \approx 1.43$ .
Confirm classification: $1.43 > 1$ , which matches the total revenue test result of elastic demand.

Exam tip: The total revenue test only applies when the change in TR is caused by a change in the own price of the good (movement along the demand curve). If TR changes because demand shifted (from a change in income or another price), the test does not apply.

4. Determinants of Price Elasticity of Demand

The AP exam regularly tests your ability to predict whether demand for a good will be elastic or inelastic based on its core characteristics, called determinants. There are four key determinants tested consistently on the exam: 1) Availability of close substitutes: more substitutes = more elastic demand, because consumers can easily switch if price rises. Narrow, specific goods (a specific brand of cereal) have more substitutes than broad categories (all breakfast food), so narrow goods are more elastic. 2) Necessity vs. luxury: necessities have inelastic demand, luxuries have elastic demand, because you will still buy a necessity even if price rises, but you can cut back on a luxury. 3) Time horizon: demand is more elastic in the long run than the short run, because consumers have more time to find substitutes and adjust their behavior. 4) Share of the good in the consumer budget: goods that make up a tiny share of your budget (salt, gum) have inelastic demand, because even a 50% price increase is only a few cents, so you don't change your behavior.

Worked Example

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

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

Exam tip: When AP MCQ asks you to pick the correct reason for a difference in elasticity, always match your answer to one of the four core determinants listed above — avoid generic reasoning that doesn't align with the CED framework.

5. Point Elasticity and Elasticity Along a Linear Demand Curve

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: $E_{d} = \frac{d Q}{d P} \times \frac{P}{Q}$ where $\frac{d Q}{d P}$ is the slope of the demand curve when quantity is written as a function of price. A key commonly tested relationship for linear demand curves: elasticity falls (|Ed| decreases) as you move down the demand curve to lower price and higher quantity. At the midpoint of the linear demand curve, |Ed| = 1 (unit elastic). Above the midpoint (higher price, lower quantity), |Ed| > 1 (elastic). Below the midpoint (lower price, higher quantity), |Ed| < 1 (inelastic). Even though the slope of a linear demand curve is constant, elasticity is not, because elasticity depends on both slope and the ratio P/Q at the point.

Worked Example

Problem: Suppose the 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 elasticity.

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

Exam tip: Don't confuse slope of a linear demand curve with elasticity. The slope is constant, but elasticity changes along the curve — this is one of the most common misconceptions tested on AP MCQ.

6. Common Pitfalls (and how to avoid them)

Wrong move: Using initial-value percentage change instead of the midpoint method when the question explicitly asks for a midpoint calculation. Why: Students remember the basic %ΔQ/%ΔP formula and forget that midpoint requires the average of the two values as the base. Correct move: Whenever the prompt requires midpoint, write (Q1+Q2)/2 and (P1+P2)/2 as the denominators for percentage change before you start any calculation.
Wrong move: Classifying $E_{d} = - 1.2$ as inelastic because $- 1.2 < 1$ . Why: Students forget that the negative sign only reflects downward sloping demand, and we classify elasticity based on absolute value. Correct move: Immediately take the absolute value of your calculated $E_{d}$ after solving, and only use that value to classify elasticity.
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 slope to compare elasticity if the question explicitly notes both curves pass through the same point; otherwise, calculate elasticity or use the determinant rule.
Wrong move: Claiming demand for the broad category "clothing" is more elastic than demand for a specific brand of running shoes. Why: Students mix up the substitute availability determinant: broad categories have fewer substitutes than specific, narrow goods. Correct move: Remember that 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 shift in the demand curve from a change in consumer income. Why: Students memorize the TR-elasticity relationship and forget it only applies to own-price changes that cause movement along the demand curve. Correct move: Before using the total revenue test, confirm that the only change is the own price of the good; if another factor shifted demand, do not use the test.
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 = |Ed| = 0, no change in quantity; unit elastic = |Ed| = 1, percentage change in Q equals percentage change in P.

7. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

When the price of an artisanal soap bar increases from $4 t o$ 6, quantity demanded falls from 100 units per week to 60 units per week. What is the price elasticity of demand calculated using the midpoint method? A) 0.8 B) 1.25 C) 1.5 D) 2.0

Worked Solution: First, label the values: $Q_{1} = 100$ , $Q_{2} = 60$ , $P_{1} = 4$ , $P_{2} = 6$ . Apply the simplified midpoint formula for absolute value: $∣ E_{d} ∣ = \frac{( Q _{2} - Q _{1} ) ( P _{1} + P _{2} )}{( P _{2} - P _{1} ) ( Q _{1} + Q _{2} )}$ . Plugging in the values gives $∣ E_{d} ∣ = \frac{( 60 - 100 ) ( 4 + 6 )}{( 6 - 4 ) ( 100 + 60 )} = \frac{- 400}{320} = 1.25$ . The correct answer is B.

Question 2 (Free Response)

A grocery store sells 800 boxes of cereal per week at a price of $3.50 p er b o x . W h e n t h ey l o w er t h e p r i ce t o$ 3.00 per box, they sell 900 boxes per week. (a) Calculate the price elasticity of demand using the midpoint method. Show your work. (b) Based on your calculation in (a), classify the demand for this cereal as elastic, inelastic, or unit elastic. Explain. (c) The grocery store wants to increase total revenue from cereal sales. Should it raise or lower the price from the original $3.50? Explain your answer using your elasticity result.

Worked Solution: (a) Label values: $Q_{1} = 800$ , $Q_{2} = 900$ , $P_{1} = 3.50$ , $P_{2} = 3.00$ . $∣ E_{d} ∣ = \frac{( 900 - 800 ) ( 3.50 + 3.00 )}{( 3.00 - 3.50 ) ( 800 + 900 )} = \frac{650}{- 850} \approx 0.76$ (b) Demand is inelastic. Classification is based on absolute value of $E_{d}$ : $0 < 0.76 < 1$ , which meets the definition of inelastic demand. (c) The grocery store should raise the price from $3.50. When demand is inelastic, price and total revenue move in the same direction: the proportional increase in price will be larger than the proportional decrease in quantity demanded, so total revenue will rise.

Question 3 (Application / Real-World Style)

A ride-sharing company analyzes its demand and finds that the price elasticity of demand for rides is 0.65 in the short run and 1.3 in the long run. The company wants to permanently raise prices to increase total revenue. Will a permanent price increase achieve the company's goal? Explain your answer, and interpret what the difference between short-run and long-run elasticity means for consumer behavior.

Worked Solution: A permanent price increase will not increase total revenue in the long run. In the long run, $∣ E_{d} ∣ = 1.3 > 1$ , so demand is elastic. When demand is elastic, price and total revenue move in opposite directions: the percentage decrease in quantity demanded will be larger than the percentage increase in price, so total revenue will fall. The difference in elasticity means that in the short run, consumers cannot easily adjust to higher ride-sharing prices, so they continue to buy roughly the same number of rides, leading to inelastic demand. In the long run, consumers can adjust their behavior (switch to public transit, buy a car, move closer to work) so they are much more responsive to higher prices, leading to elastic demand.

8. Quick Reference Cheatsheet

Category	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	$E_{d} = \frac{( Q _{2} - Q _{1} ) ( P _{1} + P _{2} )}{( P _{2} - P _{1} ) ( Q _{1} + Q _{2} )}$	Use when prompt asks for midpoint; same result for price increases/decreases
Point PED	$E_{d} = \frac{d Q}{d P} \times \frac{P}{Q}$	Use for elasticity at a single point on a demand curve
Perfectly inelastic	$	E_d
Inelastic	$0 <	E_d
Unit elastic	$	E_d
Elastic	$1 <	E_d
Perfectly elastic	$	E_d
Total revenue	$T R = P \times Q$	Base calculation for the total revenue test
Elasticity along linear demand	Elastic above midpoint, unit elastic at midpoint, inelastic below midpoint	Slope is constant, elasticity changes along the curve

9. What's Next

Price elasticity of demand is the foundational concept for all further elasticity analysis in AP Microeconomics, and it is also critical for understanding how firms set prices and how government tax policy affects consumers and producers. Next, you will apply the same proportional responsiveness framework to other types of elasticity: cross-price elasticity of demand and income elasticity of demand, followed by price elasticity of supply. Without mastering the core concepts of PED (percentage change, midpoint method, elasticity interpretation, total revenue relationship), you will not be able to correctly solve problems involving consumer behavior, tax incidence, or firm pricing strategy, all of which are heavily tested on the AP exam. PED also feeds into the bigger concepts of market efficiency and welfare analysis that you will encounter later in the course.

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Price Elasticity of Demand — AP Microeconomics Study Guide

1. What Is Price Elasticity of Demand?

2. Calculating Price Elasticity: The Midpoint (Arc) Method

Worked Example

3. Elasticity Categories and The Total Revenue Test

Worked Example

4. Determinants of Price Elasticity of Demand

Worked Example

5. Point Elasticity and Elasticity Along a Linear Demand Curve

Worked Example

6. Common Pitfalls (and how to avoid them)

7. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

Question 2 (Free Response)

Question 3 (Application / Real-World Style)

8. Quick Reference Cheatsheet

9. What's Next

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