Price Elasticity of Demand (PED) Equation, Derivation & Rearrangements

Q: What are common mistakes with the Price Elasticity of Demand (PED) formula?

Swapping the numerator and denominator. Forgetting to use percentage changes.

Core idea

Overview

Price Elasticity of Demand measures the degree of responsiveness of the quantity demanded of a good to a change in its price. It quantifies how consumers' purchasing habits shift when prices fluctuate, allowing economists to categorize goods as either elastic or inelastic.

When to use: Apply this equation when predicting how a price adjustment will impact the total units sold in a specific market. It is most effective in scenarios where the Law of Demand holds and other variables like consumer income or preference remain constant.

Why it matters: This calculation allows businesses to set prices that maximize revenue based on consumer sensitivity to cost. It also helps policymakers understand which products can be taxed effectively, such as alcohol or tobacco, without causing a total collapse in demand.

Symbols

Variables

PED = PED, \%\Delta QD = %Δ Quantity, \%\Delta P = %Δ Price

P E D

PED

V a r iab l e

%Δ Q D

%Δ Quantity

%Δ P

%Δ Price

Walkthrough

Derivation

Price Elasticity of Demand

PED is derived from the percentage change in quantity demanded relative to the percentage change in price. It measures the slope of the demand curve when expressed in percentage terms.

Other factors (income, tastes, etc.) remain constant (Ceteris Paribus).
The relationship is linear over small changes.

1

State the definition

The definition of PED as a ratio of two percentage changes.

P E D = \frac{%Δ Q D}{%Δ P}

2

Percentage change in quantity

Calculating the percentage change in quantity.

%Δ Q D = \frac{Q _{2} - Q _{1}}{Q _{1}} \times 100

3

Percentage change in price

Calculating the percentage change in price.

%Δ P = \frac{P _{2} - P _{1}}{P _{1}} \times 100

Result

%Δ P = \frac{P _{2} - P _{1}}{P _{1}} \times 100

Source: GCSE Economics Specification (AQA/Edexcel)

Free formulas

Rearrangements

Solve for $P E D$

Make PED the subject

P E D = \frac{%Δ Q D}{%Δ P}

PED is already the subject of the formula.

Difficulty: 1/5

Solve for $%Δ Q D$

Make %Delta QD the subject

%Δ Q D = P E D \times %Δ P

To make \% $Δ$ QD the subject of the Price Elasticity of Demand (PED) formula, multiply both sides by \% $Δ$ P to clear the denominator, then rearrange to isolate \% $Δ$ QD.

Difficulty: 2/5

Solve for $%Δ P$

Make %Delta P the subject

%Δ P = \frac{%Δ Q D}{P E D}

To make % $Δ$ P the subject, start with the formula for Price Elasticity of Demand (PED), multiply both sides by % $Δ$ P, then divide by PED.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph follows a hyperbolic curve because %Δ P appears in the denominator of the formula. As %Δ P approaches zero, PED approaches infinity, creating a vertical asymptote at the y-axis. The curve is restricted to positive values for %Δ P.

Graph type: hyperbolic

Why it behaves this way

Intuition

Visualize the demand curve on a graph; the elasticity at any point or along a segment measures the relative steepness or flatness of this curve, indicating how much quantity demanded 'stretches' or 'contracts'

%Δ QD

The proportional change in the quantity of a good or service that consumers are willing and able to purchase.

This represents the *effect* on consumer purchasing behavior resulting from a price change.

%Δ P

The proportional change in the market price of a good or service.

This represents the *cause* or stimulus that prompts a change in consumer purchasing behavior.

PED

A dimensionless measure quantifying the sensitivity of quantity demanded to a change in price.

A high absolute value means consumers are very responsive to price changes (elastic demand), while a low absolute value means they are not very responsive (inelastic demand).

Signs and relationships

The negative sign of the PED value: The negative sign typically arises from the Law of Demand, which posits an inverse relationship between price and quantity demanded: as price increases, quantity demanded decreases, and vice versa.

Free study cues

Insight

Canonical usage

Price Elasticity of Demand is a dimensionless ratio, representing the proportional change in quantity demanded relative to the proportional change in price.

Common confusion

A common confusion is to mistake PED for the slope of the demand curve. While related, the slope has units (e.g., dollars per unit), whereas PED is a dimensionless ratio, making it independent of the units used for price

Dimension note

Price Elasticity of Demand is a dimensionless quantity because it is calculated as a ratio of two percentage changes. Percentage changes, by definition, are unitless, making the overall elasticity value a pure number.

Ballpark figures

Quantity:

One free problem

Practice Problem

A local coffee shop increases the price of its signature latte by 8%, which leads to a 4% decrease in the number of lattes sold. Calculate the Price Elasticity of Demand.

%Δ Price8 %

%Δ Quantity-4 %

Solve for: $P E D$

Hint: Divide the percentage change in quantity demanded by the percentage change in price.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

A local cafe increases coffee prices by 10%, and sales drop by 5%. PED = -0.5.

Study smarter

Tips

PED > 1 indicates price-sensitive elastic demand
PED < 1 indicates price-insensitive inelastic demand
Results are usually negative as price and demand move in opposite directions
The calculation assumes ceteris paribus (all other factors constant)

Avoid these traps

Common Mistakes

Swapping the numerator and denominator.
Forgetting to use percentage changes.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

PED is derived from the percentage change in quantity demanded relative to the percentage change in price. It measures the slope of the demand curve when expressed in percentage terms.

Apply this equation when predicting how a price adjustment will impact the total units sold in a specific market. It is most effective in scenarios where the Law of Demand holds and other variables like consumer income or preference remain constant.

This calculation allows businesses to set prices that maximize revenue based on consumer sensitivity to cost. It also helps policymakers understand which products can be taxed effectively, such as alcohol or tobacco, without causing a total collapse in demand.

Swapping the numerator and denominator. Forgetting to use percentage changes.

A local cafe increases coffee prices by 10%, and sales drop by 5%. PED = -0.5.

PED > 1 indicates price-sensitive elastic demand PED < 1 indicates price-insensitive inelastic demand Results are usually negative as price and demand move in opposite directions The calculation assumes ceteris paribus (all other factors constant)

References

Sources

Mankiw, N. Gregory. Principles of Economics.
Wikipedia: Price elasticity of demand
Britannica: Elasticity (economics)
Mankiw, N. Gregory. Principles of Economics. Cengage Learning.
McConnell, Campbell R., Brue, Stanley L., & Flynn, Sean M. Economics: Principles, Problems, and Policies. McGraw-Hill Education.
Mankiw, N. Gregory. Principles of Economics. 9th ed. Cengage Learning, 2021.
Parkin, Michael. Economics. 14th ed. Pearson, 2020.
Wikipedia: Giffen good

Price Elasticity of Demand (PED)

Overview

Variables

Derivation

State the definition

Percentage change in quantity

Percentage change in price

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Price Elasticity of Supply

Frequently Asked Questions

Sources