How to Calculate Price Elasticity of Demand Using the Midpoint Formula

The Problem

Calculate the price elasticity of demand:

When the price of coffee increases from $4.00 to $5.00 per cup, the quantity demanded decreases from 1,000 cups per day to 800 cups per day. Calculate the price elasticity of demand using the midpoint formula.

Express your answer to two decimal places and interpret what the elasticity value means.

This is one of those fundamental microeconomics problems you'll see in every principles course. You've got a price change and a quantity change, and you need to figure out how sensitive consumers are to that price change.

The key here is using the midpoint formula instead of the simple percentage change formula. The midpoint method gives you the same answer whether you're going from point A to B or B to A, which is why it's preferred. If you're stuck on a similar problem or need to see the calculation worked out in detail, you can always generate a custom video solution on Torial.

Understanding Price Elasticity of Demand

Economics demand curve graph showing price and quantity relationship

Price elasticity of demand measures how much the quantity demanded responds to a change in price. It tells you whether consumers are sensitive (elastic) or insensitive (inelastic) to price changes.

Key concept:

Elasticity is always calculated as a percentage change in quantity divided by a percentage change in price. But here's the catch: which point do you use as your starting point?

Simple formula: Uses the initial point as the base
Midpoint formula: Uses the average of both points as the base

💡 Why elasticity matters: If demand is elastic (|E| > 1), a small price increase causes a large drop in quantity. If demand is inelastic (|E| < 1), quantity doesn't change much even with big price swings.

This determines pricing strategy, tax policy, and revenue predictions. It's not just a number—it's a decision-making tool.

Think about it: if you're selling something with elastic demand, raising prices might actually hurt your total revenue. But if demand is inelastic, you can raise prices and make more money. Need more help visualizing elasticity? Check out other economics videos in our library.

Why Use the Midpoint Formula?

The simple percentage change formula gives you different answers depending on which direction you're going. The midpoint formula fixes that.

The problem with simple percentage change:

Going from $4 to $5 (25% increase) gives a different elasticity than going from $5 to $4 (20% decrease). Same price change, different answers. That's confusing.

Simple formula (from $4 to $5):

%ΔQ = (800 - 1000) / 1000 = -20%

%ΔP = (5 - 4) / 4 = 25%

E = -20% / 25% = -0.80

Simple formula (from $5 to $4):

%ΔQ = (1000 - 800) / 800 = 25%

%ΔP = (4 - 5) / 5 = -20%

E = 25% / -20% = -1.25

Solution: The midpoint formula uses the average of the two points as the denominator. This gives you the same answer whether you're calculating from A to B or B to A. That's why it's the standard method in economics.

The midpoint formula is symmetric. It doesn't care which direction you're going. That consistency is why textbooks and exams use it. Always.

The Midpoint Formula

Mathematical formula calculation economics

Here's the midpoint formula for price elasticity of demand:

E = [(Q₂ - Q₁) / ((Q₂ + Q₁) / 2)] / [(P₂ - P₁) / ((P₂ + P₁) / 2)]

Where:

E = Price elasticity of demand
Q₁ = Initial quantity
Q₂ = New quantity
P₁ = Initial price
P₂ = New price

Notice the denominators: (Q₂ + Q₁) / 2 and (P₂ + P₁) / 2. Those are the midpoints. That's what makes this formula symmetric.

Breaking it down:

Numerator: Percentage change in quantity using midpoint
Denominator: Percentage change in price using midpoint
Result: Always negative (law of demand), but we usually report the absolute value

The formula looks intimidating, but once you plug in the numbers, it's just arithmetic. Let's work through our coffee example step by step.

Step-by-Step Calculation

Let's calculate the price elasticity of demand for coffee using the midpoint formula.

Given information:

Initial price (P₁):

$4.00

New price (P₂):

$5.00

Initial quantity (Q₁):

1,000 cups

New quantity (Q₂):

800 cups

Step 1: Calculate the midpoint for quantity

Average of Q₁ and Q₂:

(Q₂ + Q₁) / 2 = (800 + 1000) / 2 = 1800 / 2 = 900 cups

This is the midpoint quantity we'll use as the base for percentage change.

Step 2: Calculate the midpoint for price

Average of P₁ and P₂:

(P₂ + P₁) / 2 = (5.00 + 4.00) / 2 = 9.00 / 2 = $4.50

This is the midpoint price we'll use as the base for percentage change.

Step 3: Calculate percentage change in quantity

Using the midpoint as the base:

%ΔQ = (Q₂ - Q₁) / ((Q₂ + Q₁) / 2)

%ΔQ = (800 - 1000) / 900

%ΔQ = -200 / 900

%ΔQ = -0.2222... ≈ -0.2222

Quantity decreased by about 22.22% using the midpoint method.

Step 4: Calculate percentage change in price

Using the midpoint as the base:

%ΔP = (P₂ - P₁) / ((P₂ + P₁) / 2)

%ΔP = (5.00 - 4.00) / 4.50

%ΔP = 1.00 / 4.50

%ΔP = 0.2222... ≈ 0.2222

Price increased by about 22.22% using the midpoint method.

Step 5: Calculate elasticity

Divide percentage change in quantity by percentage change in price:

E = %ΔQ / %ΔP

E = -0.2222 / 0.2222

E = -1.00

The price elasticity of demand is -1.00 (or 1.00 in absolute value).

Final Answer:

E = -1.00

Or, in absolute value:

|E| = 1.00

Notice something interesting? The percentage changes in quantity and price were exactly equal (22.22% each), so the elasticity came out to exactly -1.00. This is called unit elastic demand. Want to see more worked examples? Browse through hundreds of economics solutions on Torial.

Interpreting the Elasticity Value

Elastic vs inelastic demand curves comparison

The elasticity value tells you how sensitive consumers are to price changes. Here's what different values mean:

Elasticity classifications:

Elastic demand (|E| > 1):

Quantity changes more than proportionally to price. A 10% price increase causes more than a 10% drop in quantity. Consumers are very sensitive.

Unit elastic demand (|E| = 1):

Quantity changes proportionally to price. A 10% price increase causes exactly a 10% drop in quantity. Total revenue stays constant.

Inelastic demand (|E| < 1):

Quantity changes less than proportionally to price. A 10% price increase causes less than a 10% drop in quantity. Consumers are not very sensitive.

For our coffee example: With |E| = 1.00, demand is unit elastic. This means:

A 1% increase in price causes exactly a 1% decrease in quantity
Total revenue remains constant when price changes
This is the boundary between elastic and inelastic demand

Revenue implications:

Total revenue = Price × Quantity. When demand is:

Elastic: Raising price decreases total revenue (quantity drops more than price rises)
Unit elastic: Changing price doesn't change total revenue (proportional changes cancel out)
Inelastic: Raising price increases total revenue (quantity drops less than price rises)

This is why businesses need to know elasticity. If you're selling something with elastic demand, price increases hurt you. But if demand is inelastic, you can raise prices and make more money. It's all about understanding consumer behavior.

Common Mistakes to Avoid

Here are the mistakes that cost students the most points. Learn them now so you don't make them on test day. If you want personalized help avoiding these errors, create a custom study video for your specific problem.

❌ Mistake #1: Using the simple percentage change formula

Calculating %ΔQ = (Q₂ - Q₁) / Q₁ and %ΔP = (P₂ - P₁) / P₁. This gives different answers depending on direction and is not the standard method.

Fix: Always use the midpoint formula. It's what exams expect, and it's mathematically consistent.

❌ Mistake #2: Forgetting the negative sign

Price elasticity of demand is always negative (law of demand), but students sometimes drop the sign or forget it exists.

Fix: Keep the negative sign in your calculation. When reporting, you can use absolute value (|E|), but show your work with the negative.

❌ Mistake #3: Mixing up numerator and denominator

Writing E = %ΔP / %ΔQ instead of E = %ΔQ / %ΔP. Elasticity is always quantity change over price change, not the other way around.

Fix: Remember: elasticity = (how much quantity changes) / (how much price changes). Quantity is always on top.

❌ Mistake #4: Using the wrong midpoint

Calculating (Q₁ + Q₂) / 2 correctly but then using Q₁ or Q₂ as the denominator instead of the midpoint.

Fix: Once you calculate the midpoint, use it as the denominator. Don't go back to Q₁ or P₁.

❌ Mistake #5: Not interpreting the result

Calculating E = -0.85 and stopping there without saying whether demand is elastic, inelastic, or unit elastic.

Fix: Always interpret. |E| = 0.85 means inelastic demand. Say what that means for pricing and revenue.

❌ Mistake #6: Rounding too early

Rounding 0.2222... to 0.22 before dividing, which gives E = -0.22 / 0.22 = -1.00, but if you had more decimal places, you'd get a slightly different answer.

Fix: Keep extra decimal places during calculation, then round only the final answer. This prevents rounding errors from compounding.

Practice Problems with Video Solutions

Best way to get good at this? Practice. Try these similar problems and check your work with video solutions. You can also generate instant video explanations for any elasticity problem you're working on.

Practice Problem 1: Elastic Demand

When the price of movie tickets increases from $12 to $15, the quantity demanded decreases from 500 tickets to 300 tickets per day. Calculate the price elasticity of demand using the midpoint formula.

Hint: Follow the same steps. You should get |E| > 1, indicating elastic demand.

Get instant video solution on Torial →

Practice Problem 2: Inelastic Demand

When the price of insulin increases from $50 to $60 per vial, the quantity demanded decreases from 1,000 vials to 950 vials per month. Calculate the price elasticity of demand.

Hint: Essential goods often have inelastic demand. You should get |E| < 1.

Get instant video solution on Torial →

When to Use the Midpoint Formula vs. Simple Percentage Change

Should you always use the midpoint formula, or is the simple formula okay sometimes?

✓ Use Midpoint Formula When:

Calculating elasticity between two points
You need a consistent answer regardless of direction
Taking an exam or doing homework (standard method)
Price changes are relatively large

✓ Simple Formula is Acceptable When:

Calculating elasticity at a single point (point elasticity)
Price changes are very small (approximation)
You're doing quick estimates, not precise calculations
The problem explicitly asks for point elasticity

For most problems? Use the midpoint formula. It's the standard, it's consistent, and it's what your professor expects. When you're working with elasticity calculations, it helps to have a step-by-step video walkthrough that shows exactly which formula to use and when.