Price Elasticity of Demand Calculator
Measure how much demand reacts to a price change with the midpoint method, and see what it does to revenue.
What it does
Price elasticity of demand measures how strongly buyers react to a price change. If a small price move sends volumes swinging, demand is elastic. If volumes barely move, demand is inelastic. The number decides whether a price rise grows or shrinks the money coming in.
There are two ways to compute the percentage changes. The simple method uses the original value as the base, which makes the answer depend on the direction of the change. The midpoint method divides by the average of the two prices and the average of the two quantities, so the answer is the same whichever way round you enter the data. OpenStax uses the midpoint method in its worked examples, and this page follows it.
The result comes out negative for ordinary goods, because a price rise and a demand rise pull in opposite directions. Textbooks often quote the magnitude instead, so this page shows both, along with a plain label for what the number means.
Elasticity is about the local response at one point on a demand curve. It is not a fixed property of a product, and it changes with the price level, the substitutes on offer and how much of the budget a product takes.
The revenue line is where the number earns its keep. Total revenue is price times quantity. When demand is inelastic, a price rise lifts revenue, because the extra price outweighs the sales that are lost. When demand is elastic, the opposite happens.
How to use
- Enter the first price and the quantity demanded at that price.
- Enter the second price and the quantity demanded at that price.
- Read the percentage change in quantity and in price, which use the midpoint method.
- Read the elasticity and its label.
- Compare the revenue before and after the price move.
- Use the direction of the revenue change to decide whether the price move helped.
Formula
- P1, P2
- The two prices.
- Q1, Q2
- The quantities demanded at those prices.
- Midpoint
- The average of the two prices or the average of the two quantities.
- E
- Elasticity of demand, negative for ordinary goods.
- TR
- Total revenue, price times quantity.
The midpoint method needs the price to change. If both prices are the same there is no percentage change in price, so elasticity cannot be computed and the tool asks for a different price. When one quantity is zero the average quantity is the other one, and the percentage change still works, so a market that starts from no sales is fine.
Worked example
Example: price rises from $120 to $130 and volume falls from 1,800 to 1,600
Defaults: first price $120 with 1,800 units sold, second price $130 with 1,600 units sold.
- Average quantity: (1,800 + 1,600) / 2 = 1,700.
- Change in quantity: (1,600 - 1,800) / 1,700 = -11.76%.
- Average price: ($120 + $130) / 2 = $125.
- Change in price: ($130 - $120) / $125 = 8.00%.
- Elasticity: -11.76 / 8.00 = -1.47, so demand is elastic.
- Revenue: $120 x 1,800 = $216,000.00 and $130 x 1,600 = $208,000.00, a fall of 3.70%.
- The tool shows -1.47 (elastic), a magnitude of 1.47, -11.76%, 8.00% and the revenue line.
Reference table
| Magnitude | Demand is | If the price rises | If the price falls |
|---|---|---|---|
| Below 1 | inelastic | revenue rises | revenue falls |
| Equal to 1 | unit elastic | revenue holds | revenue holds |
| Above 1 | elastic | revenue falls | revenue rises |
Limits
- Measures the response between two points, so it describes that price range rather than the whole demand curve.
- Needs observed prices and quantities, so a forecast based on assumptions can only be as good as the assumptions.
- Treats the two points as comparable, which fails when the product or the market changed between them.
- Says nothing about margins, so revenue up does not automatically mean profit up.
Common mistakes
- Dividing by the original price and quantity instead of the midpoint, which makes the answer depend on the direction of the change.
- Reading a negative elasticity as something broken, when the sign only shows the direction of the reaction.
- Entering the change in price instead of the two prices.
- Ignoring the revenue line, which is the part that tells you whether the price move was worth making.
- Using the elasticity of one product in one market as a fixed number for a different market.
Try it yourself
Quick checks. Answers sit tucked under each question.
A price rises from $10 to $12 and the quantity sold falls from 1,000 to 800. What is the elasticity?
Quantity changes by -22.22% and price changes by 18.18%, so the elasticity is -1.22 and demand is elastic. Revenue falls from $10,000.00 to $9,600.00, which is 4.00% less.
A price falls from $50 to $40 and the quantity sold rises from 500 to 700. What is the elasticity?
Quantity changes by 33.33% and price changes by -22.22%, so the elasticity is -1.50 and demand is elastic. Revenue rises from $25,000.00 to $28,000.00, which is 12.00% more.
Price rises from $4 to $6 and the quantity sold falls from 1,200 to 800. What happens to revenue?
Both the quantity and the price change by 40%, so the elasticity is -1.00 and demand is unit elastic. Revenue stays the same at $4,800.00 before and after.
Questions
What is price elasticity of demand?
It is the percentage change in quantity demanded divided by the percentage change in price, and it measures how responsive buyers are to price.
Why is the midpoint method better?
Because the answer does not change when you swap the two points. With the simple method, going from $100 to $120 and then from $120 back to $100 gives two different elasticities, which cannot be right.
What does an elasticity of -2 mean?
A 1% price change moves the quantity demanded by 2% in the opposite direction. Demand is strongly elastic, so raising the price would cut revenue.
Why is the result negative?
Price and quantity move in opposite directions for ordinary goods, so the ratio comes out negative. Textbooks often quote the magnitude, which is the number after the sign is dropped.
Is a product with inelastic demand a good thing?
It makes revenue predictable when you raise the price, and it means discounting buys very little extra volume. It also means a price rise carries less risk of losing customers, but it can cost you share.
How is this different from a revenue calculation?
Revenue is price times quantity for one point. Elasticity compares two points and tells you how sensitive the outcome is, which is what you need before you change a price.
Sources
- OpenStax Principles of Economics 3e: price elasticity of demand and price elasticity of supply
- CORE Econ, The Economy: demand elasticity and revenue