How to Use the Midpoint Method for Elasticity
The midpoint method divides the change by the average of the old and new values, so elasticity comes out the same whether price rises or falls.
Full guide: Elastic vs inelastic demand, explained
The Midpoint Method formula
Worked example: Midpoint Method
Price rises from $10 to $15 while quantity demanded falls from 200 to 120. Average price = (10 + 15) ÷ 2 = 12.5, so %ΔP = 5 ÷ 12.5 = 40%. Average quantity = (200 + 120) ÷ 2 = 160, so %ΔQ = −80 ÷ 160 = −50%. Elasticity = −50% ÷ 40% = −1.25, which is elastic. Running it backwards from $15 to $10 gives %ΔP = −40% and %ΔQ = 50%, the same −1.25.
Calculator
Enter the old and new price and quantity; this divides each change by its average and returns the elasticity.
The worked example uses a rise from $10 to $15.
Quantity at the new price. Swapping the two points must give the same elasticity.
Quantity moves 1.25% for every 1% change in price, so raising the price lowers total revenue.
- Midpoint (average) price
- $12.5
- Midpoint (average) quantity
- 160
- % change in price
- 40%
- % change in quantity demanded
- −50%
- Elasticity verdict
- Elastic
The denominator for the price change: the average of the old and new price, not the starting one.
The denominator for the quantity change.
The price change divided by the average price.
The quantity change divided by the average quantity.
How to calculate Midpoint Method, step by step
- 1Average the two quantities. Add the old and new quantities and divide by 2; that average becomes the denominator.
- 2Compute the percentage change in quantity. %ΔQ = (Q₂ − Q₁) ÷ the average quantity, then multiply by 100.
- 3Repeat the same steps for price. %ΔP = (P₂ − P₁) ÷ the average of the two prices, times 100.
- 4Divide to get the elasticity. Elasticity = %ΔQ ÷ %ΔP. Take the absolute value when classifying demand as elastic, inelastic, or unit elastic.
- 5Reverse the two points as a check. Swap the start and end values and redo the ratio; the midpoint method must return the same number, which the simple percentage-change formula does not.
Midpoint Method questions
Why does the midpoint method give the same answer in both directions?
It divides by the average of the two values rather than the starting value, and that average does not change when you swap the start and end points.
Can the midpoint method be used for other elasticities?
Yes. Every elasticity is a ratio of percentage changes, so the same midpoint percentages work for price elasticity of supply, income elasticity, and cross-price elasticity.
Do you keep the negative sign on price elasticity of demand?
The raw number is negative because price and quantity move in opposite directions, but most courses report the absolute value when labeling demand elastic or inelastic.
What is the midpoint method formula?
The midpoint method formula is %Δ = (new − old) ÷ ((new + old) ÷ 2), applied to both quantity and price, and then elasticity = %ΔQ ÷ %ΔP. When price rises from $10 to $15 and quantity demanded falls from 200 to 120, %ΔP = 5 ÷ 12.5 = 40% and %ΔQ = −80 ÷ 160 = −50%, so elasticity = −50% ÷ 40% = −1.25.
What is the midpoint formula in microeconomics?
In microeconomics, the midpoint formula computes a percentage change using the average of the two values as the base: %Δ = (new − old) ÷ ((new + old) ÷ 2). A move from 10 to 15 is 5 ÷ 12.5 = 40%, and a move from 15 to 10 is −40%, the same size in either direction. It differs from the midpoint formula in math class, which only finds the point halfway between two coordinates.
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