Price Elasticity Calculator
Elasticity of demand and supply, midpoint or point method, with the revenue effect.
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About the Price Elasticity Calculator
Work out how strongly quantity responds to a change in price or income. Give two observations — the price and the quantity before and after — and the calculator returns the price elasticity of demand, the income elasticity, the cross-price elasticity between two goods or the price elasticity of supply, by the midpoint (arc) method economics courses use or by the point method, with both percentage changes and every step.
Each answer is explained: elastic, inelastic or unit elastic; a normal good (a necessity or a luxury) or an inferior good; substitutes or complements. For demand it also shows what the price change did to total revenue and why. Two more tabs give the point elasticity anywhere on a straight-line demand curve such as Q = 100 − 2P — with the price where revenue is largest — and predict the quantity and revenue after a planned price change from a known elasticity. Without a pass, the free preview shows the elasticity or the predicted quantity in full, with its verdict and the first step of the working; the other figures, the other steps, the revenue effect and Copy result need a Pro pass.
How to use it
- Choose the kind of elasticity: Price (demand), Income, Cross-price or Supply — or Demand curve and Predict for the other two jobs.
- Pick the midpoint method (the default in most textbooks) or the point method, which measures changes from the starting values.
- Type the starting and new price (or income, or the price of the other good) and the starting and new quantity.
- Read the elasticity, what it means and, for demand, the change in total revenue. The steps show both percentage changes; copy them for your answer with a pass, or after unlocking this result.
- For a demand curve, type its equation (
Qd = 100 − 2PorP = 50 − 0.5Q) and a price or quantity. To plan a price change, enter the elasticity, today’s price and quantity, and the new price or the percentage change.
Examples
Price $70 → $60, quantity 2,800 → 3,000, midpoint
E = −0.45: inelastic; revenue falls from $196,000 to $180,000
Price $120 → $130, quantity 1,800 → 1,600
E = −1.47: elastic; the price rise lowers revenue from $216,000 to $208,000
Rent $650 → $700, apartments 10,000 → 13,000
E = 3.52: elastic supply (OpenStax rounds the two percentages first, 26.1% ÷ 7.4%, and gets 3.53)
Income 30,000 → 40,000, quantity 100 → 120
E = 0.64: a normal good, a necessity
Price of tea $2 → $3, coffee bought 50 → 60
E = 0.45: substitutes
Q = 100 − 2P at P = 20
Q = 60, E = −0.67 (inelastic); unit elastic and revenue largest at P = 25, Q = 50
E = −1.5, price $10 → $11, 100 units
About 86.7 units; revenue $1,000 → $953.33
Common uses
- Economics homework and exams: elasticity by the midpoint method with the working laid out.
- Deciding whether a price rise or a discount would raise or lower revenue.
- Classifying goods as necessities, luxuries or inferior goods from income data, and pairs of goods as substitutes or complements.
- Finding where along a straight-line demand curve demand turns elastic and revenue peaks.
The formulas
- Elasticity: E = (% change in quantity) ÷ (% change in price) — or in income, or in the price of the other good.
- Midpoint (arc) method: % change = (new − old) ÷ ((new + old) / 2) × 100. Because the base is the average of the two values, the answer is the same whether the price rises or falls.
- Point method: % change = (new − old) ÷ old × 100, which is E = (ΔQ / ΔP) × (P₁ / Q₁): the elasticity at the starting point.
- On a demand curve: E = (dQ/dP) × (P / Q). For a straight line Q = a − bP that is E = −bP / Q, so elasticity changes along the line: |E| = 1 at its midpoint (P = a/2b), elastic above, inelastic below.
- Revenue: total revenue is P × Q. With elastic demand a price rise lowers revenue and a cut raises it; with inelastic demand the reverse; with unit elastic demand revenue does not change.
Reading the result
- Price elasticity of demand is negative (price and quantity move in opposite directions) and is usually quoted as its size: above 1 elastic, below 1 inelastic, exactly 1 unit elastic, 0 perfectly inelastic, infinite perfectly elastic.
- Price elasticity of supply is positive, with the same thresholds.
- Income elasticity: negative for an inferior good; positive for a normal good — between 0 and 1 a necessity, above 1 a luxury.
- Cross-price elasticity: positive for substitutes (tea and coffee), negative for complements (coffee and sugar), zero for unrelated goods.
Sources
- OpenStax, Principles of Economics 3e: §5.1 Price Elasticity of Demand and Price Elasticity of Supply (the midpoint method and the worked examples above), §5.2 Polar Cases of Elasticity and Constant Elasticity, §5.3 Elasticity and Pricing (Table 5.3, revenue) and §5.4 Elasticity in Areas Other Than Price (income and cross-price elasticity).
Limitations
- Two observations give the elasticity between them; if the demand or supply curve itself shifted in between (because of income, tastes or other prices), the number does not measure a movement along one curve. The tool warns when the signs suggest this.
- The demand-curve tab is for straight lines; for curved demand, use two nearby points with the midpoint method.
- Predictions assume the elasticity stays the same over the price change, which is only reasonable for modest changes.
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Frequently asked questions
What do I get without a pass?
Without a pass, Price Elasticity Calculator shows the elasticity or the predicted quantity in full, with its verdict and the first step of the working; every other figure is hidden. Until you unlock it, the result can’t be copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do you calculate price elasticity of demand?
Divide the percentage change in quantity demanded by the percentage change in price. With the midpoint method each percentage change uses the average of the old and new values as its base: when the price falls from $70 to $60 and the quantity rises from 2,800 to 3,000, %ΔQ = 200 ÷ 2,900 = 6.9% and %ΔP = −10 ÷ 65 = −15.4%, so E = −0.45.
What is the difference between the midpoint and the point method?
The midpoint method measures each change against the average of the two values, so you get the same elasticity whether the price goes up or down. The point method measures against the starting values (or uses the slope of the demand curve at one point), so the answer depends on where you start. For small changes they nearly agree.
Is demand elastic or inelastic?
Look at the size of the price elasticity of demand: above 1 is elastic (buyers react strongly to price), below 1 is inelastic (they react weakly), and exactly 1 is unit elastic. Goods with close substitutes tend to be elastic; necessities with no substitutes tend to be inelastic.
Will raising the price increase revenue?
Only if demand is inelastic. When demand is inelastic, the quantity falls by a smaller percentage than the price rises, so revenue goes up; when demand is elastic, revenue goes down. On a straight-line demand curve revenue is highest where elasticity is exactly 1.
What does a negative income elasticity mean?
That the good is inferior: people buy less of it as their income rises, typically because they switch to something they prefer. A positive income elasticity marks a normal good; above 1 it is usually called a luxury and between 0 and 1 a necessity.
How can I tell substitutes from complements?
From the sign of the cross-price elasticity: if a rise in the price of good B makes people buy more of good A, it is positive and the goods are substitutes; if they buy less of A, it is negative and the goods are complements.