Cross-price elasticity of demand calculator
When coffee gets dearer, people buy more tea and fewer coffee filters. The cross-price elasticity measures that: the percentage change in demand for good A divided by the percentage change in the price of good B. Enter the old and new price of B and the old and new quantity of A. A positive result means substitutes, a negative one complements, zero independent goods.
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How to use it
- Choose the midpoint or simple method.
- Enter the price of good B before and after the change.
- Enter the quantity of good A before and after.
E = %ΔQ_A ÷ %ΔP_B
- Midpoint: %Δx = (x₂ − x₁) ÷ ((x₁ + x₂) ÷ 2)
- Simple: %Δx = (x₂ − x₁) ÷ x₁
E > 0 substitutes, E < 0 complements, E = 0 independent goods.
Worked example
Coffee goes from 4 to 5 a pack and a café sells 240 cups of tea a day instead of 200.
- %ΔQ (midpoint) = 40 ÷ 220 = 18.18 %.
- %ΔP = 1 ÷ 4.5 = 22.22 %.
- E = 18.18 ÷ 22.22 = 0.818: tea and coffee are substitutes.
With the simple method, a printer price rise from 2 to 2.5 (+25 %) that cuts cartridge sales from 1,000 to 900 (−10 %) gives E = −0.4: complements.
Common mistakes
- Mixing up the goods: the quantity is of A, the price is of B.
- Letting other things change at the same time (a sale on A, a season), which hides the cross effect.
- Reading the elasticity as fixed: it can differ for small and large price changes.
Frequently asked questions
What is the cross-price elasticity formula?
E = % change in quantity of A ÷ % change in price of B. With the midpoint method each change is taken over the average of the two values, so the answer is the same whichever point you call first.
How do I read the sign?
Positive: the goods are substitutes, demand for A rises when B gets dearer (tea and coffee). Negative: complements, demand for A falls (printers and ink). Close to zero: the goods hardly affect each other.
What does the size tell me?
How strongly the goods are linked. 0.82 means a 10 % rise in B's price raises demand for A by about 8.2 %. Large positive values mean close substitutes, which matters for pricing and for competition between products.
Midpoint or simple percent change?
Midpoint gives the same result in both directions and is the usual textbook choice. Simple change divides by the first value; it is fine for small changes or when you need it to match a report that uses it.