How this calculator works
Cross price elasticity compares the percentage change in the quantity demanded of one product with the percentage change in the price of another. A positive value means the products are substitutes: when the price of A rises, buyers switch to B. A negative value means they are complements, such as printers and ink. A value near zero means the two products are largely unrelated. The standard method divides by the initial values, while the midpoint method divides by the average of the two values so that the answer is the same whichever direction the change runs.
Formula
Standard: cross price elasticity = ((Q2 - Q1) / Q1) / ((P2 - P1) / P1). Midpoint: ((Q2 - Q1) / ((Q1 + Q2) / 2)) / ((P2 - P1) / ((P1 + P2) / 2)). P is the price of product A and Q is the demand for product B.
Worked example
The price of product A rises from $10 to $12 and demand for product B falls from 100 to 80. Standard: (80 - 100) / 100 = -0.2 and (12 - 10) / 10 = 0.2, so elasticity is -1.0. Midpoint: -20 / 90 = -0.2222 and 2 / 11 = 0.1818, so elasticity is -1.2222. The negative sign marks the products as complements.
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Frequently asked questions
What does a cross price elasticity of zero mean?
Demand for B did not change when the price of A changed, so the products are unrelated in consumers' minds. The measure is only as good as the data: small price moves can produce noisy estimates near zero.
Why is the midpoint method preferred?
It removes the direction bias of the standard method. A price rise from $10 to $12 and a fall from $12 to $10 give different standard answers but the same midpoint answer, which is why textbooks use it for arc elasticity.
Can the elasticity be used for pricing?
Only with care. It measures one pair of products at one moment. Substitution patterns change with availability, branding and income, and a large price change can push the relationship outside the range where the estimate holds.