Cross-Price Elasticity of Demand
What is Cross-Price Elasticity of Demand?
Cross-price elasticity of demand measures how responsive the quantity demanded of one good is to a change in the price of another good.
It is calculated as the percentage change in quantity demanded of Good A divided by the percentage change in price of Good B. If the ratio is positive, the goods are considered substitutes. If the ratio is negative, the goods are considered complements.
Cross-Price Elasticity of Demand: a worked example
A deli raises bagels from $2.00 to $2.40, a change of 0.40/2.00 = 20 percent. Weekly sales of its cream cheese tubs fall from 500 to 440, a change of -60/500 = -12 percent. Cross-price elasticity is -12/20 = -0.6. The sign is the real answer here: negative means bagels and cream cheese are complements, bought together, so pricier bagels drag cream cheese demand down with them. The size, 0.6, says the link is genuine but weak, since the cream cheese response is smaller in percentage terms than the bagel price change that caused it.
The mistake students make with cross-price elasticity of demand
Students strip off the negative sign, because they were drilled to report price elasticity of demand as an absolute value. Here the sign carries the entire result: positive means substitutes, negative means complements, and close to zero means the goods are unrelated. Report -0.6 as 0.6 and you have turned a complement into a substitute. The second version of this error is flipping the formula and putting a price change on top; the quantity of Good A stays upstairs, the price of Good B downstairs.
Cross-Price Elasticity of Demand questions
What does a cross-price elasticity of zero mean?
A cross-price elasticity of zero means the two goods are unrelated in buyers' decisions. Change the price of one and the quantity demanded of the other does not move, so neither substitution nor joint use is going on. These are called independent goods. Real data rarely lands on exactly zero, so treat any very small number, positive or negative, as a sign that the two markets barely talk to each other.
Is cross-price elasticity the same in both directions?
Cross-price elasticity is not symmetric, so the response of Good A to Good B's price can be far larger than the response of Good B to Good A's price. Cut the price of printers and cartridge sales may jump hard, while a change in cartridge prices barely moves printer sales. Both numbers are negative, so both label the pair complements, but the sizes differ. Always say which good's price you changed.
How is cross-price elasticity different from price elasticity of demand?
Cross-price elasticity involves two goods, while price elasticity of demand involves only one. Price elasticity of demand compares a good's quantity response to a change in that same good's price, and its usual job is predicting what happens to total revenue. Cross-price elasticity compares one good's quantity response to a different good's price, and its job is classifying the pair as substitutes, complements or unrelated.
Formula / Example
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Related terms
Common comparisons
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