Cross-price elasticity formula
The cross-price elasticity of demand measures the responsiveness of a good to a change in the price of an alternate good. The cross-price elasticity is defined
is the quantity of good X after the price of good Y changes
is the quantity of good X before the price of good Y changes
is the price of good Y after the price changes.
is the price of good Y before the price changes.
If the cross-price elasticity is negative, it implies that the quantity consumed of a good X decreases after there is a price decrease of Y. This is referred to as a complement good because consumers purchase these goods together. Examples of complement goods are:
- Computers and operating systems
- Fries and ketchup
If the cross-price elasticity is positive, it implies that the quantity consumed of good X increases after a price increase of good Y. This is referred to as a substitute good because consumers substitute towards purchasing Y instead of good X. Examples of substitute goods are:
- Coke and Pepsi
- Bus tickets and train tickets
Suppose that the cross elasticity of demand for Good X and Good Y is positive 2. What does this tell you about the relationship between these two goods? Given this cross elasticity of demand, if the price of Y increases by 15 percent, what will happen to the demand for Good Y?
Given this knowledge above, we can conclude that good X from the example above is a substitute good for good Y because the elasticity is positive. To calculate what will happen to the demand of good X we plug the value 2 into our formula for elasticity on the left-hand side and 0.15 as the denominator in the right-hand side, giving
Multiplying both sides by 0.15 gives
which allows us to conclude a 15% increase in the price of good Y will cause the quantity of good X to increase by 30% or 0.3.