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?
The cross price elasticity of demand measures the responsiveness of a good to a change in 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 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
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
Given this new knowledge, 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 an 15% increase in the price of good Y will cause the quantity of good X to increase by 30% or 0.3.