The cross-price elasticity of demand is a measure of the responsiveness of demand for goods when the price of related goods changes. In the analysis, we assume other factors do not change.
We mean, related products refer to substitute or complementary goods.
How to calculate cross-price elasticity from the demand function
You can calculate the cross-price elasticity of demand by dividing the percentage change in the demand quantity for an item by the percentage change in the price of the related item. And, in a mathematical formula, it will look like this:
The cross-price elasticity of demand = % Change in quantity of goods demand X / % Change in price of goods Y
Classification of goods based on their cross-price elasticity of demand
Based on the value of the cross-price elasticity, economists divide related goods into two:
- Substitution goods (elasticity > 0)
- Complementary goods (elasticity < 0)
The value of elasticity tells you how close both of them are as a substitute or complement. A high positive value shows both are close substitutes. And, the high absolute value of the elasticity of complementary goods indicates they are close.
Substitution has a positive cross-price elasticity. If the price of item Y rises, the demand for item X increases. The increase in the price of goods Y makes consumers reduce their demand. Some of them then turn to item X, the substitute product.
Why choose alternative products? Because both item X and item Y have similar utilities. Imagine, tea is a substitute for coffee. When the price of tea rises, consumers reduce their consumption. They then switch to coffee.
Take another example. Pepsi and Coke are substitutes. When Pepsi prices went up, some consumers turned to Coke, increasing their demand. The reverse effect applies when Coke prices rise.
Furthermore, the positive value of the cross-price elasticity tells you how closely the two goods substitute each other. If the value is high, it means both of them are close substitutes.
Close substitution means a small increase in the price of a substitute item will cause a significant increase in the quantity demand of goods. Two goods with different brands are usually close substitutions, such as Coke and Pepsi, in soft drink products.
When two items have negative cross-elasticity, that means they are complementary. Both add value to each other or consumed as a pair. Hence, when the price of item Y rises, the demand for item X decreases. And, the opposite effect applies.
Take the example of gasoline and cars. Consumers use both together. Without a car, gasoline demand is minimal. In contrast, without gasoline, the vehicle cannot run.
When the price of a car goes down, the demand for gasoline will go up. Falling prices encourage consumers to buy cars. Increasing car demand will also increase gasoline demand.