Imagine you have a lemonade stand, and your friend has a cookie stand nearby.
If you notice that when the price of your friend’s cookies increases, more people buy your lemonade, which means the two products are substitutes. People switch to your lemonade when cookies get more expensive.
Conversely, if the price of cookies increases and fewer people buy your lemonade, the two products are complements – people like to buy them together.
The best part? My cross-price elasticity calculator makes this analysis a breeze.
Cross-Price Elasticity Definition
The cross-price elasticity of demand measures how the quantity demanded of one product responds to a change in the price of another product.
If one product’s price changes, cross-price elasticity helps you understand what might happen to the sales of a different, related product.
This relationship can be categorized in two ways:
- Complements: If two goods are complements, an increase in the price of one leads to a decrease in the demand for the other. Here, the cross-price elasticity will be negative, reflecting this inverse relationship.
- Substitutes: Conversely, if two goods are substitutes, an increase in the price of one results in an increase in the demand for the other. In this situation, the cross-price elasticity is positive, indicating that the goods can be replaced with one another.
Cross-Price Elasticity Formula
The cross-price elasticity of demand (CPED) can be calculated using the following formula:
CPED = (Initial Price A + Final Price A) / (Initial Demand B + Final Demand B) × (Final Demand B - Initial Demand B)/ (Final Price A - Initial Price A)Where:
- Initial Price A — Initial price of product A.
- Final Price A — Final price of product A.
- Initial Demand B — Initial demand for product B.
- Final Demand B — Final demand for product B.
When you’re using this formula, it’s critical to pay attention to the sign of the result:
- Positive CPED >0: Products A and B are substitutes. As the price of A goes up, the demand for B increases.
- Negative CPED <0: Products A and B are complements. If A’s price rises, the demand for B falls.
Remember that the absolute value of the CPED can provide magnitude information: the larger the number, the stronger the relationship between the two products’ price and demand.
Real-World Calculation Example
Imagine you run a local coffee shop and are interested in how the price of tea affects the sale of your coffee, considering these two can be substitute goods to some customers.
Let’s say you sell 400 cups of coffee per day at $2.50/cup and tea for $2.00/cup. This now becomes your base price and quantity.
You decided to increase the price of tea from $2.00/cup to $2.20/cup. With that, you noticed that your demand for coffee increased from 400 cups per day to 420 cups per day.
So we have:
- The initial price for tea: $2.00/cup
- The final price for tea: $2.20/cup
- Initial demand for coffee: 400 cups
- Final demand for coffee: 420 cups
To calculate the cross-price elasticity use our formula:
CPED = ($2.00/cup + $2.20/cup) / (400 cups + 420 cups) × (420 cups - 400 cups) / ($2.20/cup - $2.00/cup) = 4.20 / 820 * 20 / 0.2 = 0.51
A CPE of 0.51 indicates that the quantity demanded of your coffee is moderately responsive to the price change in tea. This suggests that if the price of tea increases, more customers may switch to purchasing coffee, but not in a one-to-one ratio.
By applying these steps to your data, the cross-price elasticity calculator helps you understand the relationship between the goods you sell and their substitutes, assisting in making informed pricing decisions.