The formula to calculate the Cross-Price Elasticity (CPE) is:
\[ CPE = \left( \frac{PA1 + PA2}{QB1 + QB2} \right) \cdot \left( \frac{QB2 - QB1}{PA2 - PA1} \right) \]
Where:
Cross-price elasticity measures the responsiveness of the quantity demanded of one good to a change in the price of another related good. It is calculated by dividing the percentage change in the quantity demanded of one good by the percentage change in the price of the other good.
Cross-price elasticity is crucial because it helps businesses understand how the demand for a particular good is affected by changes in the price of a related product. This information is valuable in determining pricing strategies, forecasting demand, and making informed business decisions.
When goods are substitutes, a positive cross-price elasticity indicates that an increase in the price of one good leads to an increase in the demand for the other good. For example, if the price of brand A smartphones increases, consumers may choose to buy brand B smartphones instead.
When goods are complements, a negative cross-price elasticity indicates that an increase in the price of one good leads to a decrease in the demand for the other good. Complementary goods are typically consumed together, such as coffee and cream.
Let's assume the following values:
Step 1: Calculate the average price of product A and the average quantity of product B:
\[ \text{Average Price of A} = \frac{PA1 + PA2}{2} = \frac{10 + 12}{2} = 11 \]
\[ \text{Average Quantity of B} = \frac{QB1 + QB2}{2} = \frac{100 + 120}{2} = 110 \]
Step 2: Calculate the percentage change in quantity of product B and price of product A:
\[ \text{Percentage Change in Quantity of B} = \frac{QB2 - QB1}{QB1} \times 100 = \frac{120 - 100}{100} \times 100 = 20\% \]
\[ \text{Percentage Change in Price of A} = \frac{PA2 - PA1}{PA1} \times 100 = \frac{12 - 10}{10} \times 100 = 20\% \]
Step 3: Calculate the Cross-Price Elasticity (CPE):
\[ CPE = \left( \frac{PA1 + PA2}{QB1 + QB2} \right) \cdot \left( \frac{QB2 - QB1}{PA2 - PA1} \right) = \left( \frac{10 + 12}{100 + 120} \right) \cdot \left( \frac{120 - 100}{12 - 10} \right) = \left( \frac{22}{220} \right) \cdot \left( \frac{20}{2} \right) = 0.1 \cdot 10 = 1 \]
Therefore, the cross-price elasticity is 1, indicating that the two products are substitutes.
