Cross-Price Elasticity of Demand

\[E_{xy}=\frac{\frac{Q_{A2}-Q_{A1}}{Q_{A1}}}{\frac{P_{B2}-P_{B1}}{P_{B1}}}\]

Variables

Exycross-price elasticity of demand

QA1initial quantity demanded of good A

QA2final quantity demanded of good A

PB1initial price of good B

PB2final price of good B

Description

What is this formula?

Cross-Price Elasticity of Demand measures how the demand for one good responds to changes in the price of another good.

It helps identify whether two goods are substitutes or complements.

When to use it

Use this formula when analyzing competitive products, complementary goods, consumer behavior, and market structure.

Example

Price of coffee:

PB1 = 4 USD

PB2 = 5 USD

Demand for tea:

QA1 = 1000 units

QA2 = 1200 units

Formula:

Exy = ((QA2−QA1)/QA1)/((PB2−PB1)/PB1)

Substitution:

Exy = ((1200−1000)/1000)/((5−4)/4)

Exy = 0.20/0.25

Exy = 0.80

Result:

The positive elasticity indicates that tea and coffee are substitute goods.

Applications

- Market analysis

- Competitive strategy

- Product positioning

- Demand forecasting

- Consumer behavior studies

Note

A positive cross-price elasticity generally indicates substitute goods, while a negative value indicates complementary goods. The magnitude reflects the strength of the relationship between the products.