# Cross Elasticity of Demand

Cross Elasticity: It is defined as the percentage change in the demand for an item (X) with the unit percentage change in the price of its substitute/complement item (Y). #### Example:

• Calculate the cross elasticity for X if the quantity demanded for X changes from 30 to 20, while price of Y changes from Rs 10/unit to Rs 15/unit.
• % change in demand of X = (20 - 30)/30 = (-)33.33%
• % change in price of Y = (15 - 10)/10 = 50%
• So, cross price Elasticity = (-) 33.33/50 = (-)0.67

• Price Elasticity explains the effect of the price of item(A) on demand of the same item(A). Cross elasticity, on the other hand, explains the effect of the price of another item(B) on the demand of item(A).

## Cross Elasticity for Substitute Goods

• For substitute goods X and Y, if the price of Y increases, it leads to an increase in demand for X. So, the cross elasticity comes out as positive for substitute items.
• E.g. Tea and Coffee are substitutes, so if the price of tea increases, demand for coffee will increase. Hence cross elasticity will be positive.

#### Example:

• Calculate the cross elasticity for item P if the quantity demanded item P changes from 10 to 20, while the price of Q changes from Rs 20/unit to Rs 25/unit. Also, find how X and Y items are related.
• % change in demand of P = (20 - 10)/10 = 100%
• % change in price of Q = (25 - 20)/20 = 25%
• So, cross-price Elasticity = 100/25 = 4

A positive cross elasticity suggests that items X and Y are substitute items.

#### Graph for Cross Elasticity for Substitute Items is shown below: ## Cross Elasticity for Complementary Goods

For complementary goods X and Y, if the price of Y increases, it leads to a decrease in demand for X. So, the cross-price elasticity comes out as negative for substitute items.
• E.g. Cars and Petrol are complementary, so if the price of cars increases, the demand for petrol will decrease. Hence cross elasticity will be negative.

#### Example:

• Calculate the cross elasticity for item A if the quantity demanded item X changes from 30 to 20, while the price of Y changes from Rs 10/unit to Rs 15/unit. Also, find how X and Y items are related.
• % change in demand of X = (20 - 30)/30 = (-)33.33%
• % change in price of Y = (15 - 10)/10 = 50%
• So, cross-price Elasticity = (-) 33.33/50 = (-)0.67

A negative cross elasticity suggests that items X and Y are complementary items.
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#### Graph for Cross Elasticity for Complementary Items is shown below:

• The relevance of Cross Elasticity: Cross elasticity of demand is an important concept for industries and production units. Research analysts in a company closely analyze the cross elasticity trends in the market between related products and then set prices for their products.
• A company can sell its premium product at a higher price if it has no substitutes. However, if a product has a strong substitute available in the market, then the company will strategically market and price that product to ensure a steady demand. 