cross price elasticity of demand

Cross Price Elasticity of demand measures the responsiveness of demand for a product to a change in the price of other related products. We normally focus on the links between changes in the prices of substitutes and complements.

The formula for cross price elasticity of demand

Cross Price Elasticity of Demand (CPed) = % change in the demand for Good X % change in the price of Good Y

Show cross price elasticity of demand through diagrams

The main use of cross price elasticity concerns changes in the prices of substitutes and complements.

With substitute goods such as brands of cereal or washing powder, an increase in the price of one good will lead to an increase in demand for the rival product. Cross price elasticity will be positive. In recent years, the prices of new cars have been falling. This should increase the demand for new cars and reduce the demand for second hand cars and mass transport services such as bus travel (ceteris paribus)

With goods that are in complementary demand such as the demand for DVD players and DVD videos, when there is a fall in the price of DVD players we expect to see more DVD players bought, leading to an expansion in market demand for DVD videos

When there is no relationship between two products, the cross price elasticity of demand is zero.

In other words 

Cross price elasticity (CPed) measures the responsiveness of demand for good X following a change in the price of a related good Y.
We are looking here at the effect that changes in relative prices within a market have on the pattern of demand.
With cross elasticity we make a distinction between substitute and complementary products.

Cross price elasticity of demand – analysis diagrams

Substitutes:

With substitute goods such as brands of cereal, an increase in the price of one good will lead to an increase in demand for the rival product. The cross price elasticity for two substitutes will be positive.
For example, the iPhone now provides genuine competition for the Blackberry in providing users with ‘push technology’ to send all emails through to a mobile device.
Another good example is the cross price elasticity of demand for music. Sales of digital music downloads have been soaring with the growth of broadband and falling prices for downloads. As a result, sales of traditional music CDs are declining at a steep rate.

Complements:

Complements are in joint demand
The CPED for two complements is negative.
The stronger the relationship between two products, the higher is the co-efficient of cross-price elasticity of demand.
When there is a strong complementary relationship between two products, the cross-price elasticity will be highly negative. An example might be games consoles and software games

Unrelated products

Unrelated products have a zero cross elasticity for example the effect of changes in taxi fares on the market demand for cheese!

Pricing for substitutes:

If a competitor cuts the price of a rival product, firms use estimates of CPED to predict the effect on demand and total revenue of their own product.

Pricing for complementary goods:

Popcorn, soft drinks and cinema tickets have a high negative value for cross elasticity– they are strong complements. Popcorn has a high mark up i.e. pop corn costs pennies to make but sells for more than a pound. If firms have a reliable estimate for CPed they can estimate the effect, say, of a two-for-one cinema ticket offer on the demand for popcorn.
The additional profit from extra popcorn sales may more than compensate for the lower cost of entry into the cinema. For some movie theatres, the revenue from concessions stalls selling popcorn; drinks and other refreshments can generate as much as 40 per cent of their annual turnover.

Brand and cross price elasticity

When consumers become habitual purchasers of a product, the cross price elasticity of demand against rival products will decrease.
This reduces the size of the substitution effect following a price change and makes demand less sensitive to price. The result is that firms may be able to charge a higher price, increase their total revenue and achieve higher profits.