Cross Elasticity of Demand

Types of cross elasticity of demand

The value of the cross elasticity of demand will depend on whether the two goods are substitutes, complements, or goods with no apparent relationship.

Cross elasticity of demand and substitutes

The demanded quantity of any two substitutes goes in opposite directions. In other words, the less a person consumes one good, the more they would consume this good’s substitute. The cross-price elasticity of demand for these goods will therefore be positive.

Figure 1 illustrates the relationship between substitutes, where Good A is pears and Good B is apples. On the left diagram, an increase in the price of Good A from P1 to P2 leads to a reduction in the quantity demanded from Q1 to Q2, and a movement along the demand curve for Good A. This leads to an outward shift in the demand curve from D1 to D2 of a substitute product - Good B, such that at any given price level, P, Good B is demanded more (Q2 compared to Q1). The diagram on the right illustrates this.

Figure 1. Quantity demand effects of a price increase on substitutes, StudySmarter Originals.

Cross elasticity of demand and complements

The demanded quantity for any two complementary goods goes in the same direction. In other words, the more a person consumes one good, the more they would consume this good’s complement. The cross-price elasticity of demand for these goods will therefore be negative.

Figure 2 illustrates the relationship between complements. Good A is mobile phones and Good B is sim cards. On the left diagram, there is a fall in the price of Good A from P1 to P2, which leads to an increase in the demanded quantity from Q1 to Q2, and a movement along the demand curve for Good A. This leads to an outward shift in the demand curve from D1 to D2 of a complement product - Good B, such that at any given price level, P, Good B is demanded more (Q2 compared to Q1). The diagram on the right illustrates this.

Figure 2. Quantity demanded effects of a price fall on complements, StudySmarter Originals

Cross elasticity of demand and goods with no apparent relationship

Goods that are neither substitutes nor complements are considered unrelated. In other words, there is no relationship between these goods as they are independent of one another. The value of the cross elasticity of demand between such goods is equal to zero.

The cross elasticity of demand formula

Cross elasticity of demand is calculated as a percentage change in the quantity demanded of Good A divided by a percentage change in the price of Good B.

The formula for the cross-price elasticity of demand (XED) is:

$XED=\frac{\%\Delta QuantityDemandedofGoodA}{\%\Delta PriceofGoodB}$

You can find a percentage change in a variable by using the following formula:

$\%\Delta =\frac{Newvalue-Oldvalue}{Oldvalue}*100\%$

If the goods are substitutes, their cross-price elasticity of demand is going to be positive.

This is because a price change of Good A and quantity demanded of Good B move in the same direction:

• If the price of Good A increases, the quantity demanded of Good B increases.

• If the price of Good A decreases, the quantity demanded of Good B decreases.

If the goods are complements, their cross-price elasticity of demand is going to be negative.

This is because a price change of Good A and quantity demanded of Good B move in the opposite direction:

• If the price of Good A increases, the quantity demanded of Good B decreases.

• If the price of Good A decreases, the quantity demanded of Good B increases.

Values of the cross-price elasticity of demand

The table below summarises all the values that the cross-price elasticity of demand (XED) can take.

What factors affect the cross elasticity of demand?

There are three factors that affect the value of the cross elasticity of demand.

1. If the goods are substitutes, the value of the cross elasticity of demand is positive.

2. If the goods are complements, the value of the cross elasticity of demand is negative.

3. If the goods are not related, the value of the cross elasticity of demand is equal to zero

Consumer preferences and their budget constraints affect the demand for any good. Whether the preferences or the budget play a decisive role in which product the consumer chooses, will determine whether the goods have a strong or weak relationship.

Strong and weak substitutes

The magnitude of the cross elasticity of demand for substitute goods is determined based on whether the two goods are strong or weak substitutes.

Consider substitutes such as Assam tea and Ceylon tea. These two types of black tea are strong substitutes as there is only a minor difference between them.

In this case, it is likely that consumers would not mind which type of tea they consume. Therefore, a change in the price of a substitute will outweigh consumer preferences. Thus, if the price of Assam tea increases, consumers are likely to increase the demanded quantity of Ceylon tea. This will result in a higher value of the cross elasticity of demand as the change in the price of one good is likely to significantly affect the quantity demanded of another good.

Now consider substitutes such as green loose leaf tea and matcha tea powder. There are apparent differences in flavour, texture, and smell between the two goods making them weak substitutes.

A cup of matcha tea is definitely different from a cup of green tea. Source: Unsplash.

In this case, it is likely that the differences between the two products will result in consumer preferences for a particular type of tea outweighing any changes in the price of a substitute product. Thus, if the price of green loose leaf tea decreases, consumers are still likely to stay with their preferred good: matcha. This will result in a lower value of the cross elasticity of demand as the change in the price of one good is unlikely to significantly affect the quantity demanded of another good.

Strong and weak complements

The magnitude of the cross elasticity of demand for complementary goods is determined based on whether the two goods are strong or weak complements.

Consider complements such as fish and chips. These two goods are strong complements as they are very often consumed together as a single dish.

In this case, it is likely that consumers would strongly prefer to eat fish together with chips, therefore a change in the price of a complement will outweigh consumer preferences. So if the price of fish decreases they are likely to increase their quantity demanded of chips as well. This will result in a higher value of the cross elasticity of demand as the change in the price of one good is likely to affect the quantity demanded of another good significantly.

Consider another example of complements such as pasta and basil pesto sauce. These two goods are weak complements as consumers can eat pasta with a variety of different sauces apart from the basil pesto sauce.

In this case, it is likely that the differences between the two products will result in consumer preferences for a particular type of product outweighing any changes in the price of a complementary product. Thus, if the price of pasta increases, consumers are likely to still buy the basil pesto sauce they prefer. This will result in a lower value of the cross elasticity of demand as the change in the price of one good is unlikely to significantly affect the quantity demanded of another good.

The cross-price elasticity of demand is a useful measure that allows us seeing how the consumer quantity demanded of one product will respond to price changes of another product. Businesses use cross elasticity of demand to determine how strong their product brand image is. The businesses increase the price of their products by a small margin, and if the demand shifts significantly towards competitors’ products, it is a sign that they need to work on brand loyalty. The firms will then invest more in customer loyalty programmes, packaging, and advertising to increase brand loyalty.