Cross-Price Elasticity of Demand Formula Explained

Cross-Price Elasticity of Demand Formula Explained - Smartphone in a hand, Learning written on the screen, Black board with formulas in the background
Bill Cascade   NEW 30/09/2019 00:00:00 Guides

The term cross-price elasticity of demand can sound confusing to those with little understanding of the concept. Yet, when the cross-price elasticity demand formula is broken down and explained in more detail, you’ll find that it’s a most simple of premises.

It’s also one that you’ll be able to see its effect in financial transactions for yourself.

Here we take a look at the formula cross-price elasticity of demand, considering some worked examples. This will highlight just how relevant it is and in which frameworks.

What is Meant by Cross-Price Elasticity of Demand Formula?

The cross-price elasticity of demand is an economic concept. In its simplest of definitions, it works to measure the responsiveness of quantity in goods demanded. This is done when the price of other good changes. 

You may often hear this concept, also referred to as cross-elasticity of demand. However, the meaning is the same. 

When used in economic terms, it signifies the sensitivity of the demand regarding goods against changes in other economic variables. This can mean such things as prices or that of consumer incomes.

Why is Elasticity So Important?

Elasticity can help offer vital information about strengths and weaknesses in financial relationships and links. This means that between income, price, demand, and other economic variables.

Further still, the elasticity relates to an economic variable’s responsiveness and therefore tell us a lot about supply and demand. 

The Various Types of Elasticity

As elasticity itself plays a central part in economics, it’s applied in a wide variety of situations. Thus, it pays here to get an idea beforehand of the several types of elasticity to use the demand formula effectively.

There are four elasticity types. Each one works to measure the relationship between that of two significant economic variables:

  1. PED – Price Elasticity of Demand. This measures the quantity demanded responsiveness. This is regarding a change in price. It can be measured over arc elasticity – that is, price range or point elasticity which means at one point.
  2. PES – Price Elasticity of Supply. This measures the quantity supplied responsiveness. This is concerning the change in price.
  3. XED – Cross Elasticity of Demand. This measures the responsiveness regarding the quantity demanded of a specific good. This is then in relation to that of the change in the price of another specific good. 
  4. YED – Income Elasticity of Demand. This measures the quantity demanded responsiveness. This is in relation to that of a change in consumer income.

The Formula Used for Cross-Price Elasticity of Demand

The Formula Used for Cross-Price Elasticity of Demand - Mathematical formulas

Though you may see the formula of cross-price elasticity demand displayed in several different ways, the calculation is always the same.

One of the most straightforward of formulas used is:

Cross-Price Elasticity of Demand (XED) =

Percentage Change in Quantity Demanded of Good X  /
Percentage Change in Price of Good Y


The Cross-Price Elasticity Demand Formula in Action

Using this formula with an example, here we highlight how simple it is to use the cross-price elasticity demand formula.

Using an example of a working stationery company, product A is lined paper; product B is plain paper.

Lined paper that is product A has a 10% positive change regarding the quantity demanded.

Meanwhile, plain paper, that is product B has a positive change of 5% regarding its increase in price.

Placing those two figures into our formula, we can then see that our XED is equal to 2.

Cross-Price Elasticity of Demand (XED) =

Percentage Change in Quantity Demanded of Good X   /   Percentage Change in Price of Good Y

Cross Price Elasticity of Demand (XED) =  10% / 5% = 2

When we break this down further to understand what it means, we begin to see the reasoning. Here, we can utilize a rule of thumb that allows us to find a relationship between these two goods.

Cross-Price Elasticity > 0  The two goods are substitutes for each other

Cross-Price Elasticity = 0 The two goods are independent  of each other 

Cross-Price Elasticity < 0 The two goods are complements of one another

Using this, we can see that the lined paper and the plain paper are good substitutes for one another. This means that when lined paper prices went up, more people switched to buying plain paper. 

Understanding Cross-Elasticity of Demand for Substitute Goods

Firstly, what are substitute goods? These are products or services that are seen as the same or similar to other products by the consumers. Basically, they are goods that can be used in the place of others. 

A good example of a substitute good is that of one brand of coffee for another – or even tea in place of coffee.

Thus, when there’s cross-elasticity of demand for those substitute goods, it’s positive. This is because it means the demand for one good will increase when the price for a substitute good increases.

When relating this to the coffee and tea example, it becomes clearer here. Should coffee prices increase, you’ll find quantity demand for tea increases, the tea here being the substitute beverage. Tea will increase as consumers look to switch to less expensive alternatives – but those alternatives that are substitutional.

Additionally, this substitute example can be extended further so you can see how it affects every day financial and indeed consumer decisions. So, you can look at such items as toothpaste for further good examples of substitutional goods. As one toothpaste brand price increases – a demand is created for a competitor toothpaste brand in the process.

Understanding Cross-Elasticity of Demand for Complementary Goods

Cross-Elasticity of Demand for Complementary Goods - Car and Gas

Again, what are complementary goods? These are goods or services that you’ll find used in conjunction with/together with goods or services. 

A complementary good often has little value when consumed alone. But, if combined with other goods or services, it adds more overall value to the initial offering.

A good example of a complementary good/service is that of an app for an iPhone, or car and gas.

As opposed to substitute goods, complementary goods demand regarding cross elasticity is negative.

This means that when an items price increases, those items closely linked to it, and necessary, will decrease. This is because the demand for that main good has also dropped. 

If we relate this back to the coffee example, when coffee prices increase, coffee sticks will automatically drop in demand quantity. This is self-explanatory as with fewer people drinking coffee, there’s less need to purchase such sticks. Thus, it results in what is called a negative cross- elasticity.

Where Cross-Price Elasticity of Demand Is the Most Useful

Companies find cross-price elasticity of demand the most practical. This is because they can utilize the formula to establish prices when selling their goods and services. 

Thus, those products without substitutes can be sold at higher prices. These products do not have any cross-elasticity of demand to consider here. 

Meanwhile, any incremental prices changes to those goods that do have substitutes are further analyzed. Thus, an appropriate level of demand desired can be determined, alongside associated prices of the goods.

In addition to this, cross-price elasticity has its use with complementary goods. These types of goods are strategically priced when based on the cross-elasticity of demand. An excellent example of this is selling printers at a loss with the understanding that future demand for printer ink, that is its complementary item, will increase. 

In concluding, the Cross-Price Elasticity of Demand Formula may initially sound complicated. However, hopefully, you’ll be able to see more clearly now how relevant it is to everyday business and finance. Thus, you’ll be able to spot how effective it is and what its presence means to you regarding future transactions.


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