# Cross Price Elasticity of Demand Meaning, Formula & Calculations

## What is cross price elasticity of demand?

### Cross price elasticity of demand definition

The cross-price elasticity of demand describes how quantity demanded of a product is changing when the price of another commodity is changing while all other factors are constant. Cross price elasticity of demand formula is Percentage of change in quantity demanded of the considering good/ Percentage of change in price of the another good

In other words, cross-price elasticity of demand is defined as follows.

The cross price elasticity of demand measures the sensitivity of changes in the quantity of demand as the result of changes in the price of another good when the other factors remain unchanged.

## Related topics

### The price elasticity of demand

The price elasticity of demand is a measure of the responsiveness of quantity demanded of the product when changing the price of the considered commodity while all other factors are constant. To calculate price elasticity of demand, we should divide the percentage change in quantity demanded by the percentage change in price.

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How to Calculate Price Elasticity of Demand?

### The price elasticity of supply

The price elasticity of supply measures how responsive the quantity supplied of a product is when changing the price of it while all other factors are constant. According to price elasticity of supply formula, the price elasticity of supply is equal to the percentage of change in quantity supplied /Percentage of change in price.

Price elasticity of supply formula = Percentage of change in quantity supplied /Percentage of change in price.

Price Elasticity of Supply Meaning, Formula & Examples

## Cross price elasticity of demand for substitutes and complements

According to sign of the cross-price elasticity of demand, we can identify two major types goods. They are substitute goods and complementary goods. If the cross-price elasticity of demand is positive, goods are substitute to each other and if the cross-price elasticity of demand is negative, goods are complement to each other.

### Negative elasticity of demand

There is a negative relationship between the price of complement goods and the demand for a particular good. That means when the price of a complement good is increasing, the demand for the considered good is decreased. So for the complement goods, cross price elasticity of demand is negative.

### Positive elasticity of demand

There is a positive relationship between the price of substitute goods and the demand for a particular good. That means when the price of a substitute good is increasing, the demand for the considered good is increased. So for the substitutes goods, cross price elasticity of demand is positive.

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## Cross price elasticity of demand formula

Cross price elasticity of demand formula is the percentage of the quantity of demand change of a good is divided by the percentage of the price change of another good.

In other words, basic formula for cross price elasticity of demand is

Percentage of change in quantity demanded of the considering good/ Percentage of change in price of the another good

If we do not have the percentage of change in quantity demanded of the particular good and/ or percentage of change in price of the another good, what we can do?

Then we can calculate cross price elasticity of demand using arc cross price elasticity of demand and point cross price elasticity of demand

Let’s discuss about them.

## Ways of calculating cross price elasticity of demand

There are two major ways of calculating the cross-price elasticity of demand. They are,

Arc cross price elasticity of demand

Point cross price elasticity of demand

Let’s discuss about them.

## Arc cross price elasticity of demand

Arc cross price elasticity of demand in other words, midpoint cross price elasticity of demand calculates the elasticity at the central point between the two points of the demand curve.

The arc cross price elasticity of the demand formula in other words, the midpoint cross price elasticity of the demand formula can be presented as follows

### Arc cross price elasticity of demand formula

Assume that, the good that we consider is X and the related good that we consider is Y. So, the cross-price elasticity of demand between goods x and y can be calculated using the following formula for arc cross-price elasticity of demand.

## Point cross price elasticity of demand

Point Elasticity calculates elasticity at a particular point of the demand curve. The formula for point cross price elasticity of demand is as follows.

### Point cross price elasticity of demand formula

Assume that, the good that we consider is X and the related good that we consider is Y. So, the cross-price elasticity of demand between goods x and y can be calculated using the following point cross price elasticity of demand formula.

## Cross price elasticity of demand calculations

### Calculation example 1

Assume that price of coffee is increasing 20 percent and as a result of it, demand of tea increasing 10 percent. So, calculate the cross price elasticity of demand.

**Answer**

For this example, we can apply basic formular for cross price elasticity of demand.

Cross price elasticity of demand = Percentage of change in quantity demanded of the particular good/ Percentage of change in price of the another good

Cross price elasticity of demand = 10% / 20% = 0.5

That means when price of coffee is increasing 1 percent and as a result of it, demand of tea increasing 0.5 percent.

Coffee is a substitute good for tea. When the price of a substitute good is increasing, the demand for the considered good is increases. For the substitute goods, cross price elasticity of demand is positive.

### Calculation example 2

The demand for chicken was 10,000 when the price of a kilo of fish was $10, and the demand for chicken rose to 15,000 when the price of a kilo of fish was increased to $15.

How to calculate arc cross price elasticity of demand?

**Answer**

To calculate the arc cross price elasticity of demand, we should apply arc cross price elasticity of demand formula

That means when price of fish is increasing 1 percent and as a result of it, demand of chicken increasing 1 percent.

Fish is a substitute good for Chicken. When the price of a substitute good is increasing, the demand for the considered good is increases. For the substitute goods, the cross price elasticity of demand is positive.

### Calculation example 3

The demand for tea was 10,000 when the price of a kilo of sugar was $2, and the demand for tea decreased to 7,000 when the price of a kilo of sugar was increased to $4.

How to calculate point cross price elasticity of demand when demand for tea was 10,000?

**Answer**

To calculate the point cross price elasticity of demand, we should apply point cross price elasticity of demand formula

When price of sugar is increasing 1 percent and as a result of it, the demand of tea decreasing 0.3 percent.

Sugar is a complementary good for tea. There is a negative relationship between the price of complementary goods and the demand for a particular good. That means when the price of a complement good is increasing, the demand for the considered good is decreased.

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