## Formula to Calculate Cross-Price Elasticity of Demand

Cross price elasticity of demand formula is used to measure the percentage change in the quantity demanded of a product concerning the percentage change in the price of a related product, and it can be evaluated by dividing the percentage change in quantity demanded of a particular product by the percentage change in the price of its corresponding product.

**E**

_{c}= Percent change in a quantity of good A/Percent change in the price of good Bor

**Ec = [(P****1A**** + P****2A****)/(Q****1B**** + Q****2B****)] * [(Q****1B**** – Q****2B****)/(P****1A**** – P****2A****)]**

Where,

- Ec is the cross-price elasticity of the demandCross-price Elasticity Of The DemandCross Price Elasticity of Demand measures the relationship between price and demand. Change in quantity demanded by one product with a change in price of the second product, where if both products are substitutes, it will show a positive cross elasticity of demand.read more
- P1A is the price of good A at time 1
- P2A is the price of good A at time 2
- Q1B is the quantity of good B at time 1
- Q2B is the quantity of good B at time 2

##### Table of contents

### Key Takeaways

- The cross-price elasticity of demand formula helps to find the relationship between the amount required for a product and the price of a comparable product.
- When the cross-price elasticity of two goods is positive, they are treated as supplementary goods (Car and Petrol); however, when the elasticity of the goods is negative, the two are known as complementary goods (Mobile Phones and Sim Cards).
- Large enterprises use the cross-price elasticity of demand to guide their pricing strategy. As a result, large companies typically offer a wider range of comparable and related products.

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For eg:

Source: Cross Price Elasticity of Demand Formula (wallstreetmojo.com)

### Explanation

- If the cross-price elasticity of demand is positive, the two goods are said to be supplementary goods, i.e., if the price of one good increases, then the demand for other goods will increase.
- However, if the cross-price elasticity is negative, then the two goods are complementary, i.e., if the price of one good increases, the demand for the other goods will decrease.

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### Cross Price Elasticity of Demand Explained in a Video

### Examples

#### Example #1

A company producing torches and batteries is analyzing the cross-price elasticity of the two goods. For example, the demand for torches was 10,000 when the price of batteries was $10, and the demand rose to 15,000 when the price of batteries was reduced to $8.

Solution:-

- Percentage change in the number of torches

= [(15000 – 10000) / (15000 + 10000)] / 2 = 5000 / 12500 = 40%

- Percentage change in price of batteries

= [(8 – 10) / (10 + 8)] / 2 = -2 / 9 = -22.22%

Thus, cross-price elasticity of demand = 40%/-22.22% = **-1.8**

Since the cross-price elasticity of demand for torches and batteries is negative, thus these two are complementary goods.

#### Example #2

Calculate the cross-price elasticity of demand. For example, the percentage change in the price of apple juice changed by 18%, and the percentage change in the quantity of demand changed by 12%.

The following is the data used to calculate the cross-price elasticity of demand.

Percent Change in the Quantity | 12% |

Percent Change in the Price | 18% |

Therefore, it will be

= 12%/18% =** 0.667**

**The Cross-price elasticity of demand will be –**

The cross-price elasticity of the demand formula of apple juice and orange juice is positive hence they are substitute goods.

#### Example #3

The annual price of cinema tickets sold in 2010 was $3.5, whereas the number of popcorn sold at cinema halls was 100,000. The ticket price increased from $3.5 in 2010 to $6 in 2015. There was a decrease in the sale of popcorn to 80,000 units. Calculate Ec.

The following is the data used to calculate the cross-price elasticity of demand.

Price of Ticket in 2010 | 3.5 |

Price of Ticket in 2015 | 6 |

Quantity of Popcorn sold in 2010 | 100000 |

Quantity of Popcorn sold in 2015 | 80000 |

Price of the ticket in 2010 = $3.5

Price of the ticket in 2015 = $6

Quantity of popcorn sold in 2010 = 100,000

Sold amount of popcorn in 2015 = 80,000

**Percentage change in price of ticket**

- = [(6-3.5) / (6+3.5)] / 2
- =
**0.131579**

**Percentage change in the quantity of popcorn sold**

- = [(80000-100000) / (80000+100000)] / 2
- =
**-0.05556**

**Calculation of cross-price elasticity of demand is**

**Cross price elasticity of demand will be –**

=-0.422222

Since the cross elasticity of demand is negative, the two products are complementary.

### Relevance and Use

- The cross-price elasticity of the demand formula measures the demand sensitivity of one product (say A) when the price of an unrelated product (say B) is changed.
- The cross-price elasticity of demand is used to classify goods. The goods are classified as substitute or complementary goodsComplementary GoodsA complementary good is one whose usage is directly related to the usage of another linked or associated good or a paired good i.e. we can say two goods are complementary to each other. read more based on cross-price elasticity of demand. If the cross elasticity of demand is positive, the two goods are the substitute, and if the cross elasticity is negative, the two goods are complementary. Further, if the magnitude of cross elasticity is high, the two goods are a closer substitute or closer complementary depending on the sign.
- It also helps in classifying the market structure. If the cross elasticity of demand is infinite, the markets are considered perfectly competitive, whereas zero or close to zero cross elasticity makes the market structure a monopoly. If there is a high cross-elasticity, it is called an imperfect marketImperfect MarketImperfect market structure is a part of microeconomics in which companies sell different products and services, as opposed to perfect competitive markets in which homogeneous products are sold. Companies in this sector have some pricing power with high barriers to entry, resulting in higher profit margins as each company tries to differentiate their products and services through innovative technology.read more.
- The cross-price elasticity of demand helps large firms decide their pricing policy. Large firms generally have more variety of similar and related goods. Thus, cross elasticity of demand helps such firms in deciding whether to increase the price of such related products or not.
- The cross-price elasticity of the demand formula helps classify products between various industries. The cross elasticity is negative if the complementary goods are classified in different industries. If the goods have positive cross-price elasticity, i.e., substitute goods, they belong to one industry.

### Frequently Asked Questions (FAQs)

**What does a cross-price elasticity of more than 1 mean?**

If the cross elasticity of demand is elastic, which indicates that a change in the price of good A causes a more than proportionate change in the quantity required for good B, the cross elasticity of demand has an absolute value greater than 1.

**What are the different types of elasticities of demand?**

Perfectly elastic, elastic, perfectly inelastic, inelastic, and unitary are the five major categories into which elasticities can be effectively categorized. If the elasticity is larger than one, it indicates that the demand or supply is very responsive to changes in price.

**How to calculate the cross-price elasticity of demand between two goods?**

The elasticity is calculated by dividing the change in the quantity of the product by the change in the price of the good.

**For which types of goods is the cross-price elasticity of demand positive?**

For supplementary goods, they validate each other’s existence, such as quilts and comforters, cars and fuels, etc.

### Recommended Articles:

This has been a guide to the cross-price elasticity of the demand formula. Here we discuss how to calculate the cross-price elasticity of demand using its formula and practical examples, and a downloadable excel template. You can learn more about Accounting from the following articles –

- Income Elasticity of DemandIncome Elasticity Of DemandThe income elasticity of demand formula determines the percentage change in the demand for goods or services with the fluctuation in consumers’ real income. It measures the impact of change in consumers’ real income on their buying behaviour and product demand.read more
- Demand Elasticity Examples
- Examples of OligopolyExamples Of OligopolyThe aviation, media, pharmaceutical, and telecommunications industries are all examples of oligopoly.read more
- Elastic vs Inelastic Demand

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