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Cross Price Elasticity of Demand Formula

Updated on April 11, 2024
Article byWallstreetmojo Team
Reviewed byDheeraj Vaidya, CFA, FRM

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.

Ec = Percent change in a quantity of good A/Percent change in the price of good B

or

Ec = [(P1A + P2A)/(Q1B + Q2B)] * [(Q1B – Q2B)/(P1A – P2A)]

Where,

Key Takeaways

  1. 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.
  2. 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).
  3. 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.
Cross Price Elasticity of Demand Formula

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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

You can download this Cross-Price Elasticity of Demand Formula Excel Template here – Cross-Price Elasticity of Demand Formula Excel Template

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 Quantity12%
Percent Change in the Price18%

Therefore, it will be

CPE formula example 1.3

= 12%/18% = 0.667

The Cross-price elasticity of demand will be –

cross price elasticity formula example 1.4

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 20103.5
Price of Ticket in 20156
Quantity of Popcorn sold in 2010100000
Quantity of Popcorn sold in 201580000

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

CPE example 2.2
  • = [(6-3.5) / (6+3.5)] / 2
  • = 0.131579

Percentage change in the quantity of popcorn sold

cross price elasticity formula example 2.3
  • = [(80000-100000) / (80000+100000)] / 2
  • = -0.05556

Calculation of cross-price elasticity of demand is

cross price elasticity formula example 2.4

Cross price elasticity of demand will be –

cross price elasticity formula example 2.5

=-0.422222

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

Relevance and Use

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:

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