Cross Price Elasticity of Demand Formula

Formula to Calculate Cross-Price Elasticity of Demand

Cross price elasticity of demand formula is used to measure the percentage change in quantity demanded of a product with respect to 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 related 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,

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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 said to be complementary goods i.e. if the price of one good increases the demand for the other good will be decreased.

Examples

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

Example #1

The Company producing torches and batteries is analyzing the cross-price elasticity of the two goods. 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 quantity 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 of torches and batteries is negative, thus these two are complementary goods.

Example #2

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

The following is the data used for the calculation of 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

Cross-price elasticity of demand will be –

cross price elasticity formula example 1.4

The cross-price elasticity of 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 the year 2010 was $ 3.5 whereas the number of popcorns sold at cinema halls was 100,000. The ticket price increased from $ 3.5 in 2010 to $ 6 in the year 2015. There was a decrease in the sale of popcorns to 80,000 units.

The following is the data used for the calculation of 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

Percentage Change in Price of Ticket

CPE example 2.2
  • Percentage change in the price of ticket = (6-3.5)/(6+3.5)/2
  • =0.131579

Percentage Change in the Quantity of Popcorn Sold

cross price elasticity formula example 2.3
  • Percentage change in the quantity of popcorn sold = (80000-100000)/(80000+100000)/2
  • =-0.05556

Calculation of Cross Price Elasticity of Demand is as follows –

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

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