Cross Price Elasticity Of Demand Definition Calculation

Cross Price Elasticity of Demand Definition

Cross Price Elasticity of Demand Formula

It is calculated by dividing the percentage change in the quantity of good X by the percentage change in the price of good Y, which is represented mathematically as:

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Further, the formula for cross-price elasticity of demand can be elaborated into:

Where,

Q0X = Initial demanded quantity of good X,Q1X = Final demanded quantity of good X,P0Y = Initial price of good Y andP1Y = Final price of good Y.

Step by Step Calculation of the Cross Price Elasticity of Demand

That can be determined in the following five steps: –

Examples

Example #1

Let us take the simple example of gasoline and passenger vehicles. Now let us assume that a surge of 50% in gasoline prices resulted in a decline in the purchase of passenger vehicles by 10%. Calculate the cross-price elasticity of demand in this case.

Firstly, identify P0Y and Q0X, the initial price of good Y, and the quantity demanded of good X, respectively. Now, determine the final demanded quantity of good X and the final price of good Y, termed Q1X and P1Y, respectively. Next, work out the numerator of the formula, which represents the percentage change in quantity. It is arrived at by dividing the difference obtained from the last and initial quantities (Q1X u2013 Q0X) by the summation of the final and initial quantities. (Q1X + Q0X) i.e. (Q1X u2013 Q0X) / (Q1X + Q0X). Now, determine the denominator of the formula, which represents the percentage change in price. It is arrived at by dividing the final and initial costs (P1Y u2013 P0Y) by the summation of the last and initial outlay. (P1Y + P0Y) i.e. (P1Y u2013 P0Y) / (P1Y + P0Y). Lastly, the cross-price elasticity of demand is calculated by dividing the expression in step 3 by step 4, as shown below. Cross price elasticity of demand formula = (Q1X u2013 Q0X) / (Q1X + Q0X) / (P1Y u2013 P0Y) / (P1Y + P0Y).

(Q1X + Q0X) i.e. (Q1X u2013 Q0X) / (Q1X + Q0X).

(P1Y + P0Y) i.e. (P1Y u2013 P0Y) / (P1Y + P0Y).

Cross price elasticity of demand formula = (Q1X u2013 Q0X) / (Q1X + Q0X) / (P1Y u2013 P0Y) / (P1Y + P0Y).

Using the formula mentioned above can calculate the cross-price elasticity of demand as: –

Percentage change then the number of passenger vehicles ÷ Percentage change the price of gasoline.

Since we can see a negative value for cross elasticity of demand, it vindicates the complementary relationship between gasoline and passenger vehicles.

Example #2

Let us assume that two companies are selling soft drinks. At present, company no. 2 sells soft drinks Y at $3.50 per bottle, while company no. 1 can sell 4,000 bottles of soft drinks Y per week. To bump the sales of company 1, company 2 decided to decrease the price to $2.50, which resulted in reduced sales of 3,000 bottles of soft drinks Y per week. Calculate the cross-price elasticity of demand in the case.

Given, Q0X = 4,000 bottles, Q1X = 3,000 bottles, P0Y = $3.50 and P1Y = $2.50

Therefore, the cross-price elasticity of demand can be calculated using the above formula as: –

Cross price elasticity of demand = (3,000 – 4,000) / (3,000 + 4,000) ÷ ($2.50 – $3.50) / ($2.50 + $3.50)= (-1 / 7) ÷ (-1 / 6)= 6/7 or 0.857.

Since we can see a positive value for cross elasticity of demand, it vindicates the competitive relationship between soft drink X and soft drink Y.

Relevance and Uses

It is of paramount importance for a business to understand the concept and relevance of cross-price elasticity of demand to understand the relationship between the price of a good and the quantity demanded of another good at that price. One can use it to decide the pricing policy for different markets and various products or services. The cross-price elasticity behaves differently based on the relationship between the goods, which are discussed below.

#1 – Substitute products

If both goods that are perfect substitutes for each other result in perfect competitionPerfect CompetitionPerfect competition is a market in which there are a large number of buyers and sellers, all of whom initiate the buying and selling mechanism. Furthermore, no restrictions apply in such markets, and there is no direct competition. It is assumed that all of the sellers sell identical or homogenous products.read more, then an increase in the price of one goodwill leads to a rise in demand for the rival product. For example, various brands of cereal are examples of substitute goods. It is to be noted that the cross-price elasticity for two substitutes will be positive.

#2 – Complementary products

If one good is complementary to the other good, a goodwillGoodwillIn accounting, goodwill is an intangible asset that is generated when one company purchases another company for a price that is greater than the sum of the company’s net identifiable assets at the time of acquisition. It is determined by subtracting the fair value of the company’s net identifiable assets from the total purchase price.read more price decreases and increases the complementary good’s demand. The stronger the relationship between the two products, the higher the coefficient of cross-price elasticity of the demand will be. For example, game consoles and software games are examples of 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. It is to be noted that the cross elasticity will be negative for complementary goods.

#3 – Unrelated products

If there is no relationship between the goods, then an increase in the price of one good will not affect the demand for the other product. As such, unrelated products have a zero cross elasticity. For example, the effect of changes in taxi fares on the market demand for milk.

Cross Price Elasticity Of Demand Definition Calculation