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# Cross Price Elasticity of Demand

Updated on January 25, 2024
Article byWallstreetmojo Team
Edited by
Reviewed byDheeraj Vaidya, CFA, FRM

## What Is Cross Price Elasticity of Demand?

Cross Price Elasticity of Demand refers to metric that that helps measure the change in the demand of one product with respect to the change in the price of the other. If both products are substitutes, it may show a positive cross elasticity of demand. On the other hand, if both are complementary goods, it may indicate an indirect or a negative cross elasticity of demand.

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

Cross Price Elasticity of Demand is about the relationship between the price and demand, i.e., a change in quantity demanded by one product with a difference in the cost of the second product. In simple terms, it measures the sensitivity of demand for one quantity X when the price of related goods Y is changed.

### Key Takeaways

1. The cross-price elasticity of demand determines the relation between price and demand.
2. In other words, the variation in the quantity that a product demands and the pricing of a different product.
3. For calculation, one must divide the percentage change in the quantity of good X by the percentage change in the price of goods.
4. For different markets, services, or products, one can utilize it to decide the price strategy. Based on the connections between the items, it can act differently.

### Cross Price Elasticity of Demand Explained

Cross price elasticity of demand helps assess the change in the quantity of demand for a product with respect to the changes in the price of another product in the market. The figure obtained signifies how the changes in the prices of one product have affected the demand for the other item. This elasticity of demand is the best metric to study this effect when the products, the demand and price of which are being compared, belong to the same category, i.e., they are each other’s substitute products.

However, there may be certain other products, the change in the prices of which, affect the change in the quantity of demand of the others. Some such items may include those that are consumed together or maybe, some that are not related to each other in any manner. While the former becomes the complementary product and hence affects the price-demand relationship between each other, the latter has hardly any effect on the respective pricing and demand.

When the price of one substitute product increases, the demand for the other competitorâ€™s item automatically increases, given the lesser amount consumers have to spend to buy the latter.

On the contrary, the increase in the price of a product leads to a decrease in the demand for its complementary products. This is because when two products are meant to be used complementarily, the rise in the price of one will lead to reduced consumer spending on it, thereby decreasing the demand for the related products at the same time. Based on the figures obtained using the formula, the businesses can assess how the products are related to each other and hence maintain the inventory in accordance with their requirement and changing demands.

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### Types

There are three types of such elasticity of demand, which have been mentioned below:

• Positive â€“ It is positive when the changes are directly proportional to each other. This means the increase in the price of product A leads to an increase in the demand for product B. Such instances occur when the products are a substitute for each other.
• Negative â€“ The value tends to be negative when the changes are inversely proportional to each other. This means the increase in the price of product A leads to a decrease in the demand for product B. Such instances occur in the case of complementary products.
• Zero â€“ When the elasticity of demand comes to zero, it indicates that the changes in the price and demand of the products do not affect each other in any manner. This happens when two products in question are completely unrelated to each other.

### Determinants

While there are various factors that affect the cross price elasticity of demand, the two most commonly known and major ones are as follows:

• The type of product, i.e., substitute goods, complementary goods, or unrelated goods.
• The loyalty of consumers towards the brand. When the consumers are loyal, they hardly get affected by the price change of one product and there are fewer chances of them switching to other brands. In such cases, the increasing prices do not tend to affect the demand for other brandâ€™s products. They stick to the products or brands despite the changes in the prices.

### How To Calculate?

The cross price elasticity of demand 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:

Cross Price Elasticity of Demand = (âˆ†QX/QX) Ã· (âˆ†PY/PY)

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

Cross Price Elasticity of Demand = (Q1X â€“ Q0X) / (Q1X + Q0X) Ã· (P1Y â€“ P0Y) / (P1Y + P0Y),

Where,

• Q0X = Initial demanded quantity of good X,
• Q1X = Final demanded quantity of good X,
• P0Y = Initial price of good Y and
• P1Y = Final price of good Y.

The five steps to be followed to calculate the cross price elasticity appropriately are as follows:â€“

1. Firstly, identify P0Y and Q0X, the initial price of good Y, and the quantity demanded of good X, respectively.

2. Now, determine the final demanded quantity of good X and the final price of good Y, termed Q1X and P1Y, respectively.

3. 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).

4. 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).

5. 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).

### Examples

Let us consider the following examples to understand how to calculate cross price elasticity of demand:

#### 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.

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

Percentage change then the number of passenger vehicles Ã· 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 â€“ 4,000) / (3,000 + 4,000) Ã· (\$2.50 â€“ \$3.50) / (\$2.50 + \$3.50)
• = (-1 / 7) Ã· (-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.

### 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 , 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 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 . 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.

How to determine whether the cross-price elasticity of demand is positive or negative?

When a good’s price drops, fewer people will buy its equivalent and vice versa. Thus, the cross-price elasticity will be positive, and the quantity and price change will go toward substitution. However, the cross-price elasticity of demand is negative if changes in one good’s demand and its price move in the opposite direction.

What is the cross-price elasticity of demand substitutes and complements?

The cross-price elasticity of demand for substitute goods is always positive; the demand for one good increases as the price increases. Conversely, the cross-price elasticity of demand is negative as the price of one product increases; the demand for complementary goods decreases.

What are the types of cross-price elasticity of demand?

The cross-price elasticity of demand is of three types: complementary goods, unrelated goods, and substitute goods.

What is the advantage of cross-price elasticity of demand?

The cross-price elasticity of demand helps identify the other products’ price effects. It calculates the relationship between two products when the price of one good changes. It is done by estimating the increase or decrease in the demand for a product with a subsequent shift in another product’s price.

This article has been a guide to what is Cross Price Elasticity of Demand. Here, we explain it with its examples, how to calculate it, uses, determinants, and types. You can learn more about it from the following articles: –