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Cross Price Elasticity Calculator

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Cross price elasticity calculator helps you determine how the price change of one product affects how much people buy another. This tool helps you understand how two products are connected in terms of demand. It's useful for businesses, economists, and policymakers to figure out how these products affect each other in the market.

What is the cross-price elasticity of demand?

Cross-price elasticity of demand evaluates how the quantity demanded of one product changes in response to a change in the price of another product.

The cross-price elasticity of demand measures how sensitive the demand for one good (good B) is to changes in the price of another good (good A). In simpler terms, it tells you how much the quantity demanded of good B will change when the price of good A goes up or down.

Positive cross-price elasticity (substitutes): 

  • This occurs when an increase in the price of one good leads to an increase in the demand for another. 
  • For example, if the price of coffee (good A) goes up, people might choose tea (good B) more often because it's a cheaper alternative.

Negative cross-price elasticity (complements): 

  • This happens when an increase in the price of one good leads to a decrease in the demand for another. 
  • For instance, if movie ticket prices (good A) rise, there might be a decrease in the demand for popcorn (good B) as fewer people go to the movies.

Zero Cross-Price Elasticity (Unrelated Goods): 

  • This is when changes in the price of one good don't affect the demand for another.
  • If the price of one item changes, there is no impact on the demand for the other.

Cross-price elasticity formula:

To calculate the cross-price elasticity of demand, you can use the formula below, which is:

\text{Elasticity} = \frac{\text{Price}_{1A} + \text{Price}_{2A}}{\text{Quantity}_{1B} + \text{Quantity}_{2B}} \times \frac{\Delta\text{Quantity}_{B}}{\Delta\text{Price}_{A}}

Where,

  • \(Price_{1A}\) is the initial price for product A
  • \(Price_{2A}\) is the final price for product A
  • \(Quantity_{1B}\) is the initial demand of product B
  • \(Quantity_{2B}\) is the final demand of product B
  • \(\Delta\text{Price}_{A}\) is the difference between the final and initial price of product A
  • \(\Delta\text{Quantity}_{B}\) is the difference between the final and initial demand for product B

How to calculate the cross-price elasticity?

You can calculate this value using the formula we discussed above. Now let’s go through the example below, this will help you learn how to calculate cross price elasticity of demand by yourself. 

Example:

Consider an example involving coffee (product A) and tea (product B).

  • Initial price of coffee \((Price_{1A} = $4)\)
  • Final price of coffee \((Price_{2A} = $5)\)
  • Initial quantity demanded for tea \((\text{Quantity}_{1B}) = 200 \text{ units}\)
  • Final quantity demanded for tea \((\text{Quantity}_{2B}) = 180 \text{ units}\)
  • Change in price of coffee \((\Delta\text{Price}_{A}) = $1\)
  • Change in quantity demanded for tea \((\Delta\text{Quantity}_{B}) = -20 \text{ units}\) (decrease)

Now, let's add these values to the cross-price elasticity formula:

\(\text{Elasticity} = \frac{(4 + 5)}{(200 + 180)} \times \frac{-20}{1}\)

Solve the calculation step by step:

\(\text{Elasticity} = \frac{9}{380} \times -20\)

\(\text{Elasticity} \approx -0.4737\)

The calculated cross price elasticity is approximately -0.4737. The negative value suggests that coffee and tea are complements, when the price of coffee increases, the quantity demanded for tea decreases, indicating a complementary relationship between these two goods.

Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.


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