Math Problem Statement

If a 20% price increase for Product A causes a 10% decrease in its quantity demanded, but no change in the quantity demanded for Product B, what is the cross elasticity of these goods? Round your answer to one decimal place.

Solution

To solve this problem, we need to calculate the cross-price elasticity of demand between Product A and Product B.

Cross-Price Elasticity of Demand Formula

The cross-price elasticity of demand is calculated as:

Cross-Price Elasticity=Percentage Change in Quantity Demanded of Product BPercentage Change in Price of Product A\text{Cross-Price Elasticity} = \frac{\text{Percentage Change in Quantity Demanded of Product B}}{\text{Percentage Change in Price of Product A}}

In this problem:

  • The percentage change in price of Product A is +20% (since there is a 20% increase in price).
  • The percentage change in quantity demanded of Product B is 0% (since there is no change in the quantity demanded of Product B).

Calculation

Cross-Price Elasticity=0%20%=0\text{Cross-Price Elasticity} = \frac{0\%}{20\%} = 0

Interpretation

The cross-price elasticity is 0, which indicates that there is no relationship between these goods. When the price of Product A changes, it does not affect the demand for Product B.

Answer

  • The cross elasticity of these goods is: 0.0
  • The relationship between these goods is: No relationship

If you have more questions or need additional details, feel free to ask!

Related Questions:

  1. How is cross-price elasticity different from price elasticity of demand?
  2. What does a positive cross-price elasticity indicate about the relationship between two products?
  3. How would you interpret a negative cross-price elasticity value?
  4. What factors can cause cross-price elasticity between two products to change over time?
  5. How is cross-price elasticity used in market analysis?

Tip:

When interpreting cross-price elasticity, always remember:

  • A positive value indicates substitute goods.
  • A negative value indicates complementary goods.
  • A value of zero indicates no relationship between the goods.

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Math Problem Analysis

Mathematical Concepts

Economics
Elasticity
Cross-Price Elasticity of Demand

Formulas

Cross-Price Elasticity = (Percentage Change in Quantity Demanded of Product B) / (Percentage Change in Price of Product A)

Theorems

Cross-Price Elasticity Interpretation

Suitable Grade Level

Grades 11-12, Undergraduate