https://file.aiquickdraw.com/mathbot/file/1730001937923ketnq182.jpg

Let's solve each scenario step by step using the formula for cross-price elasticity of demand, which is given by:

\[
\text{Cross-price elasticity of demand} = \frac{\%\text{ change in quantity demanded of Good Y}}{\%\text{ change in price of Good X}}
\]

### a. 
- **Given**: A 20% increase in the price of Product A causes a 10% decrease in the quantity demanded of Product B.
  
\[
\text{Cross-price elasticity} = \frac{-10\%}{20\%} = -0.5
\]

Since the cross-price elasticity is negative, Products A and B are **complements**.

### b.
- **Given**: The price of Product C increases from $1 to $2, and the quantity demanded for Product D increases from 27 units to 81 units.
  
First, calculate the percentage change:
1. **Percentage change in price of Product C**:
   \[
   \frac{2 - 1}{(2 + 1)/2} \times 100 = \frac{1}{1.5} \times 100 = 66.7\%
   \]

2. **Percentage change in quantity demanded of Product D**:
   \[
   \frac{81 - 27}{(81 + 27)/2} \times 100 = \frac{54}{54} \times 100 = 100\%
   \]

Now, calculate the cross-price elasticity:
\[
\text{Cross-price elasticity} = \frac{100\%}{66.7\%} \approx 1.5
\]

Since the cross-price elasticity is positive, Products C and D are **substitutes**.

### c.
- **Given**: The price of Product E decreases by 9%, and the quantity demanded of Product F increases by 12%.

\[
\text{Cross-price elasticity} = \frac{12\%}{-9\%} = -1.33
\]

Since the cross-price elasticity is negative, Products E and F are **complements**.

### Summary:
a. **Cross-price elasticity between A and B**: -0.5 (Complements)  
b. **Cross-price elasticity between C and D**: 1.5 (Substitutes)  
c. **Cross-price elasticity between E and F**: -1.33 (Complements)  

Would you like further details on any of these calculations or have any other questions? 

Here are some related questions:
1. What does a zero cross-price elasticity indicate about two goods?
2. How does the midpoint formula for elasticity differ from the standard elasticity formula?
3. Can you explain how cross-price elasticity affects company pricing strategies?
4. What are some real-world examples of complementary goods?
5. How does income elasticity differ from cross-price elasticity?

**Tip**: When calculating percentage changes, using the midpoint method helps to reduce biases associated with large changes in variables.

For each scenario, calculate the cross-price elasticity between the two goods, and identify how the goods are related. Use the midpoint method when applicable, and specify answers to one decimal place.

Learn how to calculate cross-price elasticity between two goods to identify their relationship as substitutes or complements. Detailed solutions include scenarios with percentage changes in quantity and price using the midpoint method.

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