Suppose that when the price of good X falls from $10 to $8, the quantity demanded of good Y rises from 20 units to 25 units. Using the midpoint method, the cross-price elasticity of demand is

To calculate the cross-price elasticity of demand using the midpoint method, we use the following formula:

\[
E_{xy} = \frac{\Delta Q_y / \text{Average } Q_y}{\Delta P_x / \text{Average } P_x}
\]

Where:
- $\Delta Q_y$ = change in quantity demanded of good Y
- $\Delta P_x$ = change in price of good X
- Average $Q_y$ = average quantity of good Y before and after the change
- Average $P_x$ = average price of good X before and after the change

### Step 1: Calculate the changes and averages

1. **Change in quantity demanded of good Y ($\Delta Q_y$)**:
   \[
   \Delta Q_y = 25 - 20 = 5
   \]

2. **Change in price of good X ($\Delta P_x$)**:
   \[
   \Delta P_x = 8 - 10 = -2
   \]

3. **Average quantity of good Y**:
   \[
   \text{Average } Q_y = \frac{20 + 25}{2} = 22.5
   \]

4. **Average price of good X**:
   \[
   \text{Average } P_x = \frac{10 + 8}{2} = 9
   \]

### Step 2: Plug values into the formula

Now we can substitute these values into the formula:

\[
E_{xy} = \frac{5 / 22.5}{-2 / 9}
\]

### Step 3: Calculate

1. **Calculate the numerator**:
   \[
   \frac{5}{22.5} \approx 0.2222
   \]

2. **Calculate the denominator**:
   \[
   \frac{-2}{9} \approx -0.2222
   \]

3. **Now divide**:
   \[
   E_{xy} = \frac{0.2222}{-0.2222} \approx -1
   \]

### Conclusion

The cross-price elasticity of demand is approximately $-1$. This indicates that goods X and Y are substitutes; as the price of good X decreases, the quantity demanded of good Y increases.

If you have any questions or need further details, feel free to ask!

### Related Questions
1. What does a cross-price elasticity of -1 indicate about the relationship between goods?
2. How would the cross-price elasticity change if the quantities or prices were different?
3. What factors influence the cross-price elasticity of demand?
4. Can you give examples of other pairs of substitute goods?
5. How does the concept of elasticity affect pricing strategies for businesses?

**Tip:** Always consider the signs of elasticity; positive values indicate substitutes while negative values indicate complements.

Suppose that when the price of good X falls from $10 to $8, the quantity demanded of good Y rises from 20 units to 25 units. Using the midpoint method, the cross-price elasticity of demand is?

Explore how to calculate the cross-price elasticity of demand when the price of good X decreases from $10 to $8, leading to an increase in quantity demanded of good Y from 20 to 25 units. This detailed solution explains the midpoint method and its implications for substitute goods.

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