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.