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.