The result of cross-price elasticity can be positive or negative, depending on the relationship between the two goods involved. Here’s how you determine whether it’s positive or negative and why:

1. Positive Cross-Price Elasticity (Substitute Goods)

When the price of one good increases, the quantity demanded for another good increases. This happens because consumers switch to a substitute good.

• Example from the Image:
  • Price of coffee increased (by 25%).
  • Quantity demanded for tea increased (by 30%).
  • Cross-price elasticity was positive (1.2), which indicates that tea and coffee are substitutes.

Mathematically:

• % Change in Quantity Demanded → Positive (tea increases)
• % Change in Price of the other good → Positive (coffee increases).

Since both changes are positive, the ratio is positive.

2. Negative Cross-Price Elasticity (Complementary Goods)

When the price of one good increases, the quantity demanded for another good decreases. This occurs because complementary goods are used together.

• Example: If the price of tennis rackets increases, fewer rackets are bought, and thus fewer tennis balls are demanded.

Mathematically:

• % Change in Quantity Demanded → Negative (tennis balls decrease).
• % Change in Price of the other good → Positive (tennis rackets increase).

Since one value is positive and the other is negative, their ratio will be negative.

3. Summary Table for Relationships

How to Determine Positivity or Negativity:

1. Identify the changes:
   • Look at the price of one good (has it increased or decreased?).
   • Check how the quantity demanded of the other good changes.
2. Use the formula:
   $E_{xy} = \frac{\text{\% Change in Quantity Demanded of Good Y}}{\text{\% Change in Price of Good X}}$
3. Analyze the sign:
   • If both numerator and denominator have the same sign → Positive result (substitutes).
   • If numerator and denominator have opposite signs → Negative result (complements).

Example Recap:

In Problem 1 (tea and coffee):

• Both values were positive → Result was 1.2 (positive), indicating substitutes.

In Problem 2 (tennis rackets and balls):

• You would calculate and interpret based on the sign. Since price decreased for rackets and quantity increased for balls, this suggests a negative relationship (likely complements).

Does this explanation clarify when the result will be positive or negative? Let me know if you need the solution to Problem 2!

Related Questions

1. How do you calculate percentage changes for price or quantity?
2. What would happen if the goods were perfect substitutes?
3. What does it mean if cross-price elasticity equals zero?
4. Can cross-price elasticity be greater than 1, and what does that imply?
5. How do complements affect business pricing strategies?

Tip:

Always identify whether two goods are likely used together (complements) or used instead of one another (substitutes) before interpreting results.