Questions: UNIT 2 - CHALLENGE 2A: The Consumer: A store recently marked a hydration belt on sale, lowering the price by 40% from 20 to 12. The store also sells a hydration bottle, which is similar to the belt except that runners can hold it in their hands with a strap while running. When the store lowered the price of the hydration belt, the quantity of hydration bottles sold decreased by 28%. Using the cross-price elasticity formula, the cross-price elasticity is and the goods are a.) -1.333; complements b.) 0.70 ; substitutes c) 1.4 ; substitutes d.) -1.40; complements

UNIT 2 - CHALLENGE 2A: The Consumer: A store recently marked a hydration belt on sale, lowering the price by 40% from 20 to 12. The store also sells a hydration bottle, which is similar to the belt except that runners can hold it in their hands with a strap while running. When the store lowered the price of the hydration belt, the quantity of hydration bottles sold decreased by 28%. Using the cross-price elasticity formula, the cross-price elasticity is and the goods are a.) -1.333; complements b.) 0.70 ; substitutes c) 1.4 ; substitutes d.) -1.40; complements
Transcript text: UNIT 2 - CHALLENGE 2A: The Consumer: A store recently marked a hydration belt on sale, lowering the price by $40 \%$ from $\$ 20$ to $\$ 12$. The store also sells a hydration bottle, which is similar to the bell except that runners can hold it in their hands with a strap while running. When the store lowered the price of the hydration belt, the quantity of hydration bottles sold decreased by $28 \%$. Using the cross-price elasticity formula, the cross-price elasticity is $\qquad$ and the goods are $\qquad$ a.) -1.333; complements b.) 0.70 ; substitutes c) 1.4 ; substitutes d.) -1.40; complements
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Solution

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To solve this problem, we need to calculate the cross-price elasticity of demand between the hydration belt and the hydration bottle. The cross-price elasticity of demand measures how the quantity demanded of one good changes in response to a price change of another good. The formula for cross-price elasticity of demand is:

\[ \text{Cross-price elasticity} = \frac{\% \text{ change in quantity demanded of good B}}{\% \text{ change in price of good A}} \]

In this scenario:

  • Good A is the hydration belt.
  • Good B is the hydration bottle.

  1. Calculate the percentage change in price of the hydration belt:

    The price of the hydration belt decreased from $20 to $12. The percentage change in price is calculated as:

    \[ \% \text{ change in price} = \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100 \]

    \[ \% \text{ change in price} = \frac{12 - 20}{20} \times 100 = \frac{-8}{20} \times 100 = -40\% \]

  2. Calculate the percentage change in quantity demanded of the hydration bottle:

    The quantity of hydration bottles sold decreased by 28%, so:

    \[ \% \text{ change in quantity demanded} = -28\% \]

  3. Calculate the cross-price elasticity:

    \[ \text{Cross-price elasticity} = \frac{-28\%}{-40\%} = \frac{28}{40} = 0.70 \]

  4. Determine the relationship between the goods:

    • If the cross-price elasticity is positive, the goods are substitutes.
    • If the cross-price elasticity is negative, the goods are complements.

Since the cross-price elasticity is 0.70, which is positive, the goods are substitutes.

Therefore, the answer is:

b.) 0.70; substitutes

Explanation for each option:

a.) -1.333; complements

  • Incorrect because the calculated cross-price elasticity is not -1.333, and the goods are not complements.

b.) 0.70; substitutes

  • Correct because the calculated cross-price elasticity is 0.70, indicating the goods are substitutes.

c.) 1.4; substitutes

  • Incorrect because the calculated cross-price elasticity is not 1.4.

d.) -1.40; complements

  • Incorrect because the calculated cross-price elasticity is not -1.40, and the goods are not complements.
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