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Question
Macroeconomics
Posted 3 months ago

Fernanda's cross-price elasticity of demand for pawpaws, in response to a change in the price of crackers is -2 .

If the price of crackers increases by 50%50 \%, how will her purchase of pawpaws change?

Choose 1 answer:
(A) She will buy 25 fewer pawpaws
(B) She will buy 100%100 \% fewer pawpaws
(c) She will buy 100%100 \% more pawpaws
(D) She will buy 2%2 \% more pawpaws
(E) She will buy 2 fewer pawpaws
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Answer from Sia
Posted 3 months ago
Solution
a
Understanding Cross-Price Elasticity of Demand: Cross-price elasticity of demand measures the responsiveness of the quantity demanded for one good when the price of another good changes. It is calculated using the formula: Exy=%ΔQx%ΔPyE_{xy} = \frac{\% \Delta Q_x}{\% \Delta P_y}, where ExyE_{xy} is the cross-price elasticity of demand for good x with respect to the price of good y, %ΔQx\% \Delta Q_x is the percentage change in quantity demanded of good x, and %ΔPy\% \Delta P_y is the percentage change in price of good y
b
Applying the Given Information: Given that Fernanda's cross-price elasticity of demand for pawpaws with respect to the price of crackers is -2, and the price of crackers increases by 50%, we can use the formula to find the percentage change in quantity demanded for pawpaws: Exy=%ΔQx%ΔPy2=%ΔQpawpaws50%E_{xy} = \frac{\% \Delta Q_x}{\% \Delta P_y} \Rightarrow -2 = \frac{\% \Delta Q_{pawpaws}}{50\%}
c
Calculating the Percentage Change in Quantity Demanded: Solving for %ΔQpawpaws\% \Delta Q_{pawpaws} gives us %ΔQpawpaws=2×50%=100%\% \Delta Q_{pawpaws} = -2 \times 50\% = -100\%. This means that the quantity demanded for pawpaws will decrease by 100%
Answer
Fernanda will buy 100% fewer pawpaws.
Key Concept
Cross-Price Elasticity of Demand
Explanation
A negative cross-price elasticity of demand indicates that the two goods are complements. In this case, an increase in the price of crackers leads to a decrease in the quantity demanded for pawpaws.

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