Question

Macroeconomics

Posted 3 months ago

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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 $50 \%$, how will her purchase of pawpaws change?
Choose 1 answer:
(A) She will buy 25 fewer pawpaws
(B) She will buy $100 \%$ fewer pawpaws
(c) She will buy $100 \%$ more pawpaws
(D) She will buy $2 \%$ 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: $E_{xy} = \frac{\% \Delta Q_x}{\% \Delta P_y}$, where $E_{xy}$ is the cross-price elasticity of demand for good x with respect to the price of good y, $\% \Delta Q_x$ is the percentage change in quantity demanded of good x, and $\% \Delta P_y$ 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: $E_{xy} = \frac{\% \Delta Q_x}{\% \Delta P_y} \Rightarrow -2 = \frac{\% \Delta Q_{pawpaws}}{50\%}$

c

Calculating the Percentage Change in Quantity Demanded: Solving for $\% \Delta Q_{pawpaws}$ gives us $\% \Delta Q_{pawpaws} = -2 \times 50\% = -100\%$. 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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