Question

Suppose the cross-price elasticity of apples with respect to the price of oranges is 0.4, and the price of oranges falls by \(3\%\). What will happen to the demand for apples?

Short answer

The demand for apples will decrease by 1.2% when the price of oranges falls by 3%.

Step-by-step solution

Identify the formula for cross-price elasticity of demand

We can use the formula for cross-price elasticity of demand (Exy), which is: \[ Exy = \frac{% \Delta Q_x}{% \Delta P_y} \] Where: - \(Exy\) is the cross-price elasticity of demand, - %\(\Delta Q_x\) represents the percentage change in the quantity demanded of good x (apples), - %\(\Delta P_y\) represents the percentage change in the price of good y (oranges).

Plug in the given values

We are given that \(Exy = 0.4 \) and the price of oranges falls (decreases) by 3% (\(% \Delta P_y = -3\%\)). We will use these values to solve for %\(\Delta Q_x \): \[ 0.4 = \frac{% \Delta Q_x}{-3 \%} \]

Solve for %\(\Delta Q_x \)

We can now solve for %\(\Delta Q_x \) by multiplying both sides of the equation by -3%: \[ % \Delta Q_x = 0.4 \times -3 \% \] %\( \Delta Q_x = -1.2 \% \)

Interpret the result

Since %\(\Delta Q_x = -1.2 \% \), this means that the demand for apples decreases by 1.2% when the price of oranges falls by 3%. Thus, the demand for apples will decrease by 1.2%.