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

In conclusion, as the price of oranges falls by 3%, the demand for apples will decrease by 1.2% due to a cross-price elasticity of 0.4.

Step-by-step solution

Understand the Cross-Price Elasticity of Demand Formula

The cross-price elasticity of demand (Exy) measures the responsiveness of the quantity demanded of one good (x) to a change in the price of another good (y). The formula for cross-price elasticity of demand is: \( Exy = \frac{\% \Delta Q_x}{\% \Delta P_y} \) Where: - \( Exy \) = Cross-price elasticity of demand - \( \% \Delta Q_x \) = Percentage change in quantity demanded of good x - \( \% \Delta P_y \) = Percentage change in price of good y

Identify the Given Information

We know the following information: - Cross-price elasticity of apples with respect to the price of oranges: 0.4 - Percentage change in price of oranges: -3% (a fall in price is considered a negative percentage change)

Plug the Given Information into the Formula

Insert the given information into the cross-price elasticity of demand formula: \( 0.4 = \frac{\% \Delta Q_{apples}}{-3\%} \)

Solve for the Percentage Change in Quantity Demanded of Apples

We need to solve for the percentage change in quantity demanded of apples, which can be done by multiplying both sides of the equation by the percentage change in price of oranges (-3%): \( 0.4 * -3\% = \% \Delta Q_{apples} \) \( -1.2\% = \% \Delta Q_{apples} \)

Interpret the Result

The result we obtained is -1.2%, which implies a decrease of 1.2% in the quantity demanded of apples. In conclusion, as the price of oranges falls by 3%, the demand for apples will decrease by 1.2%.