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?

Cross-price elasticity of two goods measures the responsiveness of the demand for one good to a change in the price of another good. The formula for cross-price elasticity (Exy) is: Exy = (% change in quantity demanded for good X) / (% change in price of good Y) A positive value of Exy indicates that the goods are substitutes (an increase in the price of one good leads to an increase in the demand for the other good), while a negative value indicates that the goods are complements (an increase in the price of one good leads to a decrease in the demand for the other good). In this exercise, the cross-price elasticity of apples with respect to the price of oranges is 0.4, which means the goods are substitutes.

We are given that the price of oranges falls by 3%, and the cross-price elasticity of apples with respect to the price of oranges is 0.4. Therefore, using the formula for cross-price elasticity, we can calculate the percentage change in the demand for apples: % change in the quantity demanded for apples = Exy * (% change in the price of oranges) = 0.4 * (-3\%) = -1.2\%

The result of -1.2% means that the demand for apples is expected to decrease by 1.2% as a result of a 3% decrease in the price of oranges. Since the cross-price elasticity was positive, it confirms that apples and oranges are substitutes. If the price of one substitute (oranges) decreases, people tend to consume more of that good and less of the other substitute (apples).