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.

Step-by-step solution

Step 1. Introduction:

The percentage fluctuation in the quantity demanded of a commodity divided by the percentage variation in the price of other commodity is the cross-price elasticity of demand.

Step 2. Solution:

The formula used to compute the cross-price elasticity of apples is given below:

$\mathrm{Cross}-\mathrm{price}\mathrm{elasticity}\mathrm{of}\mathrm{apples}=\frac{\%\mathrm{change}\mathrm{in}\mathrm{demand}\mathrm{for}\mathrm{apples}}{\%\mathrm{change}\mathrm{in}\mathrm{price}\mathrm{of}\mathrm{oranges}}$

The cross price elasticity of apples is 0.4 and change in price of oranges is -3% (as the price has decreased). Substituting the values, we get:

$0.4=\frac{\%\mathrm{change}\mathrm{in}\mathrm{demand}\mathrm{for}\mathrm{apples}}{-3\%}$

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{demand}\mathrm{for}\mathrm{apples}& =& 0.4\times -3\%\\ & =& -1.2\%\end{array}$

Thus, the demand for apple changes by -1.2%

Step 3. Conclusion:

As the % change in demand for apples is a negative number, it means the demand for apples will decrease by 1.2%.