Question

Suppose that a change in the price of bread from R10 to R12.50 leads to a change in the quantity demanded of bread from 65 units to 90 .use the arc elasticity method to calculate and interpret the cross price elasticity of demand for the bread

Answer 1

Using the arc elasticity method the elasticity is computed using the following formula:

$\text{Arc elasticity}=\dfrac{\dfrac{Q_2-Q_1}{\frac{Q1+Q_2}{2}}}{{\dfrac{P_2-P_1}{\frac{P_1+P_2}{2}}}}$

$\text{Arc elasticity}=\dfrac{\dfrac{90-65}{\frac{65+90}{2}}}{{\dfrac{12.5-10}{\frac{10+12.5}{2}}}}$

$\text{Arc elasticity}=\blue{1.45}$

The cross price elasticity of demand will be:

$\text{Cross price elasticity of damand}=\dfrac{\delta Q}{\delta P} \times \dfrac{P}{Q}$

$\text{Cross price elasticity of damand}=\dfrac{90-65}{12.5-10} \times \dfrac{12.5}{90}$

$\text{Cross price elasticity of damand}=\blue{1.33}$