Cross Elasticity of Demand : Cross elasticity of demand occurs when a change in price of a commodity brings the change in demand of another commodity. The cross elasticity of demand for two goods X and Y, is the ratio of the percentage change of quantity purchased of X to the percentage change in price of Y.
Here, ec = cross elasticity of demand
ΔQx = change in quantity of X
ΔPy = change in price of Y
Qx = initial quantity of X
Py = initial price of Y
Example : For example we are taking two complementary goods. The price of the Y commodity is changing from $100 to $150. For this change, the quantity purchased of X is changing to 1000 units from 3000 units. Thus,
Py = $100 Qx = 3000 units
ΔPy = $50 ΔQx = 2000 units
The cross elasticity of demand,
Thus, the cross elasticity is of demand is approximately 1.3
For substitutable goods, a rise in the price of Y will bring a rise in the demand of X and vice versa. The cross elasticity of complementary goods are positive and that of substitutable goods are negative.