Cross-elasticity is the measure of responsiveness of demand for a commodity to the changes in price of its substitutes and complementary goods. For example, cross-elasticity of demand for tea (T) is the percentage change in its quantity demanded with respect to change in the price of its substitute, coffee (C). Formula for measuring cross-elasticity of demand for tea (et,c) with respect to price of coffee (Pc )
et,c = proportionate change in demand for tea (Qt)/ Proportionate change in price of coffee (Pc)
= (Pc/Qt). (ΔQt/ δPc)
Cross elasticity of demand for coffee (QC) with respect to price of tea (Pt) is
Ec, t = (Pt/ Qc). (ΔQc/ΔPt)
For illustration suppose that price of coffee (Pe) increases from 10$ to 15$, per 10grams and consequently demand for tea increases from 20 tons to 30 tons per week, price of tea remaining constant. By substituting these values in Eq. V we get cross-elasticity of demand for tea with respect to price of coffee, as
et, c = 10/20 . 20-30/10-15
=10/20. -10/-5
=1.0
It is vital to note that cross-elasticity between any two substitute goods is always positive.
The same formula is used to calculate cross-elasticity of demand for a good in reaction to the change in price of its complementary goods. Petrol to automobile, Electricity to electrical gadgets,sugar and milk, butter to bread, tea to coffee, are the illustrations of complementary goods. Notice that demand for complementary goods has negative cross-elasticity for example rise in the price of a good decreases the demand for its complementary goods.
Animportant characteristic of cross-elasticity is that if cross-elasticity between two goods is positive, two may be regarded as substitutes for each other. Furthermore, the greater the cross-elasticity, the closer the substitute. Similarly, if cross-elasticity of demand for two related goods is negative, two may be regarded as complementary of each other: the higher the negative cross-elasticity, the higher the degree of complementarily.