The concept of Cross Elasticity of Demand is based on the fact that many of the goods are related; they are either substitutes for each other or are complementary. The demand for a particular good A would thus depend, other things being equal, upon the prices of these related good. A change in the price of related goods may cause a change in the demand for this good A as well. Thus, cross elasticity of demand measures the degrees of change in the demand for say, good A due to the change in the some commodities are close substitutes and therefore the consumer can use one in place of another. Now take the case of tea and coffee. A person in need of hot drink can take either tea or coffee. Now suppose the price of coffee goes up. Then some people may start taking less of coffee and to meet their need for a hot drink, may start taking tea. Thus, the demand for tea goes up not because the price of tea has gone down, but because the price of a close substitute, i.e. coffee has gone up. Similarly, some goods are complementary in the séance that they are used together. If the price of bread goes up, its demand will fall. And with a fall in the demand for bread, less of butter may be purchased as people may shift to some other forms of breakfast. Thus, the rise in price of bread has caused a fall in the quantity of butter demanded.
The degree of change in the demand for one good consequent to given change in the price of another goods is called the cross elasticity of demand. Cross elasticity of demand is measured by the formula given below:
Cross Elasticity = Proportionate change in demand for goods A / Proportionate change in price of good B
The coefficient of cross elasticity between two goods A and B can, thus, be expressed as
EC = ∆QA /A ÷ ∆PB /PB = ∆QA /QA x PB /∆PB here ∆ QA is the change in quantity of A Demanded.
= ∆QA / ∆PB. PB /QA QA = original demand for A.
∆ PB = change in price of B.
PB = original price of B.