Solution to mathematical problems of cross elasticity of demand

Meaning of cross elasticity of demand

Goods we consume in our daily life are related to each other and so that the quantity demanded of a commodity is influenced by a change in not only its own prices but also by a change in the prices of related commodities. The concept of Cross elasticity of demand is used to express such a situation. 

So cross elasticity of demand measures the responsiveness of quantity demand of one good (Say good X) to the change in price of the other goods (say good Y). as goods are related to with each other and change in the price of one commodity affects the quantity demanded of others, it is defined as  the cross elasticity of demand.

It shows the relationship between percentage changes in quantity demand for good X due to a percentage change in the price of good Y. other things remaining the same. 

The term ‘other things’ refers to the income of the consumer, the own price of the commodity, taste, preferences, etc. So cross elasticity of demand of commodity X with respect to the price of another commodity Y can be measured with the help of following formula:

The coefficient of cross elasticity of demand is expressed in percentage term or in ration. Its value may be positive or negative depending on the nature of the relationship between goods under consideration. The types of cross elasticity of demand and nature of goods can be presented as;

Numerical Measures	Description	Types of Commodity
Positive	Price increase of commodity, Y increases the quantity demand of good X	Substitute goods (Coke and Pepsi)
Negative	Price increase of commodity, Y decreases the quantity demand of good X	Complementary goods (Pen and Ink)
Zero	No relationship between the change in the price of good Y and quantity demand for good X	Non-related goods (Milk and Petrol)

The major formula to calculate cross elasticity of demand can be listed as;

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