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The elasticity of demand is a measure of degree of responsiveness of quantity demanded for a product to the change in its determinants.
The law of demand helps to understand the direction in which price and quantity demanded change.
It is limited to the statement as:
If price increases, quantity demanded will decline or if income rises demand will increase.
But it cannot answer by how much?
In business or economic analysis, it is essential to address ‘by how much’ question.
It is necessary to find out the exact value of the change in quantity demanded in response to the change in price or income.
Elasticity of demand helps to find out the exact values in such cases.
The elasticity of demand is a measure of degree of responsiveness of demand for a product to the change in its determinants.
Elasticity of demand (Ep) = Percentage change in quantity demand for a good ÷ Percentage change in its price
Demand is determined by various factors such as price, income, price of other goods, taste, preferences etc.
There are various types of elasticity of demand as its determinants.
However, we discuss only price, income and cross elasticity of demand as they are the main determinants of demand whose change is visible and measurable.
There are three types of elasticity of demand. They are
Price elasticity of demand
Income elasticity of demand
Cross elasticity of demand
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Cross elasticity of demand is also called crossprice elasticity of demand.
The cross elasticity of demand measures the responsiveness in the quantity demanded of one good when the price for another good changes.
This measurement is calculated by taking the percentage change in the quantity demanded of one good and dividing it by the percentage change in the price of the other good.
As goods are related with each other, demand for good (X) responses to the change in the price of other goods (Y).
The cross elasticity of demand shows the relationship between percentage change in quantity demanded for good X and percentage change in price of good Y.
It is defined as the proportionate change in quantity demanded of X divided by the proportionate change in price of Y (being other things constants).
The term ‘other things’ refers to the income, own price, taste and preferences of the consumer etc.
It is presented by Exy
Cross elasticity of demand is a unit free measurement.
It is always expressed in terms of percentage or in ratio.
Its value may be positive or negative depending on the nature of relationship between two goods.
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Since two goods are related in three different ways, there are three types of cross elasticity of demand.
If there is positive relationship between percentage change in quantity X and percentage change in price Y, then the demand is known as positive cross elastic of demand.
In other words, cross elasticity is positive if two goods are substitute goods.
For example, tea and coffee are a pair of substitute goods.
If price of tea increases then demand for coffee also increases and viceversa.
Here, the change in price of Y and corresponding change in quantity demanded for X actually move in the same direction.
In the above figure, the demand curve for X(D_{X}) is upward sloping against the price of Y.
The Q_{X1} and P_{Y1} are the original combination of demand for X and price of Y.
As price of Y increases from P_{y1} to P_{y2}, quantity demanded also increase from Q_{X1} to Q_{X2}.
Both the price of Y and the demand for X are moving in the same direction.
It gives positive value of cross elasticity of demand.
It is found in case of substitute goods such as tea and coffee.
If there is inverse relationship between percentage change in quantity demanded for X and percentage change in price of Y, then the demand is known is negative cross elastic demand.
In other words, cross elasticity demand is to be negative when two goods are complementary goods.
Complementary goods are mobile and SIM, pen and ink, car and petrol etc.
Here, the change in price of Y and corresponding change in demand for X move in opposite directions.
An increase in price of pen, decline to demand for ink and vice versa; it results negative value of cross elasticity of demand.
It is found in complementary goods like pen and ink, motorcycle and petrol, tennis balls and tennis racket etc.
In the above figure, the demand curve for X(D_{X}) is downward sloping against the price of Y.
The demand curves shows an increase in price of Y leads to a decrease in quantity demanded for X and vice versa, which results negative value of cross elasticity of demand.
Keep in Mind
Some scholars write three types of cross elasticity of demand. 
They write positive cross elasticity, negative cross elasticity and zero cross elasticity. 
But, zero elasticity is already included in price elasticity [Perfectly Inelastic Demand (Ep = 0)]. 
Therefore, here only two elasticity were explained. 
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