# Income Elasticity of Demand

When demand for a product changes due to a change in the incomes of consumers we have income elasticity of demand. The degree of responsiveness of demand to a change in incomes of the consumers is known as income elasticity of demand. The formula for income elasticity of demand is,

Ey =

Or, The income elasticity of demand is defined, as the rate of change in the quantity demanded of a good due to change in the income of the consumer. As we have seen in “Demand Analysis and Consumer Behavior”, income is one of the determinants of the quantity demanded. In functional form it can be represented as follows:

Q = f (Y)

Where Q is the amount of quantity demanded and Y the income of the consumer. In this context it should be noted that the curve, which captures the changes in the quantity, demanded due to change in the income of the consumer is known as the “Engel Curve”. The income elasticity of demand of the consumer is given by

ex =

It is clear that the sign of the elasticity depends on the sign of the derivative ¶Q/¶Y as both of the expressions Q and Y are positive, i.e. Q > 0 and Y > 0. If the amount of good demanded rises as the income of the consumer increases, then the value of the income elasticity is positive. When the demand for a particular good increases due to an increase in the level of income of the consumer, then such a good is called a normal good. The income effect of a normal good is always positive. For some goods it is seen that due to an increase in the income of the consumer the demand for the good falls. Such a good is known as inferior good and the income effect of such a good is negative. The underlying reason for the income effect being negative is that the derivative ¶Q/¶Y for such a good is negative. Similarly it can be inferred that if the income effect of the good is zero then the concept of income elasticity of demand can be utilized for the classification of goods into normal and inferior goods. Goods with positive income elasticity of demand are called normal goods and goods with negative income elasticity of demand are called inferior goods.

Income elasticity of demand can be used to classify goods into luxuries or necessities. If the income elasticity of a good is greater than one, it is called a luxury. If the income elasticity of a good is less than one, it is called a necessity. If it is equal to one it can be called a semi-luxury good.

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