Income elasticity of demand
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In economics, the income elasticity of demand measures the responsiveness of the quantity demanded of a good to the income of the people demanding the good.
It is measured as the percentage change in demand that occurs in response to a percentage change in income. For example, if, in response to a 10% increase in income, the quantity of a good demanded increased by 20%, the income elasticity of demand would be 20%/10% = 2.
More formally, for a given Marshallian demand function 
for a good is
With income I, and vector of prices 
.
A negative income elasticity of demand is associated with inferior goods; an increase in income will lead to a fall in the quantity demanded and may lead to changes to more luxurious substitutes.
A positive income elasticity of demand is associated with normal goods; an increase in income will lead to a rise in the quantity demanded. A high positive income elasticity of demand is associated with luxury goods.
A zero income elasticity of demand is an increase in income without leading to a change in the quantity demanded of a good.
Many necessities have an income elasticity of demand between zero and one: expenditure on these goods may increase with income, but not as fast as income does, so the proportion of expenditure on these goods falls as income rises. This observation for food is known as Engel's law.
