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 change in the income of the people demanding the good. It is calculated as the ratio of the percent change in quantity demanded to the percent 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.

[edit] Interpretation

Image:Income elasticity of demand - inferior goods.svg

Inferior good's demand falls as consumer income increases.

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. If income elasticity of demand of a commodity is less than 1, it is a necessity good. If the elasticity of demand is greater than 1, it is a luxury good.

A zero income elasticity (or inelastic) demand occurs when an increase in income is not associated with a change in the quantity demanded of a good.

[edit] Mathematical definition

More formally, the income elasticity of demand, <math>\ \epsilon_d</math>, for a given Marshallian demand function <math> Q(I,\vec{P}) </math> for a good is

<math>\epsilon_d = \frac{\partial Q}{\partial I}\frac{I}{Q} </math>

or alternatively:

<math>\epsilon_d={Y_1 + Y_2 \over Q_1 + Q_2}\times{\Delta Q \over \Delta Y}</math>

With income <math> I </math>, and vector of prices <math>\vec{P}</math>. 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.