Income elasticity

In economics, income elasticity of demand measures the responsiveness of the quantity demanded for a good or service to a change in the income of the people demanding the good, ceteris paribus. It is calculated as the ratio of the percentage change in quantity demanded to the percentage change in income. For example, if in response to a 10% increase in income, the quantity demanded for a good increased by 20%, the income elasticity of demand would be 20%/10% = 2.

Income elasticity of demand can be used as an indicator of industry health, future consumption patterns and as a guide to firms investment decisions. For example, the "selected income elasticities" below suggest that an increasing portion of consumer's budgets will be devoted to purchasing automobiles and restaurant meals and a smaller share to tobacco and margarine.

Income elasticities are closely related to the population income distribution and the fraction of the product's sales attributable to buyers from different income brackets. Specifically when a buyer in a certain income bracket experiences an income increase, their purchase of a product changes to match that of individuals in their new income bracket. If the income share elasticity is defined as the negative percentage change in individuals given a percentage increase in income bracken the income-elasticity, after some computation, becomes the expected value of the income-share elasticity with respect to the income distribution of purchasers of the product. When the income distribution is described by a gamma distribution, the income elasticity is proportional to the percentage difference between the average income of the product's buyers and the average income of the population.

More formally, the income elasticity of demand, ${\displaystyle \ \epsilon _{d}}$, for a given Marshallian demand function ${\displaystyle Q(I,{\vec {P}})}$ for a good is

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