Income elasticity of demand
In economics, the income elasticity of demand is the responsivenesses of the quantity demanded for a good to a change in consumer income. It is measured as the ratio of the percentage change in quantity demanded to the percentage change in income. If a 10% increase in Mr. Ruskin Smith's income causes him to buy 20% more bacon, Smith's income elasticity of demand for bacon is 20%/10% = 2. Mathematical definition. The point elasticity version, which defines it as an instantaneous rate of change of quantity demanded as income changes, is as follows. For  a given Marshallian demand function formula_2 with arguments income and a vector of prices of all goods, This can be rewritten in the form For discrete changes the elasticity is (using the arc elasticity) where subscripts 1 and 2 refer to values before and after the change. Interpretation. The most commonly used elasticity in economics, the price elasticity of demand, is almost always negative, but many goods have positive income elasticities, many have negative. Income elasticity of demand can be used as an indicator of future consumption patterns and as a guide to firms' investment decisions. For example, the "selected  income elasticities" below suggest that as incomes increase over time, an increasing portion of consumers' budgets will be devoted to purchasing automobiles and restaurant meals and a smaller share to tobacco and margarine. Income elasticities and budget shares. Being a normal good (elasticity > 1) means that with higher income, consumption of the good will rise, but it does not mean that the good's share of the consumer's budget will rise with income. That depends on whether the elasticity is below or above +1. If the elasticity is negative, such as margarine's -.20 (from the "Selected income  elasticities" section of this article), then it is obvious that margarine's share of the consumer's budget will fall if his income rises 10%. If the elasticity is tobacco's +.42, however, an income increase of 10% generates a spending increase of 4.2%, so tobacco's share of the budget falls. His purchases of books, with an elasticity of +1.44, will rise 14.4%, however, and so will have a higher budget share after his income rises. In aggregate, food has an income elasticity of demand between zero and one, so expenditure increases with income, but not as fast  as income does. This observation is known as Engel's law. 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. When buyers in a certain income bracket get a pay raise, the income elasticity can be used to predict how much more the market will consume of that product. 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.