In economics, income elasticity

Elasticity (economics)

In economics, elasticity is the measurement of how changing one economic variable affects others. For example:* "If I lower the price of my product, how much more will I sell?"* "If I raise the price, how much less will I sell?"...

 of demand

Supply and demand

Supply and demand is an economic model of price determination in a market. It concludes that in a competitive market, the unit price for a particular good will vary until it settles at a point where the quantity demanded by consumers will equal the quantity supplied by producers , resulting in an...

measures the responsiveness of the demand for a good to a change in the income of the people demanding the good, ceteris paribus

Ceteris paribus

or is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...

. It is calculated as the ratio of the percentage change in demand to the percentage change in income. For example, if, in response to a 10% increase in income, the demand for a good increased by 20%, the income elasticity of demand would be 20%/10% = 2.

Interpretation

• A negative income elasticity of demand is associated with inferior good
  Inferior good
  In consumer theory, an inferior good is a good that decreases in demand when consumer income rises, unlike normal goods, for which the opposite is observed. Normal goods are those for which consumers' demand increases when their income increases....
  
  s; an increase in income will lead to a fall in the demand and may lead to changes to more luxurious substitutes.
• A positive income elasticity of demand is associated with normal good
  Normal good
  In economics, normal goods are any goods for which demand increases when income increases and falls when income decreases but price remains constant, i.e. with a positive income elasticity of demand...
  
  s; an increase in income will lead to a rise in demand. If income elasticity of demand of a commodity is less than 1, it is a necessity good
  Necessity good
  In economics a necessity good is a type of normal good. Like any other normal good, when income rises, demand increases. But the increase for a necessity good is less than proportional to the rise in income, so the proportion of expenditure on these goods falls as income rises. This observation...
  
  . If the elasticity of demand is greater than 1, it is a luxury good
  Luxury good
  Luxury goods are products and services that are not considered essential and associated with affluence.The concept of luxury has been present in various forms since the beginning of civilization. Its role was just as important in ancient western and eastern empires as it is in modern societies...
  
   or a superior good
  Superior good
  Superior goods make up a larger proportion of consumption as income rises, and therefore are a type of normal goods in consumer theory. Such a good must possess two economic characteristics: it must be scarce, and, along with that, it must have a high price...
  
  .
• A zero income elasticity (or inelastic) demand occurs when an increase in income is not associated with a change in the demand of a good. These would be sticky
  Sticky (economics)
  Sticky, in the social sciences and particularly economics, describes a situation in which a variable is resistant to change. Sticky prices are an important part of macroeconomic theory since they may be used to explain why markets might not reach equilibrium right away. Nominal wages are often said...
  
   goods.

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 elasticitites are closely related to the population income distribution and the fraction of a 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 bracket, then 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. (Bordley and McDonald, "Estimating Income Elasticitities from the Average Income of a Product's Buyers and the Population Income Distribution. " Journal of Business and Economic Statistics.

Mathematical definition

More formally, the income elasticity of demand, , for a given Marshallian demand function

Marshallian demand function

In microeconomics, a consumer's Marshallian demand function specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the utility maximization problem...

  for a good is


or alternatively:

This can be rewritten in the form:

With income , and vector of prices .

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

Engel's law

Engel's law is an observation in economics stating that as income rises, the proportion of income spent on food falls, even if actual expenditure on food rises...

.

Selected income elasticities

• Automobiles 2.46
• Books 1.44
• Restaurant Meals 1.40
• Tobacco 0.64
• Margarine −0.20
• Public Transportation −0.36

Income elasticities are notably stable over time and across countries.