Engel curve

In microeconomics, an Engel curve describes how household expenditure on a particular good or service varies with household income. There are two varieties of Engel curves. Budget share Engel curves describe how the proportion of household income spent on a good varies with income. Alternatively, Engel curves can also describe how real expenditure varies with household income. They are named after the German statistician Ernst Engel (1821–1896), who was the first to investigate this relationship between goods expenditure and income systematically in 1857. The best-known single result from the article is Engel's law which states that the poorer a family is, the larger the budget share it spends on nourishment.

Graphically, the Engel curve is represented in the first-quadrant of the Cartesian coordinate system. Income is shown on the Y-axis and the quantity demanded for the selected good or service is shown on the X-axis.

The shapes of Engel curves depend on many demographic variables and other consumer characteristics. A good's Engel curve reflects its income elasticity and indicates whether the good is an inferior, normal, or luxury good. Empirical Engel curves are close to linear for some goods, and highly nonlinear for others.

For normal goods, the Engel curve has a positive gradient. That is, as income increases, the quantity demanded increases. Amongst normal goods, there are two possibilities. Although the Engel curve remains upward sloping in both cases, it bends toward the Y-axis for necessities and towards the X-axis for luxury goods.

For inferior goods, the Engel curve has a negative gradient. That means that as the consumer has more income, they will buy less of the inferior good because they are able to purchase better goods.

For goods with a Marshallian demand function generated from a utility function of Gorman polar form, the Engel curve has a constant slope.

Many Engel curves feature saturation properties in that their slope tends toward infinity at high income levels, which suggests that there exists an absolute limit on how much expenditure on a good will rise as household income increases. This saturation property has been linked to slowdowns in the growth of demand for some sectors in the economy, causing major changes in an economy's sectoral composition to take place.

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