In Microeconomics
In microeconomics, an Engel curve shows how the quantity demanded of a good or service changes as the consumer's income level changes. In order to be consistent with the standard model of utility-maximization, Engel curves must possess certain properties. For example, Gorman (1981) proved that a system of Engel curves must have a matrix of coefficients with rank three (or less) in order to be consistent with utility maximization.
When considering a system of Engel curves, the adding-up theorem also dictates that the sum of all total expenditure elasticities, when weighted by the corresponding budget share, must add up to unity. This rules out the possibility of saturation being a general property of Engel Curves across all goods as this would imply that the income elasticity of all goods approaches zero starting from a certain level of income. The adding-up restriction stems from the assumption that consumption always takes place at the upper boundary of the household's opportunity set, which is only fulfilled if the household cannot completely satisfy all its wants within the boundaries of the opportunity set
Other scholars argue that an upper saturation level exists for all types of goods and services.
Read more about this topic: Engel Curve