Quasilinear Utility - Quasilinearity in Microeconomics

Quasilinearity in Microeconomics

A preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope. It is possible to extend this definition to utility functions: a continuous preference relation is quasilinear in commodity 1 if there is a utility function that represents it in the form, where is a function. In the case of two goods, this function could be, for example,

More formally, the preference relation on a set is quasilinear with respect to commodity 1 (called, in this case, the numeraire commodity) if:

• All the indifference sets are parallel displacements of each other along the axis of commodity 1. That is, if a bundle "x" is indifferent to a bundle "y" (x~y), then
• good 1 is desirable; that is,