In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. Quasilinear preferences can be represented by the utility function ${\displaystyle u(x,y_{1},..,y_{n})=x+\theta _{1}(y_{1})+..+\theta _{n}(y_{n})}$ where ${\displaystyle \theta _{i}}$ is strictly increasing and concave. A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for ${\displaystyle y_{1},\ldots ,y_{n}}$ does not depend on wealth and is thus not subject to a wealth effect; The absence of a wealth effect simplifies analysis and makes quasilinear utility functions a common choice for modelling. Furthermore, when utility is quasilinear, compensating variation (CV), equivalent variation (EV), and consumer surplus are algebraically equivalent. In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments.

A preference relation ${\displaystyle \succsim }$ is quasilinear with respect to commodity 1 (called, in this case, the numeraire commodity) if:

In other words: 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.

In the two dimensional case, the indifference curves are parallel. This is useful because it allows the entire utility function to be determined from a single indifference curve.

A utility function is quasilinear in commodity x if it is in the form

where ${\displaystyle \theta _{i}}$ is an arbitrary function. In the case of two goods this function could be, for example, ${\displaystyle u\left(x,y\right)=x+{\sqrt {y}}.}$

The quasilinear form is special in that the demand functions for all but one of the consumption goods depend only on the relation between the good and the numeraire good (x) and not on the income.

Example: