Quasilinear utility

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 ${\displaystyle u(x_{1},x_{2},\ldots ,x_{n})=x_{1}+\theta (x_{2},\ldots ,x_{n})}$ where ${\displaystyle \theta }$ is strictly concave.^: 164 A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for ${\displaystyle x_{2},\ldots ,x_{n}}$ does not depend on wealth and is thus not subject to a wealth effect;^{: 165–166} The absence of a wealth effect simplifies analysis^: 222 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.^: 163 In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments.