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. A nice 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 therefore is 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's surplus are algebraically equivalent. In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments.

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