In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. This utility function has the representation
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Informally, an agent has quasilinear utility if it can express all its preferences in terms of money and the amount of money it has will not create a wealth effect. As a practical matter in mechanism design, quasilinear utility ensures that agents can compensate each other with side payments. In regard to surplus, quasilinear preferences entail that Marshallian surplus will equal Hicksian surplus since there would be no wealth effect for a change in price.
Definition in terms of utility functions
A utility function is quasilinear in commodity 1 if it is in the form:
where
The quasilinear form is special in that the demand function for the consumption goods depends only on the prices and not on the income. E.g, with two commodities, if:
then the demand for y is derived from the equation:
so:
which is independent of the income I.
The indirect utility function in this case is:
which is a special case of the Gorman polar form.
Equivalence of definitions
The cardinal and ordinal definitions are equivalent in the case of a convex consumption set with continuous preferences that are locally non-satiated in the first argument.