Definition in Terms of Preferences
Quasilinearity can also be defined as a property of preferences directly; is quasilinear if (1) if then, where and is a real number. The two definitions are equivalent in the case of a convex consumption set with continuous preferences that are locally non-satiated in the first argument.
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 regards to surplus, quasilinear preferences entail that Marshallian surplus will equal Hicksian surplus since there would be no wealth effect for a change in price.
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